\XjP^J Taylor & Francis Group. Model-Based Control. Tensor Product Model Transformation in Polytopic. Yeung Yam. CRC Press.

Transcription

1 Automation and Control Engineering Series Tensor Product Model Transformation in Polytopic Model-Based Control Peter Baranyi Yeung Yam Peter Varlaki CRC Press \XjP^J Taylor & Francis Group ^ ' Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business

2 Contents Preface xi Acronyms and Abbreviations xiii 1 Introduction An overview TP model HOSVD-based computation Convex optimization via LMIs/PDC framework Model convexity and convex hull manipulation Significant paradigm changes Outline of the book 7 1 Tensor Product (TP) Model Formulation 9 2 TP Model 11.' 3 TP Model Transformation Introduction to HOSVD Transformation procedures The extracted model Addition of sampling grid lines 29 4 TP Canonical Model Form Definition Numerical reconstruction The TORA example Equations of motion TP canonical model 47 5 Approximation and Complexity Trade-Off TP model form of bounded order 51 vii

3 viii CONTENTS 5.2 The nowhere dense property Trade-off examples A mass-spring-damper system A mass-spring-damper system with nonlinear term Trade-off study on the TORA example 60 6 TP Model Convexity Incorporation TP model convexity Incorporation of convexity conditions Incorporating the SN condition Incorporating the NN condition Incorporating the NO condition Incorporating the RNO condition Alternate method for INO and RNO conditions The partial algorithm The complete algorithm The TORA example 80 7 Introduction to the TPtool Toolbox Generating the TP canonical model Incorporating convexity conditions 86 8 Centralized Model Form The centralized model Mathematical properties Control properties Computational advantages Illustrating examples 93 9 Computational Relaxed TP Model Transformation SVD-based column equivalence Modified transformation algorithm Evaluation of computational reduction Discretization complexity HOSVD computation Tensor product computation Ill 9.4 Examples A simple numerical example The double inverted pendulum example 112 II TP Model-Based Control System Design Overview of TP Model-Based Design Strategy 119

4 CONTENTS ix 11 LMI Theorems under the PDC Framework LMIs for control system design Definition oflmis Constraints expressed via LMIs Generic problems for LMIs LMI optimization under the PDC framework Lyapunov stability criteria Control design for stability Multiobjective control optimization Simultaneous observer/controller design TP model-based control design procedures LMI-based control design for the TORA example Control specifications State feedback control design Observer-based output feedback control design Convex Hull Manipulation Nonlinear sensitivity of control solutions Conservativeness of control solutions 150 III Control Design Examples Control Design with TPtool Toolbox D Prototypical Aeroelastic Wing Section with Structural Nonlinearity Dynamics modeling The TP model State feedback control design Controller for asymptotic stabilization Controller for decay tate control Controller for constraint on the control value Comparison to other control solutions Observer-based output feedback control design An alternative TP model Control system design Control performance Convex hull manipulation Convex hull geometry Effects on LMI-based controller performance Effects on LMI-based observer performance 178

5 X CONTENTS 15 3-D Prototypical Aeroelastic Wing Section with Structural Nonlinearity Dynamics modeling The TP model LMI-based output feedback control design Controller 1: Asymptotic stabilization Controller 2: Constraint on the control value Control performance DoF Helicopter with Four Propellers Dynamics Modeling A simplified model Modeling of uncertainty The TP model Control system design Control performance Heavy Vehicle Rollover Prevention Problem Problem introduction A qlpv model for heavy vehicles The TP model Control system design and performance 212 References 217 Index 229