SlideShare ist ein Scribd-Unternehmen logo
1 von 10
ISA
                                                                                                          TRANSACTIONS®
                                               ISA Transactions 42 ͑2003͒ 63–72




                         Auto-tuning of cascade control systems
                                 Sihai Song, Wenjian Cai, Ya-Gang Wang
              School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
                                       ͑Received 8 August 2001; accepted 16 April 2002͒



Abstract
   In this paper, a novel auto-tuning method for a cascade control system is proposed. By employing a simple relay
feedback test, both inner and outer loop model parameters can be simultaneously identified. Consequently, well-
established proportional-integral-derivative ͑PID͒ tuning rules can be applied to tune both loops. Compared with
existing methods, the new method is simpler and yet more effective. It can be directly integrated into commercially
available industrial auto-tuning systems. Some examples are given to illustrate the effectiveness and robustness of the
proposed method. © 2003 ISA—The Instrumentation, Systems, and Automation Society.

Keywords: Cascade control; Relay feedback; PID auto-tuning; Model matching



1. Introduction                                                    controller is tuned. Subsequently, the inner loop
                                                                   controller is commissioned and the outer loop con-
   Proportional-integral-derivative ͑PID͒ control-                 troller is tuned to complete the tuning process. If
lers are widely used in the process control industry               the control performance achieved is unsatisfactory,
due to their relatively simple structure, which can                the entire sequence must be repeated. Thus it is a
be easily understood and implemented. In practice,                 fairly cumbersome and time consuming task to
it has often been integrated into complex control                  tune a cascade control system, especially for sys-
structures in order to achieve a better control per-               tems with large time constant and time delay.
formance. Among those complex control struc-                          PID auto-tuning relieves the pain of manually
tures, the cascade control scheme is commonly                      tuning a controller and has been successfully ap-
used for the purpose of reducing both maximum                      plied in many industry fields ͓1,2͔. However, very
deviation and integral error of disturbance re-                    little has been reported so far in the literature on
sponses. The advantages of easy implementation                     the development of auto-tuning techniques for cas-
and potentially large control performance im-                      cade control systems. Among few of them, Li et
provement have led to widespread applications of                   al. ͓3͔ made use of fuzzy logic for self-tuning of
cascade control for several decades. It has become                 cascade controllers. Hang et al. ͓4͔ applied a re-
a standard application provided by industrial pro-                 newed relay automatic tuning method to tune a
cess controllers.                                                  cascade control system where the relay feedback
   Cascade control systems are constructed by two                  test is carried out twice, first to the inner loop and
control loops: an inner loop with fast dynamic to                  then to the outer loop. While the individual con-
eliminate input disturbances, and an outer loop to                 troller tuning has been automated, the sequential
regulate output performance. Conventionally, they                  nature of the tuning process remains unchanged.
are tuned in a sequential manner. First, the outer                 Tan ͓5͔ proposed a method to carry out the entire
loop controller is put on manual and the inner loop                tuning process in one experiment, but the experi-

0019-0578/2003/$ - see front matter © 2003 ISA—The Instrumentation, Systems, and Automation Society.
64                    Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72




                                Fig. 1. Configuration of the cascade control system.


ment requires prior information of the process.              the phase lag of the closed inner loop will be much
Furthermore, the ultimate frequency used for outer           less than that of the outer loop. This feature leads
loop design is based on initial ultimate frequency           to the rationale behind the use of cascade control.
without considering changes in inner loop control            The crossover frequency for the inner loop is
parameters.                                                  higher than that for the outer loop, which allows
  This paper presents a novel auto-tuning method             higher gains in the inner loop controller in order to
for the cascade control system. By utilizing the             regulate more effectively the effect of a distur-
fundamental characteristic of cascade control sys-           bance occurring in the inner loop without endan-
tems, a simple relay feedback test is applied to the         gering the stability of the system.
outer loop to identify simultaneously both inner
and outer loop process model parameters. A model
matching the PID controller tuning method based
        ´
on Pade coefficients and the Markov parameter is              3. Relay feedback test for cascade control
proposed to control the overall system perfor-               systems
mance. Two examples are given to illustrate the
effectiveness of the proposed method.                          The Astrom-Hagglund relay feedback test is
                                                             based on the observation: when the process output
2. Fundamentals of cascade control systems                   lags behind the input by Ϫ␲ radians, the closed-
                                                             loop system may generate sustained oscillation
   The configuration of the cascade control scheme            around the ultimate frequency ͑the frequency
is shown in Fig. 1, where an inner loop is embed-            where the phase lag is Ϫ␲͒. The proposed relay
ded within an outer loop and the outer loop output           feedback test for the auto-tuning cascade control
variable is to be controlled. The control system             system is shown as in Fig. 2. When the relay feed-
consists of two processes and two controllers with           back test begins, switch A points to position 2,
outer loop transfer function G p1 , inner loop trans-        switch B points to position 4, and switch C points
fer function G p2 , outer loop controller G c1 , and         to position 5. After the test, switch A points to
inner loop controller G c2 , respectively.                   position 1, switch B points to position 3, and
   The two controllers of cascade control systems            switch C points to position 6. As the inner loop
are standard feedback controllers ͑i.e., P, PI, or           process acts much faster than the outer loop pro-
PID͒. Usually, a proportional controller is used for         cess, output u of the inner loop process in Fig. 2
the inner loop, integral action is needed when the           under the relay feedback test acts as a step re-
inner loop process contains essential time delays,           sponse in half of the period of the stationary os-
and the outer process is such that the loop gain in          cillation, as shown in Fig. 3. Therefore a single
the inner loop must be limited ͓1͔.                          relay feedback test can be used to obtain simulta-
   To serve the purpose of reducing or eliminating           neously both the inner loop and outer loop process
the inner loop disturbance d 2 before its effect can         models parameters.
spill over to the outer loop, it is essential that the         In practice, the real process model is usually
inner loop exhibit a faster dynamic response than            represented by low order plus dead-time model.
that of the outer loop ͑as industry rule of thumb, it        Here, the transfer function with the following form
should be at least five times ͓1͔͒. Consequently,             ͑first-order plus dead time͒ is adopted:
Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72                               65




                                   Fig. 2. Configuration of the proposed identification model.


                                 ki                               tϭ0 in the process input; the process input and
              G pi ͑ s ͒ ϭ           e ϪL i s ,          ͑1͒      output are collected until process enters a new
                             T i sϩ1
                                                                  steady state again. The process response after dead
where iϭ1 stands for the outer process model and                  time tϭL 2 is described by
iϭ2 stands for the inner process model, respec-
tively. This model is characterized by three param-                     u ͑ t ͒ ϭk 2 ͑ 1Ϫe ͑ tϪL 2 ͒ /T 2 ͒ ϩw ͑ t ͒ , tуL 2 , ͑2͒
eters: the static gain k, the time constant T, and the
                                                                  where w ( t ) is the white noise in measurement of
dead time L. It describes a linear monotonic pro-
                                                                  u ( t ) . It follows from the above relation that
cess quite well in many industrial applications and
is often sufficient for PID controller tuning.
                                                                                   ͫ ͬT2
                                                                      ͓ u ͑ t ͒ k 2 ͔ L ϭk 2 tϪA ͑ t ͒ ϩ ␦ ͑ t ͒ , tуL 2 ,
                                                                                       2
3.1. Inner loop process model identification                                                                                   ͑3͒
  As the inner loop output u can be considered as                 where A ( t ) is the area under the process response
a step response in half period of the relay feedback              and ␦͑t͒ is the integration of measurement noise;
test, some well-developed step testing methods                    they are given as following, respectively:
͓2,6,7͔ can be readily applied to identify param-
eters of the inner loop. In this paper, the method
proposed by Ref. ͓2͔ is adopted due to its robust-
                                                                                      A͑ t ͒ϭ   ͵ u͑ t ͒dt,
                                                                                                 0
                                                                                                     t



ness; it is briefly described as follows:
  Suppose that the inner process model is repre-
sented by Eq. ͑1͒, and a unit step change occurs at
                                                                                      ␦͑ t ͒ϭ   ͵ w͑ t ͒dt.
                                                                                                 t

                                                                                                 0
                                                                                                                              ͑4͒




                   Fig. 3. Inner loop and outer loop response under the proposed relay feedback test.
66                          Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72


The inner process model’s static gain k 2 is com-                        where T u is the period of the stationary oscillation,
puted from the process steady states of input and                        and
output,                                                                                                     2␲
                                                                                                   ␻ uϭ        .                        ͑10͒
                                ⌬u                                                                          Tu
                           k 2ϭ      ,                             ͑5͒
                                ⌬u d                                     As the overall open loop transfer model function is
where ⌬u denotes the change of process output                                 G p ͑ s ͒ ϭG p1 ͑ s ͒ G p2 ͑ s ͒
and ⌬u d stands for the deviation in the manipu-
lated input. Eq. ͑2͒ falls into a system of linear                                                k 1k 2
                                                                                      ϭ                          e Ϫ ͑ L 1 ϩL 2 ͒ s ,
equations,                                                                                ͑ T 1 sϩ1 ͒͑ T 2 sϩ1 ͒
             ⌿Xϭ⌫ϩ⌬                    for tуL 2 ,                 ͑6͒   the outer loop process model transfer function
where                                                                                                       k1
                                                                                         G p1 ͑ s ͒ ϭ           e ϪL 1 s

                                   ͫ ͬ
                                                                                                        T 1 sϩ1
                              T2
                           Xϭ L ,                                        can be obtained by the following steps.




                  ͫ                                ͬ
                               2
                                                                           ͑1͒ Read off the overall system time delay L
                           u ͓ mT s ͔         k2                         ϭL 1 ϩL 2 of G p in the transfer function from the
                       u ͓͑ mϩ1 ͒ T s ͔       k2                         initial part of the relay feedback test, since the
             ⌿ϭ                                        ,                 inner loop transfer function delay L 2 is already
                                  ]            ]                         available, the time delay L 1 can be computed as
                       u ͓͑ nϩ1 ͒ T s ͔       k2



         ͫ                                                     ͬ
                                                                                                 L 1 ϭLϪL 2 .                           ͑11͒
                  k 2 t ͓ mT s ͔ ϪA ͓ mT s ͔                               ͑2͒ Obtain the frequency response of G p1 ( j ␻ )
        k 2 t ͓͑ mϩ1 ͒ T s ͔ ϪA ͓͑ mϩ1 ͒ T s ͔                           at ␻ ϭ ␻ u from
     ⌫ϭ                         ]               ,
                                                                                                            G p͑ j ␻ u ͒
         k 2 t ͓͑ nϩ1 ͒ T s ͔ ϪA ͓͑ nϩ1 ͒ T s ͔                                          G p1 ͑ j ␻ u ͒ ϭ                  ,            ͑12͒



                       ͫ                      ͬ
                                                                                                            G p2 ͑ j ␻ u ͒
                              ␦ ͓ mT s ͔                                 and calculate
                           ␦ ͓͑ mϩ1 ͒ T s ͔                                                             G p1 ͑ j ␻ u ͒
                 ⌬ϭ              ]          .                      ͑7͒                          k1
                                                                           GЈ ͑ j ␻u͒ϭ                 ϭ Ϫ jL 1 ␻ u ϭ ␣ ϩ j ␤ ,
                                                                            p1             jT 1 ␻ u ϩ1   e
                           ␦ ͓͑ nϩ1 ͒ T s ͔                                                                                 ͑13͒
T s is the sampling interval, and mT s уL 2 . The                        which is the frequency response for G p1 ( j ␻ )
best estimation X * of X can be obtained using the                       without delay, where ␣ has positive sign and ␤ has
standard least-square method as                                          negative sign.
                 X * ϭ ͑ ⌿ T ⌿ ͒ Ϫ1 ⌿ T ⌫.                         ͑8͒     ͑3͒ Calculate T 1 and k 1 , respectively, by
                                                                                                           ␤
The best estimation of T 2 and L 2 can then be ob-                                            T 1 ϭϪ           ,                        ͑14͒
tained from X * .                                                                                         ␣ϫ␻u
                                                                                                        ␣ 2ϩ ␤ 2
3.2. Outer loop process model identification                                                     k 1ϭ             .                      ͑15͒
                                                                                                           ␣
  By relay feedback test, the frequency response
                                                                         4. Controller design
of overall process model G p ( s ) at the ultimate fre-
quency ␻ u is estimated as
                                                                           As the main purpose of inner loop control is to

                     ͵ y ͑ t ͒e0
                                  Tu
                                           Ϫ j ␻ut
                                                     dt
                                                                         eliminate the input disturbance, a P or PI control-
                                                                         ler using widely accepted model based tuning
          G ͑ j ␻ ͒ϭ                                               ͑9͒   rules such as Ziegler-Nichols ͓8͔, Chien-Hrones-
                     ͵ u ͑ t ͒e
             p     u           Tu
                                                           ,
                                            Ϫ j ␻ut
                                                      dt                 Reswick ͑CHR͒ ͓9͔, or Cohen-Coon ͓10͔ tuning
                                       d
                              0                                          rules will suffice. This feature makes it very easy
Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72                                          67


to integrate the tuning method into the existing                       where ␰ stands for the desired damping ratio, usu-
auto-tuning systems. Without loss of generality,                       ally selected as 0.707, the natural frequency ␻ n
the PI control structure of the form                                   can be chosen between 0.5 and 1.0 times the ulti-
                                                                       mate frequency ␻ u from the relay feedback test
                                             K i2                      ͓13͔. An alternative of desired closed-loop transfer
                      G c2 ͑ s ͒ ϭK p2 ϩ
                                              s                        function for large dead-time systems can be ex-
                                                                       pressed as ͓14͔
and the Chien-Hrones-Reswick ͑CHR͒ ͓9͔ tuning
rule ͑20% overshoot͒ will be used for comparison                                                       ␻2
                                                                                                        n
study. The controller parameters are given, respec-                            H͑ s ͒ϭ                               e Ϫ ͑ L 1 ϩL 2 ͒ s .
                                                                                              s 2 ϩ2 ␰␻ n sϩ ␻ 2
                                                                                                               n
tively, by
                                 0.7T 2                                If the control specifications are not available, de-
                          K p2 ϭ        ,                   ͑16͒       fault settings for the parameter ␨ ϭ0.707 and
                                 k 2L 2                                ␻ u ( L 1 ϩL 2 ) ϭ2 can be used, which implies that
                                                                       the overshoot of the objective step response is
                                    0.304T 2
                        K i2 ϭ               .              ͑17͒       about 5%, the phase margin is 60°, and the gain
                                      k 2L 2
                                           2                           margin is 2.2. For simplicity, Eq. ͑20͒ can be re-
                                                                       written as the parametric form:
With the PI controller, the closed-loop transfer
function G 2 ( s ) of inner loop and the open loop                                                           d0
transfer function G 1 ( s ) are then obtained as                                       H͑ s ͒ϭ                           ,                      ͑21͒
                                                                                                      e 0 ϩe 1 sϩe 2 s 2
                 G p2 ͑ s ͒ G c2 ͑ s ͒                                 where d 0 ϭ ␻ 2 , e 0 ϭ ␻ 2 , e 1 ϭ2 ␰␻ n , and e 2 ϭ1.
   G 2͑ s ͒ ϭ                                                                        n           n
                1ϩG p2 ͑ s ͒ G c2 ͑ s ͒                                  ͑2͒ Approximating the time delays in G 1 ( s ) of
                                                                       Eq. ͑19͒, since the dead time L 2 of the inner loop
                      k 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s
           ϭ                                                ,          process model is very small, it is always approxi-
                s ͑ 1ϩT 2 s ͒ ϩk 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s            mated as 1 or
                                                            ͑18͒                              e ϪL 2 s Ϸ1ϩ ͑ ϪL 2 s ͒ ,                         ͑22͒
   G 1 ͑ s ͒ ϭG 2 ͑ s ͒ G p1 ͑ s ͒                                     e Ϫ ( L 1 ϩL 2 ) s is approximated as
                   k 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s                                                                         ͑ L 1 ϩL 2 ͒ 2 s 2
           ϭ                                                               e Ϫ ͑ L 1 ϩL 2 ͒ s Ϸ1Ϫ ͑ L 1 ϩL 2 ͒ sϩ
             s ͑ 1ϩT 2 s ͒ ϩk 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s                                                                       2
                                                                                                                                          ͑23͒
                        k1
                •           e ϪL 1 s .                      ͑19͒       in order to gain a more accurate approximation.
                    T 1 sϩ1
                                                                       Substitute Eqs. ͑22͒ and ͑23͒ to Eq. ͑19͒, and re-
As G 1 ( s ) is not a standard transfer function, it is                write G 1 ( s ) as
difficult to directly apply existing tuning rules.
Therefore a model-matching algorithm ͓11,12͔ is                                                   g 0 ϩg 1 sϩg 2 s 2 ϩg 3 s 3
                                                                                  G 1͑ s ͒ ϭ                                  ,                 ͑24͒
proposed to obtain the PID control parameters for                                                 h 0 ϩh 1 sϩh 2 s 2 ϩh 3 s 3
overall system performance. The brief theoretical
background of a controller design based on model                       where
matching is attached in the Appendix; for more
                                                                                                  g 0 ϭk 1 k 2 K i2 ,
details please refer to Refs. ͓11,12͔. Its application
to this particular problem is given as follows.                                   g 1 ϭk 1 k 2 ͓ K p2 ϪK i2 ͑ L 1 ϩL 2 ͔͒ ,
   ͑1͒ Assuming that the process dead time is
small, the desired reference model H ( s ) is chosen
as                                                                         g 2 ϭk 1 k 2   ͫ   K i2 ͑ L 1 ϩL 2 ͒ 2
                                                                                                       2
                                                                                                                  ϪK p2 ͑ L 1 ϩL 2 ͒ ,      ͬ
                                        ␻2
                                         n                                                       k 1 k 2 K p2 ͑ L 1 ϩL 2 ͒ 2
                H͑ s ͒ϭ                            ,        ͑20͒                      g 3ϭ                                   ,
                            s   2
                                    ϩ2 ␰␻ n sϩ ␻ 2
                                                 n                                                            2
68                                        Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72


and                                                                                        ͑4͒ The PID parameters can be computed as
                                        h 0 ϭk 2 K i2 ,                                                            a 1 b 1 Ϫa 0 b 2
                                                                                                          K p1 ϭ                    ,              ͑27͒
                                                                                                                          b2
              h 1 ϭk 2 T 1 K i2 ϩ1ϩk 2 K p2 Ϫk 2 K i2 L 2 ,                                                                 1


    h 2 ϭT 1 ͑ 1ϩk 2 K p2 Ϫk 2 K i2 L 2 ͒ ϩT 2 Ϫk 2 K p2 L 2 ,                                                            a0
                                                                                                                 K i1 ϭ      ,                     ͑28͒
                                                                                                                          b1
                          h 3 ϭT 1 ͑ T 2 Ϫk 2 K p2 L 2 ͒ .
                                                                                                             a 2 b 2 Ϫa 1 b 1 b 2 ϩa 0 b 2
                                                                                                                   1                     2
As indicated in Refs. ͓11,12͔, the Pade coefficients
                                      ´                                                             K d1 ϭ                                   ,     ͑29͒
and the Markov parameters characterize, respec-                                                                           b3
                                                                                                                           1
tively, the low- and high-frequency responses of a
                                                                                                                          b2
system, or the responses of the steady state and                                                                 T n1 ϭ      .                     ͑30͒
transition state. Pϭ5 and M ϭ0 are selected in                                                                            b1
order to get a good system response approxima-
tion in a steady state ͓11͔. Pade coefficients of
                                   ´                                                     5. Comparison study
H ( s ) are estimated as
                                                                                           Two examples are presented here to illustrate
                                           c 0 ϭ1,                                       the effectiveness of the proposed tuning method
                                                                                         for cascade control systems. In order to show the
                               c 1 ϭ ͑ d 1 Ϫe 1 c 0 ͒ /e 0 ,
                                                                                         accuracy of the proposed identification method in
                        c 2 ϭ ͑ d 2 Ϫe 1 c 1 Ϫe 2 c 0 ͒ /e 0 ,                           a noisy environment, the noise-to-signal ratio
                                                                                         ͑NSR͒, defined as ͓15͔ NSRϭmean͓abs͑noise͔͒/
                   c 3 ϭ ͑ d 3 Ϫe 1 c 2 Ϫe 2 c 1 Ϫe 3 c 0 ͒ /e 0 ,                       mean͓abs͑signal͔͒ is introduced. In this paper, the
                                                                                         proposed identification method is applied to both
         c 4 ϭ ͑ d 4 Ϫe 1 c 3 Ϫe 2 c 2 Ϫe 3 c 1 Ϫe 4 c 0 ͒ /e 0 .                        processes with noise level 10% NSR.
                                                                                           Example 1. Consider a cascade control system
  ͑3͒ The PID controller with pϭmϭ2 ͓11͔ is                                              discussed by Hang ͓4͔ and Tan ͓5͔ with plant mod-
given as                                                                                 els of
                                                  K i1    K d1 s                                              e Ϫs                       e Ϫ␣s
                    G c1 ͑ s ͒ ϭK p1 ϩ                 ϩ                                      G p1 ͑ s ͒ ϭ           ,     G p2 ͑ s ͒ ϭ        ,
                                                   s     1ϩT n1 s                                          ͑ 1ϩs ͒ 2                    1ϩ ␣ s
                                        a 0 ϩa 1 sϩa 2 s 2                               where ␣ϭ0.1. After the relay feedback test, the
                                    ϭ                      ,                      ͑25͒
                                        b 0 ϩb 1 sϩb 2 s 2                               parameters for the inner loop process model is ob-
                                                                                         tained as
where b 0 ϭ0 and a 0 , a 1 , a 2 , b 1 , b 2 can be com-
puted by solving the following linear matrix equa-                                                                          e Ϫ0.115s




ͫ
tions:                                                                                              G p2 ͑ s ͒ ϭ0.9563
                                                                                                                           1ϩ0.0947s




                                                                                     ΅
     g 0c 1                0                  0        h0               0
                                                                                         and the outer loop process model is estimated as
     g 0 c 2 ϩg 2 c 0      g 0c 1             0        h 0 c 1 ϩh 1     h 0c 0
     g 0 c 3 ϩg 1 c 2      g 0c 2             g 0c 1   h 0 c 2 ϩh 1 c 1 h 0 c 1                                             e Ϫ1.63s
     ϩg 2 c 1              ϩg 1 c 1                    ϩh 2             ϩh 1                         G p1 ͑ s ͒ ϭ0.965               .
                                                                                                                           1ϩ1.908s
     g 0 c 4 ϩg 1 c 3      g 0 c 3 ϩg 1 c 2 g 0 c 2    h 0 c 3 ϩh 1 c 2 h 0 c 2
     ϩg 2 c 2 ϩg 3 c 1 ϩg 2 c 1               ϩg 1 c 1 ϩh 2 c 1 ϩh 3 ϩh 1 c 1 ϩh 2       The parameters calculated for the inner loop PI




         ͫ ͬͫͬ
     0                     0                  g3       0                h3               controller G c2 using the Chien-Hrones-Reswick
                                                                                         ͑CHR͒ tuning rule ͑20% overshoot͒ are obtained
              a0          0
                                                                                         as K p2 ϭ0.603, K i2 ϭ2.277. The overall system
              a1          0                                                              reference model of the cascade control system is
     ϫ        a2 ϭ        0     .                                                 ͑26͒   chosen to be in the form of Eq. ͑20͒ with ␨ϭ0.8
              b1          0                                                              and ␻ u ϭ0.6. The outer loop controller’s param-
              b2          1                                                              eters are obtained as K p1 ϭ0.6592, K i1 ϭ0.3536,
Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72                69




                                      Fig. 4. Tuning procedure and step response.


K d1 ϭ0.2886, and T n1 ϭ1.4392. The proposed                  the inner loop are obtained as K p2 ϭ2.895, K i2
auto-tuning procedure and step response in the                ϭ0.147. The overall system reference model of
noisy environment are shown in Fig. 4. The result             the cascade control system is chosen to be in the
is also compared to the methods proposed by                   form of Eq. ͑20͒ with ␨ϭ0.707 and ␻ u ϭ0.03, the
Hang and Tan. Fig. 5 shows the closed-loop per-               outer loop controller’s parameters are obtained as
formance from tϭ0 s to tϭ80 s; a large step load              K p1 ϭϪ4.9225, K i1 ϭϪ0.1105, K d1 ϭϪ51.1205,
disturbance seeps into the process for all cases at           and T n1 ϭ6.4596. The control performance com-
tϭ50 s.                                                       parison study is carried out from tϭ0 s to
   Example 2. Consider a process model of the                 tϭ2000 s, a large step load disturbance is added
packed-bed reactor provided by Ref. ͓16͔. The                 into the process at time tϭ1000 s, as shown in
goal is to tightly control the exit concentration             Fig. 6.
temperature, and the most significant disturbance                From the examples, the improved performance
is the heating medium temperature. The inner and              of the proposed tuning method is clearly evident.
outer loop process models are given by
                                  e Ϫ20s                      6. Conclusion
            G p1 ͑ s ͒ ϭϪ0.19            ,
                                 1ϩ50s
                                                                 This paper developed a novel auto-tuning
                               e Ϫ8s                          method for the cascade control system. As the in-
             G p2 ͑ s ͒ ϭ0.57        ,
                              1ϩ20s                           ner loop process acts much faster than the outer
                                                              loop in the cascade control system, both inner loop
respectively. To reduce the disturbance, a cascade            and outer loop process model parameters can be
control strategy is adopted. Using the relay feed-            identified using one relay feedback test by utiliz-
back test, the parameters for the inner and outer             ing this physical property under the proposed
process models from the experiment are estimated              structure. Consequently, well-established model
as                                                            based PI tuning rules can be applied to tune the
                                  e Ϫ22.6s                    inner loop, and a model matching the PID control-
           G p1 ͑ s ͒ ϭϪ0.192              ,                  ler design method was proposed to tune the outer
                                 1ϩ47.5s
                                                              loop. Finally, two examples were given to show
                                 e Ϫ8.5s                      the effectiveness of the proposed method. The
            G p2 ͑ s ͒ ϭ0.558            .                    method is very straightforward and has been inte-
                                1ϩ19.7s
                                                              grated into an existing auto-tuning system. It is
The PI controller using the Chien-Hrones-                     now being tested in a centralized HVAC system
Reswick ͑CHR͒ tuning rule ͑20% overshoot͒ for                 and the field results will be reported soon.
70                     Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72




                                           Fig. 5. Performance comparison.



Appendix                                                       and a controller’s transfer function model

     Suppose we have a process model                                                a 0 ϩa 1 sϩ¯ϩa p s p
                                                                          C͑ s ͒ϭ                        .    ͑A2͒
                                                                                    b 0 ϩb 1 sϩ¯ϩb m s m
                    g 0 ϩg 1 sϩ¯ϩg q s q
            G͑ s ͒ϭ                      ,         ͑A1͒
                    h 0 ϩh 1 sϩ¯ϩh n s n                       It is desired that C ( s ) be obtained in such a way




                Fig. 6. Performances of the proposed method ͑solid line͒ and of Ref. ͓16͔ ͑dashed line͒.
Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72                        71

                                            ´
that the overall system matches a set of Pade co-                                  i
efficients and Markov parameters of a given a ref-                         x i ϭ ͚ a j g iϪ j ,     iϭ0,1, . . . ,qϩp, ͑A9͒
                                                                                  jϭ0
erence model
                                                                              i
                   d 0 ϩd 1 sϩ¯ϩd r s r
           H͑ s ͒ϭ                      ,                  ͑A3͒        y i ϭ ͚ b j h iϪ j ,      iϭ0,1, . . . ,nϩm.    ͑A10͒
                   e 0 ϩe 1 sϩ¯ϩe r s r                                      jϭ0

and a simple controller C ( s ) can be found such                  Using the constraint PϩM ϭpϩmϩ1, where P P
that                                                                                       ´
                                                                   is the number of Pade coefficients, M is the num-
                                                                   ber of Markov parameters, p is the numerator’s
             C͑ j ␻ ͒G͑ j ␻ ͒                                      order of C ( s ) , and m is the denominator’s order of
                                  ХH ͑ j ␻ ͒ .             ͑A4͒
            1ϩC ͑ j ␻ ͒ G ͑ j ␻ ͒                                  C ( s ) . The parameters a, b i of C ( s ) can be ob-
                                                                   tained uniquely by solving the set of linear Eqs.
The model matching of time moments and Mar-                        ͑A5͒–͑A10͒.
kov parameters is very effective in model reduc-
tion for obtaining approximate models, because
        ´
the Pade coefficients and the Markov parameters                     References
characterize, respectively, the low- and high-                      ͓1͔ Astrom, K. J. and Hagglund, T., PID Controller:
                                        ´
frequency responses of a system. The Pade coeffi-                        Theory, Design and Tuning. Instrument Society of
cients of H ( s ) are defined as                                         America, Research Triangle Park, NC, 1995.
                                                                    ͓2͔ Bi, Q., Cai, Wenjian, Lee, E. L., Wang, Qingguo,
                          c 0 ϭd 0 /e 0 ,                               Hang, C. C., and Zhang, Y., Robust identification of
                                                                        first order plus dead-time model from step response.


                  ͫ                         ͬͲ
                             k                                          Control Eng. Pract. 1, 71–77 ͑1999͒.
                                                                    ͓3͔ Li, M. X., Bruijn, P. M., and Verbruggen, H. B., Tun-
           c k ϭ d k Ϫ ͚ e j c kϪ j              e0 ,      ͑A5͒         ing of cascade PID controller with fuzzy inference.
                            jϭ1
                                                                        Asia-Pac. Eng. Part A, Electr. Eng. 2, 65–70 ͑1994͒.
                        ´                                           ͓4͔ Hang, C. C., Loh, A. P., and Vasnani, V. U., Relay
where c k is the kth Pade coefficient.                                   feedback auto-tuning of cascade controllers. IEEE
 The Markov parameters of H ( s ) are defined as                         Trans. Control Syst. Technol. 2, 42– 45 ͑1994͒.
                                                                    ͓5͔ Tan, K. K., Lee, T. H., and Ferdous, R., Simultaneous
                          m 0 ϭd r /e r ,                               online automatic tuning of cascade control for open


              ͫ                              ͬͲ
                                                                        loop stable process. ISA Trans. 39, 233–243 ͑2000͒.
                             k
                                                                    ͓6͔ Shinskey, F. G., Process Control System: Application,
        m k ϭ d rϪk Ϫ ͚ e rϪ j m kϪ j               er ,   ͑A6͒         Design, and Tuning. 3rd ed., McGraw-Hill, New York,
                            jϭ1                                         1998.
                                                                    ͓7͔ Marlin, T. E., Process Control: Designing Process and
where m k is the kth Markov parameter.                                  Control System for Dynamic Performance. McGraw-
  A set of liner equations as shown in the follow-                      Hill, New York, 1995.
                                             ´
ing can be gained in order to match the Pade co-                    ͓8͔ Ziegler, J. G. and Nichols, N. B., Optimum settings for
                                                                        automatic controllers. Trans. ASME 64, 759–768
efficients and Markov parameters:
                                                                        ͑1942͒.
                                                                    ͓9͔ Chien, K. L., Hrones, J. A., and Reswick, J. B., On the
                          ␣ 0 c 0 ϭx 0 ,                                automatic control of generalized passive systems.
                      k                                                 Trans. ASME 74, 175–185 ͑1952͒.
                                                                   ͓10͔ Cohen, G. H. and Coon, G. A., Theoretical consider-
  ␣ 0 c k ϭx k Ϫ ͚ ␣ j c kϪ j , kϭ1,2, . . . , PϪ1,                     ation of retarded control. Trans. ASME 75, 827– 834
                  jϭ1
                                                                        ͑1953͒.
                                                                   ͓11͔ Aguirre, L. A., New algorithm for closed-loop model
                          1ϭ ␣ nϩm ,                       ͑A7͒         matching. IEEE Electron Device Lett. 27, 2260–2262
                                                                        ͑1991͒.
                                  k
                                                                   ͓12͔ Aguirre, L. A., PID tuning on model matching. IEEE
        m k ϭx nϩmϪk Ϫ ͚ ␣ nϩmϪ j m kϪ j ,                              Electron Device Lett. 28, 2269–2271 ͑1992͒.
                                 jϭ1                               ͓13͔ Wang, Q. G., Hang, C. C., and Biao, Zou, A frequency
                                                                        response approach to autotuning of multivariable con-
                  kϭ1,2, . . . ,M Ϫ1,                                   trollers. Trans. Inst. Chem. Eng., Part A 75, 64 –72
                                                                        ͑1997͒.
where                                                              ͓14͔ Kiong Tan, K. K., Wang, Qing-Guo, and Hang, Chang
                                                                        Chien, Advances in Industrial Control. Springer-
         ␣ i ϭx i ϩy i ,         iϭ0,1, . . . ,nϩm,        ͑A8͒         Verlag, London, 1999.
72                           Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72

͓15͔ Haykin, S., An Introduction to Analog & Digital Com-               pany, U. S. A.; Research Scientist at National University of Singapore;
     munication. Wiley, New York, 1989.                                 Principal Engineer and R&D Manager at Supersymmetry Services Pte
͓16͔ Marlin, Thomas E., Process Control: Designing Pro-                 Ltd, Singapore; Senior Research Fellow at Environmental Technology
                                                                        Institute, Singapore, respectively. He is currently serving as Associate
     cesses and Control Systems for Dynamic Perfor-                     Professor at Nayang Technological University, Singapore. Dr. Cai’s
     mance. 2nd ed., McGraw-Hill, New York, 2000.                       current research interests include multivariable control and HVAC sys-
                                                                        tem optimization.

                                      Sihai Song was born in 1974,
                                      Zhejiang, P. R. China. He                                                 Ya-Gang Wang was born in
                                      graduated from Zhejiang Uni-                                              1967, Shanxi, P. R. China. He
                                      versity with a bachelor degree                                            received his B.Eng., M.Eng.,
                                      in electrical engineering in                                              and Ph.D. from Department of
                                      1997, and a second bachelor                                               Automation, China University
                                      degree of international com-                                              of Mining and Technology,
                                      modities inspection in 1998. In                                           Taiyuan University of Technol-
                                      2001, he started his postgradu-                                           ogy and Shanghai Jiao Tong
                                      ation studies at Nanyang Tech-                                            University, P. R. China, in
                                      nological University, Sin-                                                1988, 1991, and 2000, respec-
                                      gapore. He is interested in PID                                           tively. After graduation, he
                                      auto-tuning and computer-                                                 worked as a lecturer in Taiyuan
                                      aided control system design.                                              University of Technology, P. R.
                                                                                                                China, and a Postdoctoral Re-
                                                                        search Fellow in Nanyang Technological University, Singapore. He is
                                                                        interested in process control and instrumentation, PID auto-tuning, and
                                       Wenjian Cai received his
                                                                        multivariable control.
                                       B.Eng., M.Eng., and Ph.D.
                                       from Department of Precision
                                       Instrumentation Engineering,
                                       Department of Control Engi-
                                       neering, Harbin Institute of
                                       Technology, P. R. China, and
                                       Department of Electrical Engi-
                                       neering, Oakland University,
                                       U. S. A., in 1980, 1983, and
                                       1992,     respectively.  After
                                       graduation, he worked as a
                                       Postdoctoral Research Fellow
                                       at the Center for Advanced Ro-
botics, Oakland University, U. S. A.; Engineer at CEC Controls Com-

Weitere ähnliche Inhalte

Was ist angesagt?

Non integer order controller based robust performance analysis of a conical t...
Non integer order controller based robust performance analysis of a conical t...Non integer order controller based robust performance analysis of a conical t...
Non integer order controller based robust performance analysis of a conical t...Editor Jacotech
 
Pid controller tuning using fuzzy logic
Pid controller tuning using fuzzy logicPid controller tuning using fuzzy logic
Pid controller tuning using fuzzy logicRoni Roshni
 
Robust PID controller design for non-minimum phase time delay systems
Robust PID controller design for non-minimum phase time delay systemsRobust PID controller design for non-minimum phase time delay systems
Robust PID controller design for non-minimum phase time delay systemsISA Interchange
 
Model Predictive Control For Integrating Processes
Model Predictive Control For Integrating ProcessesModel Predictive Control For Integrating Processes
Model Predictive Control For Integrating ProcessesEmerson Exchange
 
Design of fuzzzy pid controller for bldc motor
Design of fuzzzy pid controller for bldc motorDesign of fuzzzy pid controller for bldc motor
Design of fuzzzy pid controller for bldc motorMishal Hussain
 
PID Tuning using Ziegler Nicholas - MATLAB Approach
PID Tuning using Ziegler Nicholas - MATLAB ApproachPID Tuning using Ziegler Nicholas - MATLAB Approach
PID Tuning using Ziegler Nicholas - MATLAB ApproachWaleed El-Badry
 
Tuning of PID controllers for integrating systems using direct synthesis method
Tuning of PID controllers for integrating systems using direct synthesis methodTuning of PID controllers for integrating systems using direct synthesis method
Tuning of PID controllers for integrating systems using direct synthesis methodISA Interchange
 
A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...
A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...
A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...IRJET Journal
 
10 Tips for Tuning of Pid Looops
10 Tips for Tuning of Pid Looops10 Tips for Tuning of Pid Looops
10 Tips for Tuning of Pid LooopsLiving Online
 
10.1.1.193.2962
10.1.1.193.296210.1.1.193.2962
10.1.1.193.2962aboma2hawi
 
Recurrent fuzzy neural network backstepping control for the prescribed output...
Recurrent fuzzy neural network backstepping control for the prescribed output...Recurrent fuzzy neural network backstepping control for the prescribed output...
Recurrent fuzzy neural network backstepping control for the prescribed output...ISA Interchange
 
Tuning PI controllers for stable processes with specifications on gain and ph...
Tuning PI controllers for stable processes with specifications on gain and ph...Tuning PI controllers for stable processes with specifications on gain and ph...
Tuning PI controllers for stable processes with specifications on gain and ph...ISA Interchange
 
Design of IEEE 1149.1 Tap Controller IP Core
Design of IEEE 1149.1 Tap Controller IP Core Design of IEEE 1149.1 Tap Controller IP Core
Design of IEEE 1149.1 Tap Controller IP Core csandit
 
Thompson tchobanian ni_li)
Thompson tchobanian ni_li)Thompson tchobanian ni_li)
Thompson tchobanian ni_li)trtrungviet
 
Speed control of dc motor by fuzzy controller
Speed control of dc motor by fuzzy controllerSpeed control of dc motor by fuzzy controller
Speed control of dc motor by fuzzy controllerMurugappa Group
 
Effects of Macrocycle Time and Sampling Rates on Control Loop Performance
Effects of Macrocycle Time and Sampling Rates on Control Loop PerformanceEffects of Macrocycle Time and Sampling Rates on Control Loop Performance
Effects of Macrocycle Time and Sampling Rates on Control Loop PerformanceJim Cahill
 
Adaptive predictive functional control of a class of nonlinear systems
Adaptive predictive functional control of a class of nonlinear systemsAdaptive predictive functional control of a class of nonlinear systems
Adaptive predictive functional control of a class of nonlinear systemsISA Interchange
 
Frequency response method to derive transfer function of servo motor using Qu...
Frequency response method to derive transfer function of servo motor using Qu...Frequency response method to derive transfer function of servo motor using Qu...
Frequency response method to derive transfer function of servo motor using Qu...IRJET Journal
 
pH Control Solutions - Greg McMillan
pH Control Solutions - Greg McMillanpH Control Solutions - Greg McMillan
pH Control Solutions - Greg McMillanJim Cahill
 

Was ist angesagt? (20)

Non integer order controller based robust performance analysis of a conical t...
Non integer order controller based robust performance analysis of a conical t...Non integer order controller based robust performance analysis of a conical t...
Non integer order controller based robust performance analysis of a conical t...
 
Pid controller tuning using fuzzy logic
Pid controller tuning using fuzzy logicPid controller tuning using fuzzy logic
Pid controller tuning using fuzzy logic
 
Robust PID controller design for non-minimum phase time delay systems
Robust PID controller design for non-minimum phase time delay systemsRobust PID controller design for non-minimum phase time delay systems
Robust PID controller design for non-minimum phase time delay systems
 
Model Predictive Control For Integrating Processes
Model Predictive Control For Integrating ProcessesModel Predictive Control For Integrating Processes
Model Predictive Control For Integrating Processes
 
Design of fuzzzy pid controller for bldc motor
Design of fuzzzy pid controller for bldc motorDesign of fuzzzy pid controller for bldc motor
Design of fuzzzy pid controller for bldc motor
 
PID Tuning using Ziegler Nicholas - MATLAB Approach
PID Tuning using Ziegler Nicholas - MATLAB ApproachPID Tuning using Ziegler Nicholas - MATLAB Approach
PID Tuning using Ziegler Nicholas - MATLAB Approach
 
Tuning of PID controllers for integrating systems using direct synthesis method
Tuning of PID controllers for integrating systems using direct synthesis methodTuning of PID controllers for integrating systems using direct synthesis method
Tuning of PID controllers for integrating systems using direct synthesis method
 
A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...
A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...
A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushles...
 
10 Tips for Tuning of Pid Looops
10 Tips for Tuning of Pid Looops10 Tips for Tuning of Pid Looops
10 Tips for Tuning of Pid Looops
 
06 control.systems
06 control.systems06 control.systems
06 control.systems
 
10.1.1.193.2962
10.1.1.193.296210.1.1.193.2962
10.1.1.193.2962
 
Recurrent fuzzy neural network backstepping control for the prescribed output...
Recurrent fuzzy neural network backstepping control for the prescribed output...Recurrent fuzzy neural network backstepping control for the prescribed output...
Recurrent fuzzy neural network backstepping control for the prescribed output...
 
Tuning PI controllers for stable processes with specifications on gain and ph...
Tuning PI controllers for stable processes with specifications on gain and ph...Tuning PI controllers for stable processes with specifications on gain and ph...
Tuning PI controllers for stable processes with specifications on gain and ph...
 
Design of IEEE 1149.1 Tap Controller IP Core
Design of IEEE 1149.1 Tap Controller IP Core Design of IEEE 1149.1 Tap Controller IP Core
Design of IEEE 1149.1 Tap Controller IP Core
 
Thompson tchobanian ni_li)
Thompson tchobanian ni_li)Thompson tchobanian ni_li)
Thompson tchobanian ni_li)
 
Speed control of dc motor by fuzzy controller
Speed control of dc motor by fuzzy controllerSpeed control of dc motor by fuzzy controller
Speed control of dc motor by fuzzy controller
 
Effects of Macrocycle Time and Sampling Rates on Control Loop Performance
Effects of Macrocycle Time and Sampling Rates on Control Loop PerformanceEffects of Macrocycle Time and Sampling Rates on Control Loop Performance
Effects of Macrocycle Time and Sampling Rates on Control Loop Performance
 
Adaptive predictive functional control of a class of nonlinear systems
Adaptive predictive functional control of a class of nonlinear systemsAdaptive predictive functional control of a class of nonlinear systems
Adaptive predictive functional control of a class of nonlinear systems
 
Frequency response method to derive transfer function of servo motor using Qu...
Frequency response method to derive transfer function of servo motor using Qu...Frequency response method to derive transfer function of servo motor using Qu...
Frequency response method to derive transfer function of servo motor using Qu...
 
pH Control Solutions - Greg McMillan
pH Control Solutions - Greg McMillanpH Control Solutions - Greg McMillan
pH Control Solutions - Greg McMillan
 

Andere mochten auch

Smithes - Coop Presentation 1
Smithes - Coop Presentation 1Smithes - Coop Presentation 1
Smithes - Coop Presentation 1Jeremy Smithes
 
Fall emailable catalog
Fall emailable catalogFall emailable catalog
Fall emailable catalogJulie Elmquist
 
Smithes - Coop Presentation 3
Smithes - Coop Presentation 3Smithes - Coop Presentation 3
Smithes - Coop Presentation 3Jeremy Smithes
 
Problems faced by IT Startups
Problems faced by IT StartupsProblems faced by IT Startups
Problems faced by IT StartupsSohil Ghoghari
 
Nawałka story, czyli jak budować zespół
Nawałka story, czyli jak budować zespółNawałka story, czyli jak budować zespół
Nawałka story, czyli jak budować zespółBPSC
 
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...ISA Interchange
 
Identification and real time position control of a servo-hydraulic rotary act...
Identification and real time position control of a servo-hydraulic rotary act...Identification and real time position control of a servo-hydraulic rotary act...
Identification and real time position control of a servo-hydraulic rotary act...ISA Interchange
 
Eurekaforbes- Sales strategy
Eurekaforbes- Sales strategyEurekaforbes- Sales strategy
Eurekaforbes- Sales strategyArjama Mukherjee
 
Urban Renewal In Lyon Confluence
Urban Renewal In Lyon ConfluenceUrban Renewal In Lyon Confluence
Urban Renewal In Lyon ConfluenceAdhitya Arjanggi
 

Andere mochten auch (12)

Smithes - Coop Presentation 1
Smithes - Coop Presentation 1Smithes - Coop Presentation 1
Smithes - Coop Presentation 1
 
Fall emailable catalog
Fall emailable catalogFall emailable catalog
Fall emailable catalog
 
Smithes - Coop Presentation 3
Smithes - Coop Presentation 3Smithes - Coop Presentation 3
Smithes - Coop Presentation 3
 
Problems faced by IT Startups
Problems faced by IT StartupsProblems faced by IT Startups
Problems faced by IT Startups
 
Nawałka story, czyli jak budować zespół
Nawałka story, czyli jak budować zespółNawałka story, czyli jak budować zespół
Nawałka story, czyli jak budować zespół
 
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...
 
Requisitos contrato docente Coar área ingles
Requisitos contrato docente Coar  área  inglesRequisitos contrato docente Coar  área  ingles
Requisitos contrato docente Coar área ingles
 
Identification and real time position control of a servo-hydraulic rotary act...
Identification and real time position control of a servo-hydraulic rotary act...Identification and real time position control of a servo-hydraulic rotary act...
Identification and real time position control of a servo-hydraulic rotary act...
 
Eurekaforbes- Sales strategy
Eurekaforbes- Sales strategyEurekaforbes- Sales strategy
Eurekaforbes- Sales strategy
 
Urban Renewal In Lyon Confluence
Urban Renewal In Lyon ConfluenceUrban Renewal In Lyon Confluence
Urban Renewal In Lyon Confluence
 
Cadbury Final
Cadbury FinalCadbury Final
Cadbury Final
 
Ferrouscementhouse 2
Ferrouscementhouse 2Ferrouscementhouse 2
Ferrouscementhouse 2
 

Ähnlich wie Auto tuning of cascade control systems

Autotuning of a new PI-PD Smith predictor based on time domain specifications
Autotuning of a new PI-PD Smith predictor based on time domain specificationsAutotuning of a new PI-PD Smith predictor based on time domain specifications
Autotuning of a new PI-PD Smith predictor based on time domain specificationsISA Interchange
 
Fuzzy controlled mine drainage system based on embedded system
Fuzzy controlled mine drainage system based on embedded systemFuzzy controlled mine drainage system based on embedded system
Fuzzy controlled mine drainage system based on embedded systemIRJET Journal
 
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...IRJET Journal
 
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...IRJET Journal
 
aa-automation-apc-complex-industrial-processes
aa-automation-apc-complex-industrial-processesaa-automation-apc-complex-industrial-processes
aa-automation-apc-complex-industrial-processesDavid Lyon
 
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...Model-based Approach of Controller Design for a FOPTD System and its Real Tim...
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...IOSR Journals
 
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...A fuzzy model based adaptive pid controller design for nonlinear and uncertai...
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...ISA Interchange
 
Improving performance using cascade control and a Smith predictor
Improving performance using cascade control and a Smith predictorImproving performance using cascade control and a Smith predictor
Improving performance using cascade control and a Smith predictorISA Interchange
 
Artificial Neural Network Based Closed Loop Control of Multilevel Inverter
Artificial Neural Network Based Closed Loop Control of Multilevel InverterArtificial Neural Network Based Closed Loop Control of Multilevel Inverter
Artificial Neural Network Based Closed Loop Control of Multilevel InverterIJMTST Journal
 
Design PID controllers for desired time domain or frequency domain response
Design PID controllers for desired time domain or frequency domain responseDesign PID controllers for desired time domain or frequency domain response
Design PID controllers for desired time domain or frequency domain responseISA Interchange
 
Implementation of closed loop control technique for improving the performance...
Implementation of closed loop control technique for improving the performance...Implementation of closed loop control technique for improving the performance...
Implementation of closed loop control technique for improving the performance...IJERA Editor
 
Flexible structure control a strategy for releasing input constraints
Flexible structure control a strategy for releasing input constraintsFlexible structure control a strategy for releasing input constraints
Flexible structure control a strategy for releasing input constraintsISA Interchange
 
Controller Tuning for Integrator Plus Delay Processes.
Controller Tuning for Integrator Plus Delay Processes.Controller Tuning for Integrator Plus Delay Processes.
Controller Tuning for Integrator Plus Delay Processes.theijes
 
A novel auto-tuning method for fractional order PID controllers
A novel auto-tuning method for fractional order PID controllersA novel auto-tuning method for fractional order PID controllers
A novel auto-tuning method for fractional order PID controllersISA Interchange
 

Ähnlich wie Auto tuning of cascade control systems (20)

Autotuning of a new PI-PD Smith predictor based on time domain specifications
Autotuning of a new PI-PD Smith predictor based on time domain specificationsAutotuning of a new PI-PD Smith predictor based on time domain specifications
Autotuning of a new PI-PD Smith predictor based on time domain specifications
 
Fuzzy controlled mine drainage system based on embedded system
Fuzzy controlled mine drainage system based on embedded systemFuzzy controlled mine drainage system based on embedded system
Fuzzy controlled mine drainage system based on embedded system
 
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...
 
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...
 
Di34672675
Di34672675Di34672675
Di34672675
 
aa-automation-apc-complex-industrial-processes
aa-automation-apc-complex-industrial-processesaa-automation-apc-complex-industrial-processes
aa-automation-apc-complex-industrial-processes
 
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...Model-based Approach of Controller Design for a FOPTD System and its Real Tim...
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...
 
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...A fuzzy model based adaptive pid controller design for nonlinear and uncertai...
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...
 
Improving performance using cascade control and a Smith predictor
Improving performance using cascade control and a Smith predictorImproving performance using cascade control and a Smith predictor
Improving performance using cascade control and a Smith predictor
 
Artificial Neural Network Based Closed Loop Control of Multilevel Inverter
Artificial Neural Network Based Closed Loop Control of Multilevel InverterArtificial Neural Network Based Closed Loop Control of Multilevel Inverter
Artificial Neural Network Based Closed Loop Control of Multilevel Inverter
 
Design PID controllers for desired time domain or frequency domain response
Design PID controllers for desired time domain or frequency domain responseDesign PID controllers for desired time domain or frequency domain response
Design PID controllers for desired time domain or frequency domain response
 
Implementation of closed loop control technique for improving the performance...
Implementation of closed loop control technique for improving the performance...Implementation of closed loop control technique for improving the performance...
Implementation of closed loop control technique for improving the performance...
 
Flexible structure control a strategy for releasing input constraints
Flexible structure control a strategy for releasing input constraintsFlexible structure control a strategy for releasing input constraints
Flexible structure control a strategy for releasing input constraints
 
Controller Tuning Method for Non-Linear Conical Tank System
Controller Tuning Method for Non-Linear Conical Tank SystemController Tuning Method for Non-Linear Conical Tank System
Controller Tuning Method for Non-Linear Conical Tank System
 
B010511015
B010511015B010511015
B010511015
 
D04954148
D04954148D04954148
D04954148
 
Controller Tuning for Integrator Plus Delay Processes.
Controller Tuning for Integrator Plus Delay Processes.Controller Tuning for Integrator Plus Delay Processes.
Controller Tuning for Integrator Plus Delay Processes.
 
PID Tuning Rules
PID Tuning RulesPID Tuning Rules
PID Tuning Rules
 
Pa3426282645
Pa3426282645Pa3426282645
Pa3426282645
 
A novel auto-tuning method for fractional order PID controllers
A novel auto-tuning method for fractional order PID controllersA novel auto-tuning method for fractional order PID controllers
A novel auto-tuning method for fractional order PID controllers
 

Mehr von ISA Interchange

An optimal general type-2 fuzzy controller for Urban Traffic Network
An optimal general type-2 fuzzy controller for Urban Traffic NetworkAn optimal general type-2 fuzzy controller for Urban Traffic Network
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
 
Embedded intelligent adaptive PI controller for an electromechanical system
Embedded intelligent adaptive PI controller for an electromechanical  systemEmbedded intelligent adaptive PI controller for an electromechanical  system
Embedded intelligent adaptive PI controller for an electromechanical systemISA Interchange
 
State of charge estimation of lithium-ion batteries using fractional order sl...
State of charge estimation of lithium-ion batteries using fractional order sl...State of charge estimation of lithium-ion batteries using fractional order sl...
State of charge estimation of lithium-ion batteries using fractional order sl...ISA Interchange
 
Fractional order PID for tracking control of a parallel robotic manipulator t...
Fractional order PID for tracking control of a parallel robotic manipulator t...Fractional order PID for tracking control of a parallel robotic manipulator t...
Fractional order PID for tracking control of a parallel robotic manipulator t...ISA Interchange
 
Fuzzy logic for plant-wide control of biological wastewater treatment process...
Fuzzy logic for plant-wide control of biological wastewater treatment process...Fuzzy logic for plant-wide control of biological wastewater treatment process...
Fuzzy logic for plant-wide control of biological wastewater treatment process...ISA Interchange
 
Design and implementation of a control structure for quality products in a cr...
Design and implementation of a control structure for quality products in a cr...Design and implementation of a control structure for quality products in a cr...
Design and implementation of a control structure for quality products in a cr...ISA Interchange
 
Model based PI power system stabilizer design for damping low frequency oscil...
Model based PI power system stabilizer design for damping low frequency oscil...Model based PI power system stabilizer design for damping low frequency oscil...
Model based PI power system stabilizer design for damping low frequency oscil...ISA Interchange
 
A comparison of a novel robust decentralized control strategy and MPC for ind...
A comparison of a novel robust decentralized control strategy and MPC for ind...A comparison of a novel robust decentralized control strategy and MPC for ind...
A comparison of a novel robust decentralized control strategy and MPC for ind...ISA Interchange
 
Fault detection of feed water treatment process using PCA-WD with parameter o...
Fault detection of feed water treatment process using PCA-WD with parameter o...Fault detection of feed water treatment process using PCA-WD with parameter o...
Fault detection of feed water treatment process using PCA-WD with parameter o...ISA Interchange
 
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...Model-based adaptive sliding mode control of the subcritical boiler-turbine s...
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...ISA Interchange
 
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...ISA Interchange
 
An artificial intelligence based improved classification of two-phase flow patte...
An artificial intelligence based improved classification of two-phase flow patte...An artificial intelligence based improved classification of two-phase flow patte...
An artificial intelligence based improved classification of two-phase flow patte...ISA Interchange
 
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...ISA Interchange
 
Load estimator-based hybrid controller design for two-interleaved boost conve...
Load estimator-based hybrid controller design for two-interleaved boost conve...Load estimator-based hybrid controller design for two-interleaved boost conve...
Load estimator-based hybrid controller design for two-interleaved boost conve...ISA Interchange
 
Effects of Wireless Packet Loss in Industrial Process Control Systems
Effects of Wireless Packet Loss in Industrial Process Control SystemsEffects of Wireless Packet Loss in Industrial Process Control Systems
Effects of Wireless Packet Loss in Industrial Process Control SystemsISA Interchange
 
Fault Detection in the Distillation Column Process
Fault Detection in the Distillation Column ProcessFault Detection in the Distillation Column Process
Fault Detection in the Distillation Column ProcessISA Interchange
 
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank System
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemNeural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank System
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemISA Interchange
 
A KPI-based process monitoring and fault detection framework for large-scale ...
A KPI-based process monitoring and fault detection framework for large-scale ...A KPI-based process monitoring and fault detection framework for large-scale ...
A KPI-based process monitoring and fault detection framework for large-scale ...ISA Interchange
 
An adaptive PID like controller using mix locally recurrent neural network fo...
An adaptive PID like controller using mix locally recurrent neural network fo...An adaptive PID like controller using mix locally recurrent neural network fo...
An adaptive PID like controller using mix locally recurrent neural network fo...ISA Interchange
 
A method to remove chattering alarms using median filters
A method to remove chattering alarms using median filtersA method to remove chattering alarms using median filters
A method to remove chattering alarms using median filtersISA Interchange
 

Mehr von ISA Interchange (20)

An optimal general type-2 fuzzy controller for Urban Traffic Network
An optimal general type-2 fuzzy controller for Urban Traffic NetworkAn optimal general type-2 fuzzy controller for Urban Traffic Network
An optimal general type-2 fuzzy controller for Urban Traffic Network
 
Embedded intelligent adaptive PI controller for an electromechanical system
Embedded intelligent adaptive PI controller for an electromechanical  systemEmbedded intelligent adaptive PI controller for an electromechanical  system
Embedded intelligent adaptive PI controller for an electromechanical system
 
State of charge estimation of lithium-ion batteries using fractional order sl...
State of charge estimation of lithium-ion batteries using fractional order sl...State of charge estimation of lithium-ion batteries using fractional order sl...
State of charge estimation of lithium-ion batteries using fractional order sl...
 
Fractional order PID for tracking control of a parallel robotic manipulator t...
Fractional order PID for tracking control of a parallel robotic manipulator t...Fractional order PID for tracking control of a parallel robotic manipulator t...
Fractional order PID for tracking control of a parallel robotic manipulator t...
 
Fuzzy logic for plant-wide control of biological wastewater treatment process...
Fuzzy logic for plant-wide control of biological wastewater treatment process...Fuzzy logic for plant-wide control of biological wastewater treatment process...
Fuzzy logic for plant-wide control of biological wastewater treatment process...
 
Design and implementation of a control structure for quality products in a cr...
Design and implementation of a control structure for quality products in a cr...Design and implementation of a control structure for quality products in a cr...
Design and implementation of a control structure for quality products in a cr...
 
Model based PI power system stabilizer design for damping low frequency oscil...
Model based PI power system stabilizer design for damping low frequency oscil...Model based PI power system stabilizer design for damping low frequency oscil...
Model based PI power system stabilizer design for damping low frequency oscil...
 
A comparison of a novel robust decentralized control strategy and MPC for ind...
A comparison of a novel robust decentralized control strategy and MPC for ind...A comparison of a novel robust decentralized control strategy and MPC for ind...
A comparison of a novel robust decentralized control strategy and MPC for ind...
 
Fault detection of feed water treatment process using PCA-WD with parameter o...
Fault detection of feed water treatment process using PCA-WD with parameter o...Fault detection of feed water treatment process using PCA-WD with parameter o...
Fault detection of feed water treatment process using PCA-WD with parameter o...
 
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...Model-based adaptive sliding mode control of the subcritical boiler-turbine s...
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...
 
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...
 
An artificial intelligence based improved classification of two-phase flow patte...
An artificial intelligence based improved classification of two-phase flow patte...An artificial intelligence based improved classification of two-phase flow patte...
An artificial intelligence based improved classification of two-phase flow patte...
 
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...
 
Load estimator-based hybrid controller design for two-interleaved boost conve...
Load estimator-based hybrid controller design for two-interleaved boost conve...Load estimator-based hybrid controller design for two-interleaved boost conve...
Load estimator-based hybrid controller design for two-interleaved boost conve...
 
Effects of Wireless Packet Loss in Industrial Process Control Systems
Effects of Wireless Packet Loss in Industrial Process Control SystemsEffects of Wireless Packet Loss in Industrial Process Control Systems
Effects of Wireless Packet Loss in Industrial Process Control Systems
 
Fault Detection in the Distillation Column Process
Fault Detection in the Distillation Column ProcessFault Detection in the Distillation Column Process
Fault Detection in the Distillation Column Process
 
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank System
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemNeural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank System
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank System
 
A KPI-based process monitoring and fault detection framework for large-scale ...
A KPI-based process monitoring and fault detection framework for large-scale ...A KPI-based process monitoring and fault detection framework for large-scale ...
A KPI-based process monitoring and fault detection framework for large-scale ...
 
An adaptive PID like controller using mix locally recurrent neural network fo...
An adaptive PID like controller using mix locally recurrent neural network fo...An adaptive PID like controller using mix locally recurrent neural network fo...
An adaptive PID like controller using mix locally recurrent neural network fo...
 
A method to remove chattering alarms using median filters
A method to remove chattering alarms using median filtersA method to remove chattering alarms using median filters
A method to remove chattering alarms using median filters
 

Kürzlich hochgeladen

Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessQ2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessAPCO
 
Slicing Work on Business Agility Meetup Berlin
Slicing Work on Business Agility Meetup BerlinSlicing Work on Business Agility Meetup Berlin
Slicing Work on Business Agility Meetup BerlinAnton Skornyakov
 
Data skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story pointsData skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story pointsyasinnathani
 
Anyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyAnyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyHanna Klim
 
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdfTalent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdfCharles Cotter, PhD
 
Intellectual Property Licensing Examples
Intellectual Property Licensing ExamplesIntellectual Property Licensing Examples
Intellectual Property Licensing Examplesamberjiles31
 
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...Brian Solis
 
Entrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsEntrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsP&CO
 
Mihir Menda - Member of Supervisory Board at RMZ
Mihir Menda - Member of Supervisory Board at RMZMihir Menda - Member of Supervisory Board at RMZ
Mihir Menda - Member of Supervisory Board at RMZKanakChauhan5
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursKaiNexus
 
7movierulz.uk
7movierulz.uk7movierulz.uk
7movierulz.ukaroemirsr
 
Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024Borderless Access
 
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISINGUNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISINGlokeshwarmaha
 
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfGraham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfAnhNguyen97152
 
Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024Winbusinessin
 
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdfChicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdfSourav Sikder
 
AMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdf
AMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdfAMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdf
AMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdfJohnCarloValencia4
 
Upgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking ApplicationsUpgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking ApplicationsIntellect Design Arena Ltd
 
Plano de marketing- inglês em formato ppt
Plano de marketing- inglês  em formato pptPlano de marketing- inglês  em formato ppt
Plano de marketing- inglês em formato pptElizangelaSoaresdaCo
 

Kürzlich hochgeladen (20)

Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessQ2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
 
Slicing Work on Business Agility Meetup Berlin
Slicing Work on Business Agility Meetup BerlinSlicing Work on Business Agility Meetup Berlin
Slicing Work on Business Agility Meetup Berlin
 
Data skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story pointsData skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story points
 
Anyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agencyAnyhr.io | Presentation HR&Recruiting agency
Anyhr.io | Presentation HR&Recruiting agency
 
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdfTalent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
Talent Management research intelligence_13 paradigm shifts_20 March 2024.pdf
 
Intellectual Property Licensing Examples
Intellectual Property Licensing ExamplesIntellectual Property Licensing Examples
Intellectual Property Licensing Examples
 
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
 
Entrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsEntrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizations
 
Mihir Menda - Member of Supervisory Board at RMZ
Mihir Menda - Member of Supervisory Board at RMZMihir Menda - Member of Supervisory Board at RMZ
Mihir Menda - Member of Supervisory Board at RMZ
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, Ours
 
7movierulz.uk
7movierulz.uk7movierulz.uk
7movierulz.uk
 
WAM Corporate Presentation Mar 25 2024.pdf
WAM Corporate Presentation Mar 25 2024.pdfWAM Corporate Presentation Mar 25 2024.pdf
WAM Corporate Presentation Mar 25 2024.pdf
 
Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024Borderless Access - Global Panel book-unlock 2024
Borderless Access - Global Panel book-unlock 2024
 
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISINGUNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
UNLEASHING THE POWER OF PROGRAMMATIC ADVERTISING
 
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfGraham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
 
Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024Ethical stalking by Mark Williams. UpliftLive 2024
Ethical stalking by Mark Williams. UpliftLive 2024
 
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdfChicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
Chicago Medical Malpractice Lawyer Chicago Medical Malpractice Lawyer.pdf
 
AMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdf
AMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdfAMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdf
AMAZON SELLER VIRTUAL ASSISTANT PRODUCT RESEARCH .pdf
 
Upgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking ApplicationsUpgrade Your Banking Experience with Advanced Core Banking Applications
Upgrade Your Banking Experience with Advanced Core Banking Applications
 
Plano de marketing- inglês em formato ppt
Plano de marketing- inglês  em formato pptPlano de marketing- inglês  em formato ppt
Plano de marketing- inglês em formato ppt
 

Auto tuning of cascade control systems

  • 1. ISA TRANSACTIONS® ISA Transactions 42 ͑2003͒ 63–72 Auto-tuning of cascade control systems Sihai Song, Wenjian Cai, Ya-Gang Wang School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 ͑Received 8 August 2001; accepted 16 April 2002͒ Abstract In this paper, a novel auto-tuning method for a cascade control system is proposed. By employing a simple relay feedback test, both inner and outer loop model parameters can be simultaneously identified. Consequently, well- established proportional-integral-derivative ͑PID͒ tuning rules can be applied to tune both loops. Compared with existing methods, the new method is simpler and yet more effective. It can be directly integrated into commercially available industrial auto-tuning systems. Some examples are given to illustrate the effectiveness and robustness of the proposed method. © 2003 ISA—The Instrumentation, Systems, and Automation Society. Keywords: Cascade control; Relay feedback; PID auto-tuning; Model matching 1. Introduction controller is tuned. Subsequently, the inner loop controller is commissioned and the outer loop con- Proportional-integral-derivative ͑PID͒ control- troller is tuned to complete the tuning process. If lers are widely used in the process control industry the control performance achieved is unsatisfactory, due to their relatively simple structure, which can the entire sequence must be repeated. Thus it is a be easily understood and implemented. In practice, fairly cumbersome and time consuming task to it has often been integrated into complex control tune a cascade control system, especially for sys- structures in order to achieve a better control per- tems with large time constant and time delay. formance. Among those complex control struc- PID auto-tuning relieves the pain of manually tures, the cascade control scheme is commonly tuning a controller and has been successfully ap- used for the purpose of reducing both maximum plied in many industry fields ͓1,2͔. However, very deviation and integral error of disturbance re- little has been reported so far in the literature on sponses. The advantages of easy implementation the development of auto-tuning techniques for cas- and potentially large control performance im- cade control systems. Among few of them, Li et provement have led to widespread applications of al. ͓3͔ made use of fuzzy logic for self-tuning of cascade control for several decades. It has become cascade controllers. Hang et al. ͓4͔ applied a re- a standard application provided by industrial pro- newed relay automatic tuning method to tune a cess controllers. cascade control system where the relay feedback Cascade control systems are constructed by two test is carried out twice, first to the inner loop and control loops: an inner loop with fast dynamic to then to the outer loop. While the individual con- eliminate input disturbances, and an outer loop to troller tuning has been automated, the sequential regulate output performance. Conventionally, they nature of the tuning process remains unchanged. are tuned in a sequential manner. First, the outer Tan ͓5͔ proposed a method to carry out the entire loop controller is put on manual and the inner loop tuning process in one experiment, but the experi- 0019-0578/2003/$ - see front matter © 2003 ISA—The Instrumentation, Systems, and Automation Society.
  • 2. 64 Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 Fig. 1. Configuration of the cascade control system. ment requires prior information of the process. the phase lag of the closed inner loop will be much Furthermore, the ultimate frequency used for outer less than that of the outer loop. This feature leads loop design is based on initial ultimate frequency to the rationale behind the use of cascade control. without considering changes in inner loop control The crossover frequency for the inner loop is parameters. higher than that for the outer loop, which allows This paper presents a novel auto-tuning method higher gains in the inner loop controller in order to for the cascade control system. By utilizing the regulate more effectively the effect of a distur- fundamental characteristic of cascade control sys- bance occurring in the inner loop without endan- tems, a simple relay feedback test is applied to the gering the stability of the system. outer loop to identify simultaneously both inner and outer loop process model parameters. A model matching the PID controller tuning method based ´ on Pade coefficients and the Markov parameter is 3. Relay feedback test for cascade control proposed to control the overall system perfor- systems mance. Two examples are given to illustrate the effectiveness of the proposed method. The Astrom-Hagglund relay feedback test is based on the observation: when the process output 2. Fundamentals of cascade control systems lags behind the input by Ϫ␲ radians, the closed- loop system may generate sustained oscillation The configuration of the cascade control scheme around the ultimate frequency ͑the frequency is shown in Fig. 1, where an inner loop is embed- where the phase lag is Ϫ␲͒. The proposed relay ded within an outer loop and the outer loop output feedback test for the auto-tuning cascade control variable is to be controlled. The control system system is shown as in Fig. 2. When the relay feed- consists of two processes and two controllers with back test begins, switch A points to position 2, outer loop transfer function G p1 , inner loop trans- switch B points to position 4, and switch C points fer function G p2 , outer loop controller G c1 , and to position 5. After the test, switch A points to inner loop controller G c2 , respectively. position 1, switch B points to position 3, and The two controllers of cascade control systems switch C points to position 6. As the inner loop are standard feedback controllers ͑i.e., P, PI, or process acts much faster than the outer loop pro- PID͒. Usually, a proportional controller is used for cess, output u of the inner loop process in Fig. 2 the inner loop, integral action is needed when the under the relay feedback test acts as a step re- inner loop process contains essential time delays, sponse in half of the period of the stationary os- and the outer process is such that the loop gain in cillation, as shown in Fig. 3. Therefore a single the inner loop must be limited ͓1͔. relay feedback test can be used to obtain simulta- To serve the purpose of reducing or eliminating neously both the inner loop and outer loop process the inner loop disturbance d 2 before its effect can models parameters. spill over to the outer loop, it is essential that the In practice, the real process model is usually inner loop exhibit a faster dynamic response than represented by low order plus dead-time model. that of the outer loop ͑as industry rule of thumb, it Here, the transfer function with the following form should be at least five times ͓1͔͒. Consequently, ͑first-order plus dead time͒ is adopted:
  • 3. Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 65 Fig. 2. Configuration of the proposed identification model. ki tϭ0 in the process input; the process input and G pi ͑ s ͒ ϭ e ϪL i s , ͑1͒ output are collected until process enters a new T i sϩ1 steady state again. The process response after dead where iϭ1 stands for the outer process model and time tϭL 2 is described by iϭ2 stands for the inner process model, respec- tively. This model is characterized by three param- u ͑ t ͒ ϭk 2 ͑ 1Ϫe ͑ tϪL 2 ͒ /T 2 ͒ ϩw ͑ t ͒ , tуL 2 , ͑2͒ eters: the static gain k, the time constant T, and the where w ( t ) is the white noise in measurement of dead time L. It describes a linear monotonic pro- u ( t ) . It follows from the above relation that cess quite well in many industrial applications and is often sufficient for PID controller tuning. ͫ ͬT2 ͓ u ͑ t ͒ k 2 ͔ L ϭk 2 tϪA ͑ t ͒ ϩ ␦ ͑ t ͒ , tуL 2 , 2 3.1. Inner loop process model identification ͑3͒ As the inner loop output u can be considered as where A ( t ) is the area under the process response a step response in half period of the relay feedback and ␦͑t͒ is the integration of measurement noise; test, some well-developed step testing methods they are given as following, respectively: ͓2,6,7͔ can be readily applied to identify param- eters of the inner loop. In this paper, the method proposed by Ref. ͓2͔ is adopted due to its robust- A͑ t ͒ϭ ͵ u͑ t ͒dt, 0 t ness; it is briefly described as follows: Suppose that the inner process model is repre- sented by Eq. ͑1͒, and a unit step change occurs at ␦͑ t ͒ϭ ͵ w͑ t ͒dt. t 0 ͑4͒ Fig. 3. Inner loop and outer loop response under the proposed relay feedback test.
  • 4. 66 Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 The inner process model’s static gain k 2 is com- where T u is the period of the stationary oscillation, puted from the process steady states of input and and output, 2␲ ␻ uϭ . ͑10͒ ⌬u Tu k 2ϭ , ͑5͒ ⌬u d As the overall open loop transfer model function is where ⌬u denotes the change of process output G p ͑ s ͒ ϭG p1 ͑ s ͒ G p2 ͑ s ͒ and ⌬u d stands for the deviation in the manipu- lated input. Eq. ͑2͒ falls into a system of linear k 1k 2 ϭ e Ϫ ͑ L 1 ϩL 2 ͒ s , equations, ͑ T 1 sϩ1 ͒͑ T 2 sϩ1 ͒ ⌿Xϭ⌫ϩ⌬ for tуL 2 , ͑6͒ the outer loop process model transfer function where k1 G p1 ͑ s ͒ ϭ e ϪL 1 s ͫ ͬ T 1 sϩ1 T2 Xϭ L , can be obtained by the following steps. ͫ ͬ 2 ͑1͒ Read off the overall system time delay L u ͓ mT s ͔ k2 ϭL 1 ϩL 2 of G p in the transfer function from the u ͓͑ mϩ1 ͒ T s ͔ k2 initial part of the relay feedback test, since the ⌿ϭ , inner loop transfer function delay L 2 is already ] ] available, the time delay L 1 can be computed as u ͓͑ nϩ1 ͒ T s ͔ k2 ͫ ͬ L 1 ϭLϪL 2 . ͑11͒ k 2 t ͓ mT s ͔ ϪA ͓ mT s ͔ ͑2͒ Obtain the frequency response of G p1 ( j ␻ ) k 2 t ͓͑ mϩ1 ͒ T s ͔ ϪA ͓͑ mϩ1 ͒ T s ͔ at ␻ ϭ ␻ u from ⌫ϭ ] , G p͑ j ␻ u ͒ k 2 t ͓͑ nϩ1 ͒ T s ͔ ϪA ͓͑ nϩ1 ͒ T s ͔ G p1 ͑ j ␻ u ͒ ϭ , ͑12͒ ͫ ͬ G p2 ͑ j ␻ u ͒ ␦ ͓ mT s ͔ and calculate ␦ ͓͑ mϩ1 ͒ T s ͔ G p1 ͑ j ␻ u ͒ ⌬ϭ ] . ͑7͒ k1 GЈ ͑ j ␻u͒ϭ ϭ Ϫ jL 1 ␻ u ϭ ␣ ϩ j ␤ , p1 jT 1 ␻ u ϩ1 e ␦ ͓͑ nϩ1 ͒ T s ͔ ͑13͒ T s is the sampling interval, and mT s уL 2 . The which is the frequency response for G p1 ( j ␻ ) best estimation X * of X can be obtained using the without delay, where ␣ has positive sign and ␤ has standard least-square method as negative sign. X * ϭ ͑ ⌿ T ⌿ ͒ Ϫ1 ⌿ T ⌫. ͑8͒ ͑3͒ Calculate T 1 and k 1 , respectively, by ␤ The best estimation of T 2 and L 2 can then be ob- T 1 ϭϪ , ͑14͒ tained from X * . ␣ϫ␻u ␣ 2ϩ ␤ 2 3.2. Outer loop process model identification k 1ϭ . ͑15͒ ␣ By relay feedback test, the frequency response 4. Controller design of overall process model G p ( s ) at the ultimate fre- quency ␻ u is estimated as As the main purpose of inner loop control is to ͵ y ͑ t ͒e0 Tu Ϫ j ␻ut dt eliminate the input disturbance, a P or PI control- ler using widely accepted model based tuning G ͑ j ␻ ͒ϭ ͑9͒ rules such as Ziegler-Nichols ͓8͔, Chien-Hrones- ͵ u ͑ t ͒e p u Tu , Ϫ j ␻ut dt Reswick ͑CHR͒ ͓9͔, or Cohen-Coon ͓10͔ tuning d 0 rules will suffice. This feature makes it very easy
  • 5. Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 67 to integrate the tuning method into the existing where ␰ stands for the desired damping ratio, usu- auto-tuning systems. Without loss of generality, ally selected as 0.707, the natural frequency ␻ n the PI control structure of the form can be chosen between 0.5 and 1.0 times the ulti- mate frequency ␻ u from the relay feedback test K i2 ͓13͔. An alternative of desired closed-loop transfer G c2 ͑ s ͒ ϭK p2 ϩ s function for large dead-time systems can be ex- pressed as ͓14͔ and the Chien-Hrones-Reswick ͑CHR͒ ͓9͔ tuning rule ͑20% overshoot͒ will be used for comparison ␻2 n study. The controller parameters are given, respec- H͑ s ͒ϭ e Ϫ ͑ L 1 ϩL 2 ͒ s . s 2 ϩ2 ␰␻ n sϩ ␻ 2 n tively, by 0.7T 2 If the control specifications are not available, de- K p2 ϭ , ͑16͒ fault settings for the parameter ␨ ϭ0.707 and k 2L 2 ␻ u ( L 1 ϩL 2 ) ϭ2 can be used, which implies that the overshoot of the objective step response is 0.304T 2 K i2 ϭ . ͑17͒ about 5%, the phase margin is 60°, and the gain k 2L 2 2 margin is 2.2. For simplicity, Eq. ͑20͒ can be re- written as the parametric form: With the PI controller, the closed-loop transfer function G 2 ( s ) of inner loop and the open loop d0 transfer function G 1 ( s ) are then obtained as H͑ s ͒ϭ , ͑21͒ e 0 ϩe 1 sϩe 2 s 2 G p2 ͑ s ͒ G c2 ͑ s ͒ where d 0 ϭ ␻ 2 , e 0 ϭ ␻ 2 , e 1 ϭ2 ␰␻ n , and e 2 ϭ1. G 2͑ s ͒ ϭ n n 1ϩG p2 ͑ s ͒ G c2 ͑ s ͒ ͑2͒ Approximating the time delays in G 1 ( s ) of Eq. ͑19͒, since the dead time L 2 of the inner loop k 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s ϭ , process model is very small, it is always approxi- s ͑ 1ϩT 2 s ͒ ϩk 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s mated as 1 or ͑18͒ e ϪL 2 s Ϸ1ϩ ͑ ϪL 2 s ͒ , ͑22͒ G 1 ͑ s ͒ ϭG 2 ͑ s ͒ G p1 ͑ s ͒ e Ϫ ( L 1 ϩL 2 ) s is approximated as k 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s ͑ L 1 ϩL 2 ͒ 2 s 2 ϭ e Ϫ ͑ L 1 ϩL 2 ͒ s Ϸ1Ϫ ͑ L 1 ϩL 2 ͒ sϩ s ͑ 1ϩT 2 s ͒ ϩk 2 ͑ K p2 sϩK i2 ͒ e ϪL 2 s 2 ͑23͒ k1 • e ϪL 1 s . ͑19͒ in order to gain a more accurate approximation. T 1 sϩ1 Substitute Eqs. ͑22͒ and ͑23͒ to Eq. ͑19͒, and re- As G 1 ( s ) is not a standard transfer function, it is write G 1 ( s ) as difficult to directly apply existing tuning rules. Therefore a model-matching algorithm ͓11,12͔ is g 0 ϩg 1 sϩg 2 s 2 ϩg 3 s 3 G 1͑ s ͒ ϭ , ͑24͒ proposed to obtain the PID control parameters for h 0 ϩh 1 sϩh 2 s 2 ϩh 3 s 3 overall system performance. The brief theoretical background of a controller design based on model where matching is attached in the Appendix; for more g 0 ϭk 1 k 2 K i2 , details please refer to Refs. ͓11,12͔. Its application to this particular problem is given as follows. g 1 ϭk 1 k 2 ͓ K p2 ϪK i2 ͑ L 1 ϩL 2 ͔͒ , ͑1͒ Assuming that the process dead time is small, the desired reference model H ( s ) is chosen as g 2 ϭk 1 k 2 ͫ K i2 ͑ L 1 ϩL 2 ͒ 2 2 ϪK p2 ͑ L 1 ϩL 2 ͒ , ͬ ␻2 n k 1 k 2 K p2 ͑ L 1 ϩL 2 ͒ 2 H͑ s ͒ϭ , ͑20͒ g 3ϭ , s 2 ϩ2 ␰␻ n sϩ ␻ 2 n 2
  • 6. 68 Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 and ͑4͒ The PID parameters can be computed as h 0 ϭk 2 K i2 , a 1 b 1 Ϫa 0 b 2 K p1 ϭ , ͑27͒ b2 h 1 ϭk 2 T 1 K i2 ϩ1ϩk 2 K p2 Ϫk 2 K i2 L 2 , 1 h 2 ϭT 1 ͑ 1ϩk 2 K p2 Ϫk 2 K i2 L 2 ͒ ϩT 2 Ϫk 2 K p2 L 2 , a0 K i1 ϭ , ͑28͒ b1 h 3 ϭT 1 ͑ T 2 Ϫk 2 K p2 L 2 ͒ . a 2 b 2 Ϫa 1 b 1 b 2 ϩa 0 b 2 1 2 As indicated in Refs. ͓11,12͔, the Pade coefficients ´ K d1 ϭ , ͑29͒ and the Markov parameters characterize, respec- b3 1 tively, the low- and high-frequency responses of a b2 system, or the responses of the steady state and T n1 ϭ . ͑30͒ transition state. Pϭ5 and M ϭ0 are selected in b1 order to get a good system response approxima- tion in a steady state ͓11͔. Pade coefficients of ´ 5. Comparison study H ( s ) are estimated as Two examples are presented here to illustrate c 0 ϭ1, the effectiveness of the proposed tuning method for cascade control systems. In order to show the c 1 ϭ ͑ d 1 Ϫe 1 c 0 ͒ /e 0 , accuracy of the proposed identification method in c 2 ϭ ͑ d 2 Ϫe 1 c 1 Ϫe 2 c 0 ͒ /e 0 , a noisy environment, the noise-to-signal ratio ͑NSR͒, defined as ͓15͔ NSRϭmean͓abs͑noise͔͒/ c 3 ϭ ͑ d 3 Ϫe 1 c 2 Ϫe 2 c 1 Ϫe 3 c 0 ͒ /e 0 , mean͓abs͑signal͔͒ is introduced. In this paper, the proposed identification method is applied to both c 4 ϭ ͑ d 4 Ϫe 1 c 3 Ϫe 2 c 2 Ϫe 3 c 1 Ϫe 4 c 0 ͒ /e 0 . processes with noise level 10% NSR. Example 1. Consider a cascade control system ͑3͒ The PID controller with pϭmϭ2 ͓11͔ is discussed by Hang ͓4͔ and Tan ͓5͔ with plant mod- given as els of K i1 K d1 s e Ϫs e Ϫ␣s G c1 ͑ s ͒ ϭK p1 ϩ ϩ G p1 ͑ s ͒ ϭ , G p2 ͑ s ͒ ϭ , s 1ϩT n1 s ͑ 1ϩs ͒ 2 1ϩ ␣ s a 0 ϩa 1 sϩa 2 s 2 where ␣ϭ0.1. After the relay feedback test, the ϭ , ͑25͒ b 0 ϩb 1 sϩb 2 s 2 parameters for the inner loop process model is ob- tained as where b 0 ϭ0 and a 0 , a 1 , a 2 , b 1 , b 2 can be com- puted by solving the following linear matrix equa- e Ϫ0.115s ͫ tions: G p2 ͑ s ͒ ϭ0.9563 1ϩ0.0947s ΅ g 0c 1 0 0 h0 0 and the outer loop process model is estimated as g 0 c 2 ϩg 2 c 0 g 0c 1 0 h 0 c 1 ϩh 1 h 0c 0 g 0 c 3 ϩg 1 c 2 g 0c 2 g 0c 1 h 0 c 2 ϩh 1 c 1 h 0 c 1 e Ϫ1.63s ϩg 2 c 1 ϩg 1 c 1 ϩh 2 ϩh 1 G p1 ͑ s ͒ ϭ0.965 . 1ϩ1.908s g 0 c 4 ϩg 1 c 3 g 0 c 3 ϩg 1 c 2 g 0 c 2 h 0 c 3 ϩh 1 c 2 h 0 c 2 ϩg 2 c 2 ϩg 3 c 1 ϩg 2 c 1 ϩg 1 c 1 ϩh 2 c 1 ϩh 3 ϩh 1 c 1 ϩh 2 The parameters calculated for the inner loop PI ͫ ͬͫͬ 0 0 g3 0 h3 controller G c2 using the Chien-Hrones-Reswick ͑CHR͒ tuning rule ͑20% overshoot͒ are obtained a0 0 as K p2 ϭ0.603, K i2 ϭ2.277. The overall system a1 0 reference model of the cascade control system is ϫ a2 ϭ 0 . ͑26͒ chosen to be in the form of Eq. ͑20͒ with ␨ϭ0.8 b1 0 and ␻ u ϭ0.6. The outer loop controller’s param- b2 1 eters are obtained as K p1 ϭ0.6592, K i1 ϭ0.3536,
  • 7. Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 69 Fig. 4. Tuning procedure and step response. K d1 ϭ0.2886, and T n1 ϭ1.4392. The proposed the inner loop are obtained as K p2 ϭ2.895, K i2 auto-tuning procedure and step response in the ϭ0.147. The overall system reference model of noisy environment are shown in Fig. 4. The result the cascade control system is chosen to be in the is also compared to the methods proposed by form of Eq. ͑20͒ with ␨ϭ0.707 and ␻ u ϭ0.03, the Hang and Tan. Fig. 5 shows the closed-loop per- outer loop controller’s parameters are obtained as formance from tϭ0 s to tϭ80 s; a large step load K p1 ϭϪ4.9225, K i1 ϭϪ0.1105, K d1 ϭϪ51.1205, disturbance seeps into the process for all cases at and T n1 ϭ6.4596. The control performance com- tϭ50 s. parison study is carried out from tϭ0 s to Example 2. Consider a process model of the tϭ2000 s, a large step load disturbance is added packed-bed reactor provided by Ref. ͓16͔. The into the process at time tϭ1000 s, as shown in goal is to tightly control the exit concentration Fig. 6. temperature, and the most significant disturbance From the examples, the improved performance is the heating medium temperature. The inner and of the proposed tuning method is clearly evident. outer loop process models are given by e Ϫ20s 6. Conclusion G p1 ͑ s ͒ ϭϪ0.19 , 1ϩ50s This paper developed a novel auto-tuning e Ϫ8s method for the cascade control system. As the in- G p2 ͑ s ͒ ϭ0.57 , 1ϩ20s ner loop process acts much faster than the outer loop in the cascade control system, both inner loop respectively. To reduce the disturbance, a cascade and outer loop process model parameters can be control strategy is adopted. Using the relay feed- identified using one relay feedback test by utiliz- back test, the parameters for the inner and outer ing this physical property under the proposed process models from the experiment are estimated structure. Consequently, well-established model as based PI tuning rules can be applied to tune the e Ϫ22.6s inner loop, and a model matching the PID control- G p1 ͑ s ͒ ϭϪ0.192 , ler design method was proposed to tune the outer 1ϩ47.5s loop. Finally, two examples were given to show e Ϫ8.5s the effectiveness of the proposed method. The G p2 ͑ s ͒ ϭ0.558 . method is very straightforward and has been inte- 1ϩ19.7s grated into an existing auto-tuning system. It is The PI controller using the Chien-Hrones- now being tested in a centralized HVAC system Reswick ͑CHR͒ tuning rule ͑20% overshoot͒ for and the field results will be reported soon.
  • 8. 70 Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 Fig. 5. Performance comparison. Appendix and a controller’s transfer function model Suppose we have a process model a 0 ϩa 1 sϩ¯ϩa p s p C͑ s ͒ϭ . ͑A2͒ b 0 ϩb 1 sϩ¯ϩb m s m g 0 ϩg 1 sϩ¯ϩg q s q G͑ s ͒ϭ , ͑A1͒ h 0 ϩh 1 sϩ¯ϩh n s n It is desired that C ( s ) be obtained in such a way Fig. 6. Performances of the proposed method ͑solid line͒ and of Ref. ͓16͔ ͑dashed line͒.
  • 9. Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 71 ´ that the overall system matches a set of Pade co- i efficients and Markov parameters of a given a ref- x i ϭ ͚ a j g iϪ j , iϭ0,1, . . . ,qϩp, ͑A9͒ jϭ0 erence model i d 0 ϩd 1 sϩ¯ϩd r s r H͑ s ͒ϭ , ͑A3͒ y i ϭ ͚ b j h iϪ j , iϭ0,1, . . . ,nϩm. ͑A10͒ e 0 ϩe 1 sϩ¯ϩe r s r jϭ0 and a simple controller C ( s ) can be found such Using the constraint PϩM ϭpϩmϩ1, where P P that ´ is the number of Pade coefficients, M is the num- ber of Markov parameters, p is the numerator’s C͑ j ␻ ͒G͑ j ␻ ͒ order of C ( s ) , and m is the denominator’s order of ХH ͑ j ␻ ͒ . ͑A4͒ 1ϩC ͑ j ␻ ͒ G ͑ j ␻ ͒ C ( s ) . The parameters a, b i of C ( s ) can be ob- tained uniquely by solving the set of linear Eqs. The model matching of time moments and Mar- ͑A5͒–͑A10͒. kov parameters is very effective in model reduc- tion for obtaining approximate models, because ´ the Pade coefficients and the Markov parameters References characterize, respectively, the low- and high- ͓1͔ Astrom, K. J. and Hagglund, T., PID Controller: ´ frequency responses of a system. The Pade coeffi- Theory, Design and Tuning. Instrument Society of cients of H ( s ) are defined as America, Research Triangle Park, NC, 1995. ͓2͔ Bi, Q., Cai, Wenjian, Lee, E. L., Wang, Qingguo, c 0 ϭd 0 /e 0 , Hang, C. C., and Zhang, Y., Robust identification of first order plus dead-time model from step response. ͫ ͬͲ k Control Eng. Pract. 1, 71–77 ͑1999͒. ͓3͔ Li, M. X., Bruijn, P. M., and Verbruggen, H. B., Tun- c k ϭ d k Ϫ ͚ e j c kϪ j e0 , ͑A5͒ ing of cascade PID controller with fuzzy inference. jϭ1 Asia-Pac. Eng. Part A, Electr. Eng. 2, 65–70 ͑1994͒. ´ ͓4͔ Hang, C. C., Loh, A. P., and Vasnani, V. U., Relay where c k is the kth Pade coefficient. feedback auto-tuning of cascade controllers. IEEE The Markov parameters of H ( s ) are defined as Trans. Control Syst. Technol. 2, 42– 45 ͑1994͒. ͓5͔ Tan, K. K., Lee, T. H., and Ferdous, R., Simultaneous m 0 ϭd r /e r , online automatic tuning of cascade control for open ͫ ͬͲ loop stable process. ISA Trans. 39, 233–243 ͑2000͒. k ͓6͔ Shinskey, F. G., Process Control System: Application, m k ϭ d rϪk Ϫ ͚ e rϪ j m kϪ j er , ͑A6͒ Design, and Tuning. 3rd ed., McGraw-Hill, New York, jϭ1 1998. ͓7͔ Marlin, T. E., Process Control: Designing Process and where m k is the kth Markov parameter. Control System for Dynamic Performance. McGraw- A set of liner equations as shown in the follow- Hill, New York, 1995. ´ ing can be gained in order to match the Pade co- ͓8͔ Ziegler, J. G. and Nichols, N. B., Optimum settings for automatic controllers. Trans. ASME 64, 759–768 efficients and Markov parameters: ͑1942͒. ͓9͔ Chien, K. L., Hrones, J. A., and Reswick, J. B., On the ␣ 0 c 0 ϭx 0 , automatic control of generalized passive systems. k Trans. ASME 74, 175–185 ͑1952͒. ͓10͔ Cohen, G. H. and Coon, G. A., Theoretical consider- ␣ 0 c k ϭx k Ϫ ͚ ␣ j c kϪ j , kϭ1,2, . . . , PϪ1, ation of retarded control. Trans. ASME 75, 827– 834 jϭ1 ͑1953͒. ͓11͔ Aguirre, L. A., New algorithm for closed-loop model 1ϭ ␣ nϩm , ͑A7͒ matching. IEEE Electron Device Lett. 27, 2260–2262 ͑1991͒. k ͓12͔ Aguirre, L. A., PID tuning on model matching. IEEE m k ϭx nϩmϪk Ϫ ͚ ␣ nϩmϪ j m kϪ j , Electron Device Lett. 28, 2269–2271 ͑1992͒. jϭ1 ͓13͔ Wang, Q. G., Hang, C. C., and Biao, Zou, A frequency response approach to autotuning of multivariable con- kϭ1,2, . . . ,M Ϫ1, trollers. Trans. Inst. Chem. Eng., Part A 75, 64 –72 ͑1997͒. where ͓14͔ Kiong Tan, K. K., Wang, Qing-Guo, and Hang, Chang Chien, Advances in Industrial Control. Springer- ␣ i ϭx i ϩy i , iϭ0,1, . . . ,nϩm, ͑A8͒ Verlag, London, 1999.
  • 10. 72 Sihai Song, Wenjian Cai, Ya-Gang Wang / ISA Transactions 42 (2003) 63–72 ͓15͔ Haykin, S., An Introduction to Analog & Digital Com- pany, U. S. A.; Research Scientist at National University of Singapore; munication. Wiley, New York, 1989. Principal Engineer and R&D Manager at Supersymmetry Services Pte ͓16͔ Marlin, Thomas E., Process Control: Designing Pro- Ltd, Singapore; Senior Research Fellow at Environmental Technology Institute, Singapore, respectively. He is currently serving as Associate cesses and Control Systems for Dynamic Perfor- Professor at Nayang Technological University, Singapore. Dr. Cai’s mance. 2nd ed., McGraw-Hill, New York, 2000. current research interests include multivariable control and HVAC sys- tem optimization. Sihai Song was born in 1974, Zhejiang, P. R. China. He Ya-Gang Wang was born in graduated from Zhejiang Uni- 1967, Shanxi, P. R. China. He versity with a bachelor degree received his B.Eng., M.Eng., in electrical engineering in and Ph.D. from Department of 1997, and a second bachelor Automation, China University degree of international com- of Mining and Technology, modities inspection in 1998. In Taiyuan University of Technol- 2001, he started his postgradu- ogy and Shanghai Jiao Tong ation studies at Nanyang Tech- University, P. R. China, in nological University, Sin- 1988, 1991, and 2000, respec- gapore. He is interested in PID tively. After graduation, he auto-tuning and computer- worked as a lecturer in Taiyuan aided control system design. University of Technology, P. R. China, and a Postdoctoral Re- search Fellow in Nanyang Technological University, Singapore. He is interested in process control and instrumentation, PID auto-tuning, and Wenjian Cai received his multivariable control. B.Eng., M.Eng., and Ph.D. from Department of Precision Instrumentation Engineering, Department of Control Engi- neering, Harbin Institute of Technology, P. R. China, and Department of Electrical Engi- neering, Oakland University, U. S. A., in 1980, 1983, and 1992, respectively. After graduation, he worked as a Postdoctoral Research Fellow at the Center for Advanced Ro- botics, Oakland University, U. S. A.; Engineer at CEC Controls Com-