Control Systems with Actuator Saturation


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1 Control Systems with Actuator Saturation Analysis and Design Tingshu Hu Zongli Lin With 67 Figures Birkhauser Boston Basel Berlin
2 Preface xiii 1 Introduction Linear Systems with Actuator Saturation Notation, Acronyms, and Terminology 3 2 Null Controllability ContinuousTime Systems Introduction Preliminaries and Definitions General Description of Null Controllable Region Systems with Only Real Eigenvalues Systems with Complex Eigenvalues Some Remarks on the Description of C(T) Asymptotically Null Controllable Region Conclusions 35 3 Null ControllabilityDiscreteTime Systems Introduction Preliminaries and Definitions General Description of Null Controllable Region Systems with Only Real Eigenvalues Systems with Complex Eigenvalues An Example Asymptotically Null Controllable Region Conclusions 53
3 4 Stabilization on Null Controllable Region  ContinuousTime Systems ' Introduction \ Domain of AttractionPlanar System under Saturated Linear Feedback SemiGlobal StabilizationPlanar Systems SemiGlobal StabilizationHigher Order Systems Conclusions 83 5 Stabilization on Null Controllable Region DiscreteTime Systems Introduction Global Stabilization at Set of Equilibria Planar Systems Global Stabilization  Planar Systems SemiGlobal Stabilization  Planar Systems SemiGlobal StabilizationHigher Order Systems Conclusions Ill 6 Practical Stabilization on Null Controllable Region Introduction Problem Statement and Main Results Problem Statement Main Results: SemiGlobal Practical Stabilization Proof of Main Results Properties of the Trajectories of Second Order Linear Systems Properties of the Domain of Attraction Proof of Theorem 6.2.1: Second Order Systems Proof of Theorem 6.2.1: Higher Order Systems An Example Conclusions A Proof of Lemma B Proof of Lemma Estimation of the Domain of Attraction under Saturated Linear Feedback Introduction 157
4 ix 7.2 A Measure of Set Size Some Facts about Convex Hulls _ ContinuousTime Systems under State Feedback A Set Invariance Condition Based on Circle Criterion An Improved Condition for Set Invariance The Necessary and Sufficient Condition Single Input Systems Estimation of the Domain of Attraction DiscreteTime Systems under State Feedback Condition for Set Invariance The Necessary and Sufficient Condition Single Input Systems Estimation of the Domain of Attraction Extension to Output Feedback Conclusions On Enlarging the Domain of Attraction Introduction ContinuousTime Systems DiscreteTime Systems Conclusions SemiGlobal Stabilization with Guaranteed Regional Performance Introduction Expansion of the Domain of Attraction SemiGlobalizationDiscreteTime Systems SemiGlobalizationContinuousTime Systems An Example Conclusions Disturbance Rejection with Stability Introduction ContinuousTime Systems Problem Statement Condition for Set Invariance 214
5 Disturbance Rejection with Guaranteed Domain of Attraction An Example DiscreteTime Systems Problem Statement Condition for Set Invariance Disturbance. Rejection with Guaranteed Domain of Attraction Conclusions On Maximizing the Convergence Rate Introduction ContinuousTime Systems Maximal Convergence Control and Maximal Invariant Ellipsoid Saturated High Gain Feedback Overall Convergence Rate Maximal Convergence Control in the Presence of Disturbances DiscreteTime Systems Conclusions Output Regulation ContinuousTime Systems Introduction Preliminaries and Problem Statement Review of Linear Output Regulation Theory Output Regulation in the Presence of Actuator Saturation The Regulatable Region State Feedback Controllers Error Feedback Controllers An Example Conclusions Output Regulation DiscreteTime Systems Introduction Preliminaries and Problem Statement Review of Linear Output Regulation Theory
6 xi Output Regulation in the Presence of Actuator Saturation The Regulatable Region State Feedback Controllers Error Feedback Controllers Conclusions Linear Systems with NonActuator Saturation Introduction Planar Linear Systems under State Saturation ContinuousTime Systems System Description and Problem Statement Main Results on Global Asymptotic Stability Outline of the Proof Planar Linear Systems under State Saturation DiscreteTime Systems System Description and Problem Statement Main Results on Global Asymptotic Stability Outline of the Proof SemiGlobal Stabilization of Linear Systems Subject to Sensor Saturation Introduction Main Results An Example Conclusions 371 Bibliography 375 Index 387
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