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

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 26 2003

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 26 2003

Introduction Kårstø gas processing plant: Steam pressure September 26 2003

Process Example: Neutralization in Three Tanks d ym,3 ym,2 ym,1 y3 y2 y1 r3 September 26 2003

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 26 2003

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

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 26 2003

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 26 2003

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 26 2003

Use Buffer Tanks to Modify the Response Typical buffer tank transfer function: (logarithmic scales) Figure 3.4 |h| w September 26 2003

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 26 2003

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 26 2003

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 26 2003

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 26 2003

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 26 2003

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 26 2003

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

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

Some Example Feedforward Sensitivities Gain error Delay error w w (logarithmic scale) Figure 6.2(a) and (b) September 26 2003

Some Example Feedforward Sensitivities Gain and time constant error Time constant error Figure 6.2(c) and (d) September 26 2003

Combined Feedforward and Feedback Control No model error Sff SGd SSffGd September 26 2003

Combined Feedforward and Feedback Control Delay error Sff SGd SSffGd September 26 2003

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 26 2003

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 2003

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 26 2003

Serial Processes: Model Structure September 26 2003

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

Example: Three Tanks in Series 10s delay in each tank Local PID controllers Figure 4.5(a) September 26 2003

Example: Three Tanks in Series Feedforward control Figure 4.5(b) September 26 2003

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 26 2003

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 26 2003

Example: Three Tanks in Series Controller gains Sensitivity functions Figure 4.10 September 26 2003

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 26 2003