Control Systems with Input and Output Constraints

1 Introduction.- 1.1 A Typical Case.- 1.2 A Historical Perspective.- 1.3 The Control Problem.- 1.3.1 Control Systems with Input Constraints.- 1.3.2 Control Systems with Mode Switch.- 1.3.3 Control Systems with Output Constraints.- 1.4 Expected Control Performance.- 1.5 Methods.- 1.5.1 Optimal Control.- 1.5.2 Numerical Optimization: Model Predictive Control.- 1.5.3 The Intuitive Approach.- 1.6 Contents.- 1.7 Objectives.- I Standard Techniques.- 2 PI Control with Input Saturations.- 2.1 John's Case.- 2.1.1 Modeling.- 2.1.2 The Mechanical Governor.- 2.1.3 The Electronic Regulator.- 2.1.4 Summary.- 2.2 Problem Statement and Test Cases.- 2.3 The Reset Windup Effect.- 2.4 Antiwindup Structures.- 2.4.1 The Generic Antiwindup Feedback Structure.- 2.4.2 Control Conditioning.- 2.4.3 Reference Conditioning.- 2.4.4 Self-conditioning.- 2.4.5 Summary.- 2.5 Transient Responses for the Test Cases.- 2.5.1 The Effect of Antiwindup Feedback Structure.- 2.5.2 The Effect of Controller Tuning.- 2.5.3 Overshoot Analysis.- 2.5.4 The Effect of the Relative Pole Shift UT.- 2.5.5 Summary.- 2.6 Stability properties.- 2.6.1 Motivation.- 2.6.2 Methods.- 2.6.3 A Generic Result.- 2.6.4 Stability Analysis of the Test Cases.- 2.6.5 Estimating the Range of Attraction.- 2.6.6 Summary.- 2.7 Relations to Optimal Control.- 2.7.1 Motivation.- 2.7.2 The Exact Solution.- 2.7.3 Ongoing Control.- 2.8 Case Study: Batch Reactor Temperature Control.- 2.8.1 The process and the main control task.- 2.8.2 The Plant Model.- 2.8.3 Parameter Values.- 2.8.4 The Controller.- 2.8.5 The Design Program.- 2.8.6 Typical Resuhs.- 2.9 Summary.- 3 PI Control with Output Constraints.- 3.1 Arthur's Case.- 3.1.1 Extending the Plant Model.- 3.1.2 Arthur's Solution.- 3.1.3 An Advanced Solution.- 3.2 The Basic Concept.- 3.2.1 Problem Statement.- 3.2.2 Typical Controller Structures.- 3.3 The Benchmark Test.- 3.4 Structures for Output Constraint Control.- 3.4.1 The Nonhnear-Additive Concept.- 3.4.2 The Selector Concept.- 3.4.3 The Cascade-Limiter Concept.- 3.5 The Generic Structure.- 3.5.1 A First Version, for Direct Implementation.- 3.5.2 A Second Version, for Stability Analysis.- 3.6 Stability Analysis.- 3.6.1 The Cascade-Limiter Form.- 3.6.2 The Nonhnear-Additive and Selectors Forms.- 3.7 Stability Properties of the Test Case.- 3.8 Relations to Minimum Time Control.- 3.9 Case Study (continued): Batch Reactor Temperature Control..- 3.9.1 The Process and the Main Control Task.- 3.9.2 The Plant Model.- 3.9.3 Parameter Values.- 3.9.4 The Controller.- 3.9.5 The Design Program.- 3.9.6 Typical Results.- 3.10 Summary.- 4 PI Control with Input and Output Constraints.- 4.1 Problem Statement.- 4.1.1 The Plant Model.- 4.1.2 The Basic Control Idea.- 4.2 Benchmark System.- 4.3 Structures and Transient Responses.- 4.3.1 Form A: Sequential Max-Min-Selection.- 4.3.2 Form B: Parallel Selection.- 4.3.3 Form C: "Lowest Wins".- 4.3.4 Form D: Sequential Nonhnear Additive.- 4.3.5 Form E: Cascade Limiter.- 4.4 Performance Analysis.- 4.4.1 Introduction.- 4.4.2 Applying Open Loop Control Sequences u(t).- 4.4.3 Generating u(t) by Proportional Feedback and Selection.- 4.4.4 Comparison.- 4.4.5 Adding Integral Action with Antiwindup Feedback.- 4.4.6 Back to the Benchmark.- 4.5 Stability Analysis.- 4.5.1 The Multivariable Circle Criterion Approach.- 4.5.2 An illustrative example.- 4.5.3 The Phase Plane Partitions Approach.- 4.5.4 A Modified Approach.- 4.5.5 A Fourth Approach to Design for Stability.- 4.5.6 Summary and Generalization.- 4.6 Case Study: Elevator Positioning Control.- 4.6.1 Plant Description and Data.- 4.6.2 Mathematical model.- 4.6.3 Suggestions for the Control System Design and Analysis.- 4.7 Summary.- 5 Further Topics on PI (aw) Control.- 5.1 PI Control with Actuator Slew and Stroke Constraints.- 5.1.1 Motivation.- 5.1.2 Actuator Modeling.- 5.1.3 Control Structures and Transient Response.- 5.1.4 An Approximation.- 5.1.5 Stability Analysis.- 5.1.6 An Implementation Alternative.- 5.2 Pl(aw) Control with Derivative Action.- 5.2.1 Introduction.- 5.2.2 The Benchmark.- 5.2.3 Transient Response.- 5.2.4 Some Solutions.- 5.2.5 Stability Analysis.- 5.2.6 Summary.- 5.3 PI(aw) Control with Measurement Noise.- 5.3.1 Introduction.- 5.3.2 Louis' Problem.- 5.3.3 The High-Frequency Disturbance Model.- 5.3.4 PI(aw) Control.- 5.3.5 PI(aw) Control with Derivative Action.- 5.3.6 PI(aw)-P cascade control.- 5.3.7 Some Solutions.- 5.3.8 Conclusion.- II Advanced Techniques.- 6 Generalized Antiwindup.- 6.1 Introduction.- 6.2 A Motivating Example: Peter's Case.- 6.2.1 The Control Loop.- 6.2.2 Transient Responses.- 6.2.3 Peter's Analysis.- 6.3 Problem Statement.- 6.3.1 The Plant.- 6.3.2 Controller structures.- 6.3.3 Controller Parameters.- 6.3.4 Test Sequence.- 6.3.5 Saturation Limits.- 6.3.6 Antiwindup Feedback.- 6.4 Nonlinear Stability Analysis.- 6.4.1 The P+ Case.- 6.4.2 Stability Charts.- 6.4.3 The I(aw)-P+ Case.- 6.4.4 Another Approach to the Graphic Stability Test.- 6.5 Transient Analysis.- 6.6 Design Methods: An Overview.- 6.7 Design by De-tuning ?.- 6.8 The "Nested Loops" Method.- 6.8.1 Transient Response.- 6.8.2 Stability Properties.- 6.8.3 Checking the Design Procedure.- 6.9 First-order Dynamic Antiwindup Feedback.- 6.9.1 The Design Procedure.- 6.9.2 Stability Analysis.- 6.9.3 Checking Peter's Method.- 6.10 Trajectory Generators with Antiwindup Feedback.- 6.10.1 The Design Procedure.- 6.10.2 Stability Properties.- 6.10.3 Checking the Transient Response.- 6.11 The "Continued States" Concept.- 6.12 The Group of "Add-on Output Constraints".- 6.13 The Cascade Limiter Method.- 6.13.1 Problem Specification.- 6.13.2 The Design Procedure.- 6.13.3 Transient Response.- 6.13.4 Stability Analysis.- 6.14 Selection for Approach Speed.- 6.14.1 The Design Procedure.- 6.14.2 The Second-order Case G(s) = l/(sT)2.- 6.14.3 The Third-order Case G(s) = l/(sT)3.- 6.15 Selection for Lower-bandwidth R1-Control.- 6.15.1 The Design Procedure.- 6.15.2 Stability Properties.- 6.15.3 Transient Response.- 6.15.4 Checking the design procedure.- 6.16 Links to Model Predictive Control.- 6.16.1 Introduction.- 6.16.2 The Benchmarks.- 6.16.3 Classic Model Predictive Control.- 6.16.4 Exphcit Model Predictive Control.- 6.16.5 Comparison with Previous Design Methods.- 6.17 Summary and Outlook.- 7 Generalized Override Control.- 7.1 Introduction.- 7.2 Systems with Dominant First-order Plants.- 7.2.1 Actuation on the Inflow.- 7.2.2 Actuation on the Outflow: Direct vs. Reverse Control..- 7.2.3 Main Control on the Inflow and Overrides on the Outflow.- 7.2.4 Output Limitation with N2 > N1.- 7.3 Systems with Dominant Higher-order Plants.- 7.3.1 Open Integrator Chain Plants.- 7.3.2 Output Constraint Control on a Flexible Transmission..- 7.4 Load Gradient Control.- 7.4.1 Henry's Case.- 7.4.2 Modeling.- 7.4.3 Controller Structures and Transient Response.- 7.4.4 Stability properties.- 7.4.5 Some Suggestions for Case Studies.- 7.5 Override Action on the Reference Input.- 7.5.1 Introduction.- 7.5.2 The Benchmark.- 7.5.3 The Design Targets.- 7.5.4 Form A: Nonlinear y2-Feedback.- 7.5.5 Form B: Override Structure with P Controllers.- 7.5.6 Form C: Override Control with Integral Action.- 7.5.7 Summary.- 7.6 A Compromise Between y1- and y2-Control.- 7.7 Links to Model Predictive Control.- 7.7.1 Introduction.- 7.7.2 Case ii: The Double-integrator Plant.- 7.7.3 Case iii: The Triple-integrator Plant.- 7.7.4 Conclusions.- 7.8 Summary.- 8 Multivariable Control with Constraints.- 8.1 Introduction.- 8.2 An Overview.- 8.2.1 Multiple Overrides.- 8.2.2 Multiple Actuators of the Same Type.- 8.2.3 Sequentially Acting Control Loops.- 8.2.4 Parallel-acting Control Loops.- 8.2.5 The General Multi-input Multi-output Case.- 8.3 Parallel Actuators.- 8.3.1 Structure.- 8.3.2 Transient Response and Stability Analysis.- 8.4 Sequenced Control Loops.- 8.4.1 Structure.- 8.4.2 Transient Response.- 8.4.3 Stability Analysis.- 8.5 Parallel Control Loops.- 8.5.1 The Plant Model.- 8.5.2 State Feedback Control.- 8.5.3 Additional Integral Action in the Local Controllers.- 8.5.4 Stability Analysis.- 8.6 Interacting Control Loops.- 8.6.1 The Plant.- 8.6.2 Local P Controllers.- 8.6.3 Decoupling Control.- 8.6.4 A Different Control Concept.- 8.6.5 Transient Response.- 8.7 Summary.- 9 Conclusion.- 9.1 Approach.- 9.2 Achievements.- 9.3 Limitations.- 9.4 Some Further Research Areas.- A Nonlinear Stability Tests.- A.l The Canonical Loop Structure and Stability of Motion.- A.2 Final Steady State and the Sector Criteria.- A.3 Limit Cycles and the Describing Function Method.- A.4 Summary.- References.