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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

Introduction Kårstø 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