it is PPT for the design of PID controller for Paper Machine Headbox using Bode's Integral method

1. Design of Controller and Stability
Analysis of MIMO SYSTEMS(Paper
Machine Headbox) using various
methods
Presented By:
Ishfaq Ahmad Sheikh
Student, M-Tech(Control System)
Graphic Era University, Dehradun

2.  Introduction
 Literature Survey
 Problem statement
 Methodology
 Results
 Conclusion

3.  In this paper, we are studying the stability analysis of
Paper Machine Headbox using Bode’s Integral Method.
 This technique shows the procedure to use the integrals to
determine the approximated derivatives of the system’s
amplitude and phase.
 The derivatives are approximated for a particular
frequency. The important thing to be noticed about this
method is that the knowledge of system’s static gain,
phase and amplitude is sufficient to approximate the
derivatives.
 We are using modified ZN method also for the further
analysis of the problem.
 We are making use of certain parameters such as
derivative time, proportionality gain, integral time
constant, various frequencies ,phase and gain margins.

4.  PID stands for Proportional, Integral,
Derivative
 Controllers are designed to eliminate the
need for continuous operator attention.
 With integral action, the controller output is
proportional to the amount of time the error
is present.
 With derivative action, the controller output is
proportional to the rate of change of the
measurement or error.

5. Schematic of Paper Machine
Headbox

6.  Inputs- Air Flow and Stock in flow
 Outputs- Stock Level and Pressure
 Controlled output- Pressure
 We make use of all these inputs and similarly
design the desired PID controller so that there
will be a proper uniformity in the output
which we are getting by making use of the
particular jet velocity,
 Changes in jet velocity will accordingly
change the output of the paper machine
headbox which further causes non-uniformity
in the output

7.  There has been several papers on the same
problem, which we are analysing .
 But we are trying to fetch the best results by
making use of Bodes integral method.
 We are comparing the results of the given
problem with modified ZN method.
 After comparing it with that, we found that
we are able to control the response of paper
machine headbox in a better way as
compared to other methods which are already
proposed in several papers.

8.  We will further use some more methods on the
same system such as
 Fractional order method,PID design by
LQR,Sampling method of PID Design.
 Then on the whole we will compare all the results
of the different methods and we will finally come
out with a more accurate and optimal method of
PID design
 There has been already lot of research in the
design of controllers but we are concerned to get
the best results for this system by introducing
more techniques and then finally comparing it.

9.  We are here dealing with the MIMO system and we have to
design an optimal control for the same, so that we can
handle the desired system in a suitable manner
 While we are making use other methods other than Bode’s
integral, we found that there is timely change of pressure
in paper machine headbox.
 When there is change in pressure, it directly effects the jet
velocity. Thus we get non uniformity in the output of the
paper machine headbox.
 We control this problem by designing the PID controller by
making use of Bode’s integral method of PID tuning and
then further we are going to compare the results of this
method with other methods as well so that we can be able
to judge the best or optimal method for the design of
controllers for MIMO systems(Paper Machine Headbox)

10.  Determine the static gain(Kc) of the given
plant.
 Determine the amplitude and phase of the
given plant at the crossover frequency.
 Determine the controller parameters(Ti &Td)
using modified ZN method.
 The desired phase margin is calculated at
crossover frequency.
 The approximated proportional gain(Kp) and
the time constants are obtained using the
following eqns.

11. We have the following transfer function of the
paper machine headbox
Now we use modified zn method inorder to
apply the Bodes integral method for calculation
various parameters.
 By calculations we have
 Sa(w0) = -0.8186,
 SP(W0)= -0.7919.
 Critical frequency Øc= -0.3514

12.  Kp=2.11, Ti=3.715, Td=0.9279
 We obtain the open loop response of the
system as
0 20 40 60 80 100 120 140 160 180 200
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Open Loop Step Response of SISO Loop 1
Time (seconds)
Pressure
Headbox Pressure

13.  We have obtained the following bode plot for
the given transfer function of paper machine
headbox.
10
-2
10
-1
10
0
10
1
10
2
90
180
270
360
Phase(deg)
Bode Diagram
Frequency (rad/s)
-60
-50
-40
-30
-20
-10
0
Magnitude(dB)

14. 0 10 20 30 40 50 60 70 80
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
(a): step response of loop 1 for φd = 0ᴏ
0 20 40 60 80 100 120 140 160 180
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
(b): step response of loop 1 for φd = 15º
0 200 400 600 800 1000 1200 1400
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
(c): step response of loop 1 for φd = 30º
0 20 40 60 80 100 120 140 160 180
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 20 40 60 80 100 120 140
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 10 20 30 40 50 60 70 80
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
(d): step response of loop 1 for φd = 45º (e): step response of loop 1 for φd = 60º (f): step response of loop 1 for φd = 75º

15. 0 10 20 30 40 50 60 70 80
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 10 20 30 40 50 60 70 80
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 10 20 30 40 50 60 70 80
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 10 20 30 40 50 60 70 80
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 10 20 30 40 50 60 70 80
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
0 10 20 30 40 50 60 70 80
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Step Response of SISO Loop 1
Time in secs
Pressure
HB Loop 1
(g): step response of loop 1 for φd = 90º (h): step response of loop 1 for φd = 105º (i): step response of loop 1 for φd = 120º
(j): step response of loop 1 for φd = 135º (k): step response of loop 1 for φd = 150º (l): step response of loop 1 for φd = 165º

16. 0 10 20 30 40 50 60 70 80
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
comparison of Closed Loop Step Response of G1(s) for phi-d = 105o
Time (seconds)
Pressure Bode`s Integral
Modified ZN

17. 0 10 20 30 40 50 60 70 80
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
comparison of Closed Loop Step Response of G1(s) for phi-d = 120o
Time (seconds)
Pressure Bode`s Integral
Modified ZN

18.  From the analysis, the responses are
comparatively better for Φd= 90º, 105º and 120º
(where Φd is desired phase margin).
 Bode’s integral method is based on
approximation of derivatives of amplitude and
phase of stable or minimum phase system.
 The PID controller obtained through this method
is efficient to control the process adequately.
 The response of headbox obtained through
Bode’s Integral method has been compared with
the responses obtained through modified ZN
method and it is observed that the responses
through Bode’s Integral are better than modified
ZN method.

19. THANKS