1. Controllability Analysis for Process and Control System Design
September 26, 2003

2. Thesis Overview Introduction
pH-neutralization: Integrated process and control design
Buffer tank design
Control design for serial processes
MPC without active constraints
Feedforward control under the presence of uncertainty
Offset free tracking with MPC: An experiment
Conclusions and directions for further work
Appendix A and B: Published material not covered in the other chapters
September

3. Outline of the Presentation
Introduction
Part 1 (Chapter 2 and 3):
Buffer tank design.
Idea: Handle disturbances neither handled by the process itself nor the feedback controllers
Part 2 (Chapter 6):
Feedforward control under uncertainty
Part 3 (Chapter 4, 5 and 7):
Multivariable control:
Feedforward effects
Integral action
Uncertainty
Summary
September

4. Introduction Kårstø gas processing plant: Steam pressure
September

5. Process Example: Neutralization in Three Tanksd
ym,3
ym,2
ym,1 y3 y2 y1 r3
September

6. Block Scheme d u y Process Controller ym dm G Gd Kff r K
Model scaling:
Require for output
Expect from disturbance
Given for control inputs G Gd +
Kff - r + - K
September

7. Controllability With a Scaled Model
Disturbance, d
Output, y
Expect
Require
September

8. Controllability Effect of disturbances on the output: Low frequencies
High frequencies
Required performance for all w d u
y=ym
Process
Controller G Gd + r - K
September

9. Outline of the Presentation
Introduction
Part 1 (Chapter 2 and 3):
Buffer tank design.
Idea: Handle disturbances neither handled by the process itself nor the feedback controllers
Part 2 (Chapter 6):
Feedforward control under uncertainty
Part 3 (Chapter 4, 5 and 7):
Multivariable control:
Feedforward effects
Integral action
Uncertainty
Summary
September

10. Two Sources for Disturbances
Quality disturbance
In concentration or temperature
“Averaging by mixing”
Flow rate disturbance
Slow level control
“Averaging level control”
Figure 3.1(I)
Figure 3.1(II)
September

11. Use Buffer Tanks to Modify the Response
Typical buffer tank transfer function:
(logarithmic scales)
Figure 3.4
|h| w
September

12. How Buffer Tanks Modify the Response
I Quality disturbance: Mixing tank
Assume perfect mixing
n tanks
II Flow disturbance: Slow level control
P controller
gives 1st order filter
Volume selected to keep level within limits: t t
September

13. pH-neutralization (Chapter 2)
Quality disturbance: mixing tanks
Gd,0= kd (constant) and kd is large ( 103 or larger)
Consider frequency where S=1
Obtain minimum total volume requirement
where
q is flow rate
n is number of tanks
q is time delay in control loops
May reduce total volume with more tanks
September

14. pH-neutralization (continued)
Numerical computations
Local PI/PID in each tank with different tunings:
Ziegler-Nichols, IMC, SIMC
Optimal tuning: Minimizing buffer volume
Frequency response
Step response in time domain
Conclusions:
Equal tanks
Total volume
September

15. More General Buffer Tank Design (Chapter 3)
All kinds of processes
Both mixing tanks and surge tanks
Feedback control system given or not
Two steps
Find the required transfer function h(s)
Design a tank (and possibly a level controller) to realize h(s)
September

16. Outline of the Presentation
Introduction
Part 1 (Chapter 2 and 3):
Buffer tank design.
Idea: Handle disturbances neither handled by the process itself nor the feedback controllers
Part 2 (Chapter 6):
Feedforward control under uncertainty
Part 3 (Chapter 4, 5 and 7):
Multivariable control:
Feedforward effects
Integral action
Uncertainty
Summary
September

17. Controllability (Revisited)
Effect of disturbances on the output:
Low frequencies
High frequencies
Feedforward control required if for any frequency
Feedforward from the reference d u
y=ym
Process
Controllers G Gd + r - K
Kff -
September

18. Feedforward Sensitivity Functions
Output with feedforward and feedback control:
Introduce feedforward sensitivity functions:
and obtain
Feedforward from the reference, r:
Feedforward effective:
Balchen:
September

19. Ideal Feedforward Controller
No model error:
When applied to actual plant and :
i.e. the relative errors in G/Gd and G
September

20. Some Example Feedforward Sensitivities
Gain error
Delay error w
w (logarithmic scale)
Figure 6.2(a) and (b)
September

21. Some Example Feedforward Sensitivities
Gain and
time constant error
Time constant error
Figure 6.2(c) and (d)
September

22. Combined Feedforward and Feedback Control
No model error
Sff
SGd
SSffGd
September

23. Combined Feedforward and Feedback Control
Delay error
Sff
SGd
SSffGd
September

24. Robust Feedforward Control
Scali and co-workers: H2 /H optimal combined feedforward and feedback control
Detune ideal feedforward controller (reduce gain, filter)
m-optimal feedforward controller
Figure 6.9
September

25. Outline of the Presentation
Introduction
Part 1 (Chapter 2 and 3):
Buffer tank design.
Idea: Handle disturbances neither handled by the process itself nor the feedback controllers
Part 2 (Chapter 6):
Feedforward control under uncertainty
Part 3 (Chapter 4, 5 and 7):
Multivariable control:
Feedforward effects
Uncertainty
Integral action
Summary
September

26. Serial Processes One process unit after another in a series
Material flow and information go in one direction
Example
Here: Each unit controlled separately
September

27. Serial Processes: Model Structure
September

28. Control of Serial Processes
Possibly input resetting
“Feedforward” control
Local feedback control
September

29. Example: Three Tanks in Series
10s delay in each tank
Local PID controllers
Figure 4.5(a)
September

30. Example: Three Tanks in Series
Feedforward control
Figure 4.5(b)
September

31. Example: Three Tanks in Series
MPC – Model predictive control
Input disturbance
estimation
First version:
Did not handle model
error (Fig. 4.9)
Modified version:
Correct integral action
(Fig. 4.11)
Figure 4.7(a)
September

32. MPC With No Active Constraints
Can be expressed as state feedback:
Extended to non-zero reference, output feedback, input disturbance estimation and possibly input resetting
The full controller on state-space form
Makes it possible to
Plot the controller gain of each channel
Sensitivity function for each channel
September

33. Example: Three Tanks in Series
Controller gains Sensitivity functions
Figure 4.10
September

34. Summary Design of pH neutralization plants
Design of buffer tanks to achieve required performance
Feedforward control under uncertainty
Feedforward sensitivity functions
When is feedforward needed?
When is it useful?
Multivariable control makes use of both feedforward and feedback control effects
Nominally good performance
Sensitive to uncertainty
Integral action
Model predictive controller without active constraints
State space form of controller and estimator
September