Controllability Analysis for Process and Control System Design: Controllability Analysis for Process and Control System Design
September 26, 2003
Thesis Overview: 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
Outline of the Presentation: 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
IntroductionKårstø gas processing plant: Steam pressure: Introduction Kårstø gas processing plant: Steam pressure
Process Example: Neutralization in Three Tanks: Process Example: Neutralization in Three Tanks
Block Scheme: Block Scheme
Model scaling:
Require for output
Expect from disturbance
Given for control inputs
r
Controllability With a Scaled Model: Controllability With a Scaled Model Disturbance, d Output, y Expect Require
Controllability: Controllability Effect of disturbances on the output:
Low frequencies
High frequencies
Required performance for all w
Outline of the Presentation: 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
Two Sources for Disturbances: 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)
Use Buffer Tanks to Modify the Response: Use Buffer Tanks to Modify the Response
Typical buffer tank transfer function: w (logarithmic scales) |h| Figure 3.4
How Buffer Tanks Modify the Response: 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
pH-neutralization (Chapter 2): 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
pH-neutralization (continued): 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
More General Buffer Tank Design (Chapter 3): 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)
Outline of the Presentation: 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
Controllability (Revisited): Effect of disturbances on the output:
Low frequencies
High frequencies
Feedforward control required if for any frequency
Feedforward from the reference Controllability (Revisited)
Feedforward Sensitivity Functions: Feedforward Sensitivity Functions Output with feedforward and feedback control:
Introduce feedforward sensitivity functions:
and obtain
Feedforward from the reference, r:
Feedforward effective:
Balchen:
Ideal Feedforward Controller: Ideal Feedforward Controller
No model error:
When applied to actual plant and :
i.e. the relative errors in G/Gd and G
Some Example Feedforward Sensitivities: Some Example Feedforward Sensitivities Gain error Delay error Figure 6.2(a) and (b) w w (logarithmic scale)
Some Example Feedforward Sensitivities: Some Example Feedforward Sensitivities Time constant error Gain and
time constant error Figure 6.2(c) and (d)
Combined Feedforward and Feedback Control: Combined Feedforward and Feedback Control No model error Sff SSffGd SGd
Combined Feedforward and Feedback Control: Combined Feedforward and Feedback Control Delay error Sff SSffGd SGd
Robust Feedforward Control: 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
Outline of the Presentation: 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
Serial Processes: Serial Processes One process unit after another in a series
Material flow and information go in one direction
Example
Here: Each unit controlled separately
Serial Processes: Model Structure: Serial Processes: Model Structure
Control of Serial Processes: Control of Serial Processes
Example: Three Tanks in Series: Example: Three Tanks in Series 10s delay in each tank
Local PID controllers Figure 4.5(a)
Example: Three Tanks in Series: Example: Three Tanks in Series Feedforward control Figure 4.5(b)
Example: Three Tanks in Series: 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)
MPC With No Active Constraints: 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
Example: Three Tanks in Series: Example: Three Tanks in Series Controller gains Sensitivity functions Figure 4.10
Summary : 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