Industrial Control Systems - Special Structures

Industrial Control
Behzad Samadi
Department of Electrical Engineering
Amirkabir University of Technology
Winter 2009
Tehran, Iran
Behzad Samadi (Amirkabir University) Industrial Control 1 / 59

Special Control Structures
Outline:
Set-point Weighting
[Visioli, 2006]

Outline:
Set-point Weighting
Feedforward Action
[Visioli, 2006]

Outline:
Set-point Weighting
Feedforward Action
Ratio Control
[Visioli, 2006]

Outline:
Set-point Weighting
Feedforward Action
Ratio Control
Cascade Control
[Visioli, 2006]

Outline:
Set-point Weighting
Feedforward Action
Ratio Control
Cascade Control
Override Control
[Visioli, 2006]

Outline:
Set-point Weighting
Feedforward Action
Ratio Control
Cascade Control
Override Control
Selective Control
[Visioli, 2006]

Outline:
Set-point Weighting
Feedforward Action
Ratio Control
Cascade Control
Override Control
Selective Control
Split Range Control
[Visioli, 2006]

Set-point Weighting :
High load disturbance rejection → too oscillatory set-point step
response.
[Visioli, 2006]

response.
This is actually true especially when the apparent dead time of the
process is small (with respect to the dominant time constant).
[Visioli, 2006]

response.
This is actually true especially when the apparent dead time of the
process is small (with respect to the dominant time constant).
Set-point weighting for PID controllers:
u(t) = Kp(βr(t) − y(t) +
1
Ti
t
0
e(τ)dτ − Td
dy(t)
dt
)
u(t): control signal, r(t): reference input,
y(t): process output, e(t): tracking error
[Visioli, 2006]

Set-point Weighting:
u(t) = Kp(βr(t) − y(t) +
1
Ti
t
0
e(τ)dτ − Td
dy(t)
dt
)
Intuitively, given a set of parameters Kp, Ti and Td , the adoption of
a set-point weight β < 1 allows the reduction of the overshoot in the
set-point response, since the eﬀect of the proportional action is
reduced.
[Visioli, 2006]

u(t) = Kp(βr(t) − y(t) +
1
Ti
t
0
e(τ)dτ − Td
dy(t)
dt
)
Intuitively, given a set of parameters Kp, Ti and Td , the adoption of
a set-point weight β < 1 allows the reduction of the overshoot in the
set-point response, since the eﬀect of the proportional action is
reduced.
Note that this is achieved without aﬀecting the load disturbance
rejection performance.
[Visioli, 2006]

U = Kp(βR − Y +
1
Ti s
E − Td sY )

U = Kp(βR − Y +
1
Ti s
E − Td sY )
U = Kp(β +
1
Ti s
)R − Kp(1 +
1
Ti s
+ Td s)Y

U = Kp(βR − Y +
1
Ti s
E − Td sY )
U = Kp(β +
1
Ti s
)R − Kp(1 +
1
Ti s
+ Td s)Y
U = Kp(1 +
1
Ti s
+ Td s)
βs + 1
1 + Ti s + Ti Td s2
R − Kp(1 +
1
Ti s
+ Td s)Y

U = Kp(βR − Y +
1
Ti s
E − Td sY )
U = Kp(β +
1
Ti s
)R − Kp(1 +
1
Ti s
+ Td s)Y
U = Kp(1 +
1
Ti s
+ Td s)
βs + 1
1 + Ti s + Ti Td s2
R − Kp(1 +
1
Ti s
+ Td s)Y
U = Kp(1 +
1
Ti s
+ Td s)(FR − Y )
F =
βs + 1
1 + Ti s + Ti Td s2

u(t) = Kp(βr(t) − y(t) +
1
Ti
t
0
e(τ)dτ − Td
dy(t)
dt
)
C(s) = Kp(1 +
1
Ti s
+ Td s)
F(s) =
1 + βTi s
1 + Ti s + Ti Td s2
[Visioli, 2006]

F(s) =
1 + βTi s
1 + Ti s + Ti Td s2
From another point of view, the overshoot is reduced by smoothing
the set-point signal by means of the ﬁlter F.
[Visioli, 2006]

F(s) =
1 + βTi s
1 + Ti s + Ti Td s2
From another point of view, the overshoot is reduced by smoothing
the set-point signal by means of the ﬁlter F.
Example:
P(s) =
1
10s + 1
e−4s
Ziegler-Nichols: Kp = 3, Ti = 8 and Td = 2
[Visioli, 2006]

Feedforward Action:
Set-point tracking:
[Visioli, 2006]

Feedforward Action:
Set-point tracking:
M(s) represents the desired performance.
[Visioli, 2006]

Feedforward Action:
Set-point tracking:
M(s) represents the desired performance.
G(s) = M(s)
˜P(s)
where tildeP(s) is the minimum phase part of P(s).
[Visioli, 2006]

Feedforward Action:
Set-point tracking:
Y (s)
R(s)
=
(MC + G)P
1 + PC
Therefore if ˜P(s) = P(s) and C(s) = 0 then

Feedforward Action:
Set-point tracking:
Y (s)
R(s)
=
(MC + G)P
1 + PC
Therefore if ˜P(s) = P(s) and C(s) = 0 then
Y (s)
R(s)
= G(s)P(s) = M(s)
[Visioli, 2006]

Feedforward Action:
Set-point tracking:
Example:
P(s) =
1
10s + 1
e−5s
M(s) =
1
2s + 1
e−5s
G(s) =
10s + 1
2s + 1
[Visioli, 2006]

Feedforward Action:
Disturbance rejection:
Y = PCE(s) + (H − PG)D(s)
[Visioli, 2006]

Feedforward Action (disturbance rejection):
H − PG = 0 ⇒ G = H
P
[Visioli, 2006]

H − PG = 0 ⇒ G = H
P
Example:
P(s) =
K
Ts + 1
e−Ls
H(s) =
KH
THs + 1
e−LH s
[Visioli, 2006]

H − PG = 0 ⇒ G = H
P
Example:
P(s) =
K
Ts + 1
e−Ls
H(s) =
KH
THs + 1
e−LH s
If LH = L:
G(s) =
H
P
=
KH
K
Ts + 1
THs + 1
[Visioli, 2006]

Example:
P(s) =
K
Ts + 1
e−Ls
H(s) =
KH
THs + 1
e−LH s
If LH = L:
G(s) =
H
P
≈
KH
K
(T − LH + L)s + 1
THs + 1
[Visioli, 2006]

Example:
P(s) =
K
(T1s + 1)(T2s + 1)
H(s) =
KH
THs + 1

Example:
P(s) =
K
(T1s + 1)(T2s + 1)
H(s) =
KH
THs + 1
G(s) =
H
P
≈
KH
K
(T1 + T2)s + 1
THs + 1
[Visioli, 2006]

Heat Exchanger Process:
heatexdemo - Mathworks.com

t1 = 21.8 (for 28.3% of the ﬁnal value)

τ = 3
2(t2 − t1)

τ = 3
2(t2 − t1)
θ = t2 − τ

Gp(s) =
1
23.3s + 1
e−14.7s

Gd (s) =
1
25s + 1
e−35s

PI controller setting using ITAE
Kc = 0.859(
θ
τ
)−0.997
, Ti = (
θ
τ
)0.680

Kc = 1.23 (blue) and Kc = 0.9 (red)
Ti = 24.56

F(s) = −
Gd
Gp
= −
21.3s + 1
25s + 1
e−20.3s

Ratio Control:
Keep a constant ratio between two (or more) process variables,
irrespective of possible set-point changes and load disturbances.
[Visioli, 2006]

Ratio Control:
Chemical dosing, water treatment, chlorination, mixing vessels and
waste incinerators
[Visioli, 2006]

Ratio Control:
Chemical dosing, water treatment, chlorination, mixing vessels and
waste incinerators
Air-to-fuel ratio for combustion systems
[Chau, 2002]
[Visioli, 2006]

Ratio Control:
Series metered control:
The output y2 is necessarily delayed with respect to y1, due to the
closed-loop dynamics of the second loop.
[Visioli, 2006]

Ratio Control:
Parallel metered control:
A disturbance acting on the ﬁrst process can cause a large error in the
ratio value.
[Visioli, 2006]

Ratio Control:
Cross limited control scheme:
The two loops are interlocked by using a low and a high selectors that
force the fuel to follow the air ﬂow when the set-point increases and
that force the air to follow the fuel when the set-point decreases.
[Visioli, 2006]

Ratio Control:
Blend Station:
r2(t) = a(γr1(t) + (1 − γ)y1(t))
Its use is suggested when no disturbances are likely to occur in the
processes and when the two processes exhibit a diﬀerent dynamics.
[Visioli, 2006]

Ratio Control:
Modiﬁed Blend Station:
P1(s) =
K1
T1s + 1
e−L1s
, P2(s) =
K2
T2s + 1
e−L2s

Ratio Control:
P1(s) =
K1
T1s + 1
e−L1s
, P2(s) =
K2
T2s + 1
e−L2s
u1(t) = Kp1 βr1(t) − y1(t) +
1
Ti1
t
0
(r1(τ) − y1(τ))dτ
u2(t) = Kp2 βr2(t) − y2(t) +
1
Ti2
t
0
(r2(τ) − y2(τ))dτ
[Visioli, 2006]

Ratio Control:
γ =
0 if L1 > L2 and t < t0 + L1 − L2
γ + Kp(er (t) + 1
Ti
t
0 er (τ)dτ) otherwise

Ratio Control:
γ =
0 if L1 > L2 and t < t0 + L1 − L2
γ + Kp(er (t) + 1
Ti
t
er (t) = ay1(t) − y2(t)

Ratio Control:
γ =
0 if L1 > L2 and t < t0 + L1 − L2
γ + Kp(er (t) + 1
Ti
t
er (t) = ay1(t) − y2(t)
Kp1 Ti1 β1 Kp2 Ti2 β2 γ Kp Tp
0.9T1
K1L1
3L1 0 0.9T2
K2L2
3L2 0 Ti2
Ti1
0.5 L2
T2
T1
L1
T1
L1
[Visioli, 2006]

Ratio Control:
Adaptive Blend Station (Hagglund, 2001):
dγ
dt
=
S
Ta
(ay1 − y2)

Ratio Control:
dγ
dt
=
S
Ta
(ay1 − y2)
Ta = 10 max{T1, T2}

Ratio Control:
dγ
dt
=
S
Ta
(ay1 − y2)
Ta = 10 max{T1, T2}
If r1 > max{y1, y2/a} + eps then S = 1
Else if r1 < min{y1, y2/a} − eps then S = −1
Else S = 0
[Visioli, 2006]

Cascade Control:

Cascade Control:
[Chau, 2002]

Cascade Control:
Primary (master) loop: outer loop
[Visioli, 2006]

Cascade Control:
Secondary (slave) loop: inner loop
[Visioli, 2006]

Cascade Control:
P1: slow dynamics
[Visioli, 2006]

Cascade Control:
P1: slow dynamics
P2: fast dynamics
[Visioli, 2006]

Cascade Control:
P1: slow dynamics
P2: fast dynamics
The approach can be generalized to more than two loops.
[Visioli, 2006]

Cascade Control:
It appears that the improvement in the cascade control performance
is more signiﬁcant when disturbances act in the inner loop and when
the secondary sensor is placed in order to separate as far as possible
the fast dynamics of the process from the slow dynamics
(Krishnaswami et al., 1990).
[Visioli, 2006]

Cascade Control:
Additional advantage: The nonlinearities of the process in the inner
loop are handled by that loop and therefore they are removed from
the more important outer loop.
[Visioli, 2006]

Cascade Control:
Additional advantage: The nonlinearities of the process in the inner
loop are handled by that loop and therefore they are removed from
the more important outer loop.
When the secondary process exhibits a signiﬁcant dead time or there
is an unstable (positive) zero, the use of cascade control is not useful
in general.
[Visioli, 2006]

Cascade Control:
Design procedure:
First: Design the controller for the secondary loop
[Visioli, 2006]

Cascade Control:
Design procedure:
First: Design the controller for the secondary loop
Second: Design the controller for the primary loop
[Visioli, 2006]

Cascade Control:
Example:
Gp =
0.8
2s + 1
, Gv =
0.5
s + 1
, GL =
0.75
s + 1
[Chau, 2002]

Cascade Control:
Example:
Let us consider a proportional controller Gc2(s) = Kc2 and make the
time constant of the secondary loop equal to 0.1 second.
[Chau, 2002]

Cascade Control:
Example:
1 + 0.5Kc2 = 10 ⇒ Kc2 = 18
[Chau, 2002]

Cascade Control:
Example:
1 + 0.5Kc2 = 10 ⇒ Kc2 = 18
Gv = 9
s+10
[Chau, 2002]

Cascade Control:
Example:
1 + 0.5Kc2 = 10 ⇒ Kc2 = 18
Gv = 9
s+10
Gv Gp = 0.9
0.1s+1
0.8
2s+1
[Chau, 2002]

Cascade Control:
Example:
1 + 0.5Kc2 = 10 ⇒ Kc2 = 18
Gv = 9
s+10
Gv Gp = 0.9
0.1s+1
0.8
2s+1
Gv Gp ≈ 0.72
2.05s+1 e−0.05s
[Chau, 2002]

Cascade Control:
Example:
1 + 0.5Kc2 = 10 ⇒ Kc2 = 18
Gv = 9
s+10
Gv Gp = 0.9
0.1s+1
0.8
2s+1
Gv Gp ≈ 0.72
2.05s+1 e−0.05s
SIMC tuning rule:
Kc =
1
k
τ1
τc + θ
=
1
0.72
2.05
0.15
= 18.98
τi = min{τ1, 4(τc + θ)} = min{2.05, 4(0.15)} = 0.6
[Chau, 2002]

Cascade Control:
Simultaneous tuning of the controllers:
Assume:
P2(s) = P2m(s)P2a(s)
P2a(s) is the all-pass portion of the transfer function containing all
the nonminimum phase dynamics (P2a(0) = 1)
[Visioli, 2006]

Cascade Control:
Desired inner loop transfer function:
¯Tr2y2 (s) =
P2a(s)
(λ2s + 1)n2
λ2 and n2 are design parameters.
C2(s) =
P−1
2m (s)
(λ2s + 1)n2 − P2a(s)
To approximate the controller with a PID controller:
C2(s) =
1
s
k(s) ≈
1
s
k(0) + ˙k(0)s +
¨k(0)
2
[Visioli, 2006]

Cascade Control:
Assume:
P21(s) = P1(s)
P2a(s)
(λ2s + 1)n2
= P12m(s)P12a(s)
P12a(s) is the nonminimum phase part in all-pass form.
Desired outer loop transfer function
¯Tr1y1 (s) =
P12a(s)
(λ1s + 1)n1
Primary controller transfer function
C1(s) =
P−1
12m(s)(λ2s + 1)n2
P2a(s)((λ1s + 1)n1 − P12a(s))
[Visioli, 2006]

Cascade Control:
Example:
P1(s) =
K1
T1s + 1
e−L1s
P2(s) =
K2
T2s + 1
e−L2s
¯Tr2y2 (s) =
e−L2s
λ2s + 1
¯Tr1y1 (s) =
e−(L1+L2)s
λ1s + 1
[Visioli, 2006]

Cascade Control:
Example:
Kp2 =
T2 +
L2
2
2(λ2+L2)
K2(λ2 + L2)
Ti2 = T2 +
L2
2
2(λ2 + L2)
Td2 =
L2
2
6(λ2 + L2)

3 −
L2
T2 +
L2
2
2(λ2+L2)


[Visioli, 2006]

Cascade Control:
Example:
Kp1 =
T1 + λ2 + (L1+L2)2
2(λ1+L1+L2)
K1(λ1 + L1 + L2)
Ti1 = T1 + λ2 +
(L1 + L2)2
2(λ2 + L1 + L2)
Td1 =
λ2T1 − (L1+L2)3
6(λ1+L1+L2)
T1 + λ2 + (L1+L2)2
2(λ1+L1+L2)
+
(L1 + L2)2
2(λ1 + L1 + L2)
The suggestion is to set:
λ2 = 0.5L2
λ1 = 0.5(L1 + L2)
[Visioli, 2006]

Override Control: There are two modes of operation
Normal operation: One process variable is the controlling variable.
Abnormal operation: Some other process variable becomes the
controlling variable to prevent it from exceeding a process or
equipment limit.
The limiting controller is said to override the normal process
controller.
http://pse.che.ntu.edu.tw/chencl/Process_Control

Override Control:
[Smith, 2002]

Override Control:
The set point to LC50 is somewhat above h2, as shown in the ﬁgure.
[Smith, 2002]

Override Control:
The FC50 is a reverse-acting controller, while the LC50 is a
direct-acting controller.
[Smith, 2002]

Override Control:
The FC50 is a reverse-acting controller, while the LC50 is a
direct-acting controller.
The low selector (LS50) selects the lower signal to manipulate the
pump speed.
[Smith, 2002]

Override Control:
Reset Feedback (RFB) or external reset feedback:
This capability allows the controller not selected to override the
controller selected at the very moment it is necessary.
When FC50 is being selected, its integration is working, but not that
of LC50 (its integration is being forced equal to the output of LS50).
When LC50 is being selected, its integration is working but not that
of FC50 (its integration is being forced equal to the output of LS50).
[Smith, 2002]

Selective Control:
The high selector in this scheme selects the transmitter with the
highest output, and in so doing the controlled variable is always the
highest, or closest to the highest, temperature.
[Smith, 2002]

Split range:
A very common control scheme is split range control in which the output
of a controller is split to two or more control valves. For example:
Controller output 0% Valve A is fully open and Valve B fully closed.
Controller output 25% Valve A is 75% open and Valve B 25% open.
Controller output 50% Both valves are 50% open.
Controller output 75% Valve A is 25% open and Valve B 75% open.
Controller output 100% Valve A is fully closed and Valve B fully open.
www.contek-systems.co.uk

Split range:
X: Steam Valve, air-to-open
Y: Cooling Water Valve, air-to-close
TC47: Temperature Controller
TY47: I/P converter
[Love, 2007]

Split range:
ZC47A,B: Valve positioners
TV47A,B: Valves
[Love, 2007]

Split range:
Diﬀerent arrangements are possible. For example, the split can be
conﬁgured as follows:
Controller output 0% Both valves are closed.
Controller output 25% Valve A is 50% open and Valve B still closed.
Controller output 50% Valve A is fully open and Valve B closed.
Controller output 75% Valve A is fully open and Valve B 50% open.
Controller output 100% Both valves are fully open.

Split range:
Example:

Split range:
In this application, the ﬂare valve will need to open quickly in
response to high pressures, but the compressor suction valve will need
to move much more slowly to prevent instability in the compressors.
The main problem with split range control is that the controller only
has one set of tuning parameters.

Split range:
In this application, the ﬂare valve will need to open quickly in
response to high pressures, but the compressor suction valve will need
to move much more slowly to prevent instability in the compressors.
The main problem with split range control is that the controller only
has one set of tuning parameters.
The solution is to replace the split range controller with two
independent controllers, both reading the same pressure transmitter,
but one controlling the ﬂare valve and the other the suction valve.

Two controller implementation:

Marriage analogy:
Split - range control is like a good marriage. One partner may be
doing 90of the work, but both partners are occasionally going to share
the work.
[Lieberman, 2008]

Marriage analogy:
the work.
Override control is like a bad marriage. One partner plays a potentially
dominating role, even though the other partner is doing all the work.
[Lieberman, 2008]

Marriage analogy:
the work.
Override control is like a bad marriage. One partner plays a potentially
dominating role, even though the other partner is doing all the work.
Cascade control is more like my marriage. I do the best I can, but my
wife Liz constantly and lovingly recalibrates my eﬀorts. She dampens
down the extremes in my behavior so as to promote a stable
relationship and home life.
[Lieberman, 2008]

Smith predictor:
To handle systems with a large dead time

Smith predictor:
To handle systems with a large dead time
[Chau, 2002]

Chau, P. C. (2002).
Process Control: A First Course with MATLAB (Cambridge Series in
Chemical Engineering).
Cambridge University Press, 1 edition.
Lieberman, N. (2008).
Troubleshooting Process Plant Control.
Wiley.
Love, J. (2007).
Process Automation Handbook: A Guide to Theory and Practice.
Springer, 1 edition.
Smith, C. A. (2002).
Automated Continuous Process Control.
Wiley-Interscience, 1 edition.
Visioli, A. (2006).
Practical PID Control (Advances in Industrial Control).
Springer, 1 edition.

Industrial Control Systems - Special Structures

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (11)

Andere mochten auch

Andere mochten auch (20)

Mehr von Behzad Samadi

Mehr von Behzad Samadi (12)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

Industrial Control Systems - Special Structures