Controllability Analysis for Process and Control System Design

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

Thesis Overview 1. 2. 3. 4. 5. 6. 7. 8. Introduction p. H-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 26 2003 2

Outline of the Presentation l Introduction l Part 1 (Chapter 2 and 3): Buffer tank design. – Idea: Handle disturbances neither handled by the process itself nor the feedback controllers l Part 2 (Chapter 6): Feedforward control under uncertainty l Part 3 (Chapter 4, 5 and 7): Multivariable control: – Feedforward effects – Integral action – Uncertainty l Summary September 26 2003 3

Introduction Kårstø gas processing plant: Steam pressure September 26 2003 4

Process Example: Neutralization in Three Tanks u 1 d u 2 u 3 ym, 1 ym, 2 ym, 3 y 1 y 3 y 2 r 3 September 26 2003 5

Block Scheme d r Gd dm - + Kff K + u Controller G y + + ym Process Model scaling: – Require for output – Expect from disturbance – Given for control inputs September 26 2003 6

Controllability With a Scaled Model Disturbance, d Expect September 26 2003 Output, y Require 7

Controllability l Effect of disturbances on the output: d + r Gd Controller u K - y=ym + + G Process l Low frequencies l High frequencies l Required performance September 26 2003 for all w 8

Outline of the Presentation l Introduction l Part 1 (Chapter 2 and 3): Buffer tank design. – Idea: Handle disturbances neither handled by the process itself nor the feedback controllers l Part 2 (Chapter 6): Feedforward control under uncertainty l Part 3 (Chapter 4, 5 and 7): Multivariable control: – Feedforward effects – Integral action – Uncertainty l Summary September 26 2003 9

Two Sources for Disturbances l Quality disturbance In concentration or temperature “Averaging by mixing” Figure 3. 1(I) l Flow rate disturbance Slow level control “Averaging level control” Figure 3. 1(II) September 26 2003 10

Use Buffer Tanks to Modify the Response (logarithmic scales) Figure 3. 4 |h| Typical buffer tank transfer function: September 26 2003 w 11

How Buffer Tanks Modify the Response I Quality disturbance: Mixing tank Assume perfect mixing n tanks t t II Flow disturbance: Slow level control P controller gives 1 st order filter Volume selected to keep level within limits: September 26 2003 12

p. H-neutralization (Chapter 2) l Quality disturbance: mixing tanks l Gd, 0= kd (constant) and kd is large ( 103 or larger) l Consider frequency where S=1 l Obtain minimum total volume requirement where q is flow rate n is number of tanks q is time delay in control loops l May reduce total volume with more tanks September 26 2003 13

p. H-neutralization (continued) l Numerical computations l Local PI/PID in each tank with different tunings: – Ziegler-Nichols, IMC, SIMC l Optimal tuning: Minimizing buffer volume l Frequency response l Step response in time domain l Conclusions: – Equal tanks – Total volume September 26 2003 14

More General Buffer Tank Design (Chapter 3) l l All kinds of processes Both mixing tanks and surge tanks Feedback control system given or not Two steps 1. Find the required transfer function h(s) 2. Design a tank (and possibly a level controller) to realize h(s) September 26 2003 15

Outline of the Presentation l Introduction l Part 1 (Chapter 2 and 3): Buffer tank design. – Idea: Handle disturbances neither handled by the process itself nor the feedback controllers l Part 2 (Chapter 6): Feedforward control under uncertainty l Part 3 (Chapter 4, 5 and 7): Multivariable control: – Feedforward effects – Integral action – Uncertainty l Summary September 26 2003 16

Controllability (Revisited) l Effect of disturbances on the output: d l Low frequencies r Gd Kff + - l High frequencies K - u + Controllers + + y=ym G Process l Feedforward control required if for any frequency l Feedforward from the reference September 26 2003 17

Feedforward Sensitivity Functions l Output with feedforward and feedback control: l Introduce feedforward sensitivity functions: and obtain l Feedforward from the reference, r: l Feedforward effective: l Balchen: September 26 2003 18

Ideal Feedforward Controller l No model error: l When applied to actual plant i. e. the relative errors in September 26 2003 and : G/Gd and G 19

Some Example Feedforward Sensitivities Gain error w Delay error w (logarithmic scale) Figure 6. 2(a) and (b) September 26 2003 20

Some Example Feedforward Sensitivities Time constant error Gain and time constant error Figure 6. 2(c) and (d) September 26 2003 21

Combined Feedforward and Feedback Control 1. No model error Sff SGd SSff. Gd September 26 2003 22

Combined Feedforward and Feedback Control 2. Delay error Sff SGd SSff. Gd September 26 2003 23

Robust Feedforward Control l Scali and co-workers: H 2 /H optimal combined feedforward and feedback control l Detune ideal feedforward controller (reduce gain, filter) l m-optimal feedforward controller Figure 6. 9 September 26 2003 24

Outline of the Presentation l Introduction l Part 1 (Chapter 2 and 3): Buffer tank design. – Idea: Handle disturbances neither handled by the process itself nor the feedback controllers l Part 2 (Chapter 6): Feedforward control under uncertainty l Part 3 (Chapter 4, 5 and 7): Multivariable control: – Feedforward effects – Uncertainty – Integral action l Summary September 26 2003 25

Serial Processes l One process unit after another in a series l Material flow and information go in one direction l Example l Here: Each unit controlled separately September 26 2003 26

Serial Processes: Model Structure September 26 2003 27

Control of Serial Processes Possibly input resetting “Feedforward” control September 26 2003 Local feedback control 28

Example: Three Tanks in Series l 10 s delay in each tank l Local PID controllers Figure 4. 5(a) September 26 2003 29

Example: Three Tanks in Series l Feedforward control Figure 4. 5(b) September 26 2003 30

Example: Three Tanks in Series l MPC – Model predictive control l Input disturbance estimation l First version: Did not handle model error (Fig. 4. 9) l Modified version: Correct integral action (Fig. 4. 11) Figure 4. 7(a) September 26 2003 31

MPC With No Active Constraints l Can be expressed as state feedback: l Extended to non-zero reference, output feedback, input disturbance estimation and possibly input resetting l The full controller on state-space form l Makes it possible to – Plot the controller gain of each channel – Sensitivity function for each channel September 26 2003 32

Example: Three Tanks in Series Controller gains Sensitivity functions Figure 4. 10 September 26 2003 33

Summary l Design of p. H neutralization plants l Design of buffer tanks to achieve required performance l Feedforward control under uncertainty – Feedforward sensitivity functions – When is feedforward needed? – When is it useful? l Multivariable control makes use of both feedforward and feedback control effects – Nominally good performance – Sensitive to uncertainty – Integral action l Model predictive controller without active constraints – State space form of controller and estimator September 26 2003 34