Robust Control-Oriented Linear Fractional Transform Modelling: Applications for the µ-Synthesis Based H∞ Control

Description

This book covers a new paradigm of system modeling – the robust control-oriented linear fractional transformation (LFT) modeling. A dynamic system expressed in LFT modeling framework paves the way for the application of modern robust controller design technique like μ-synthesis method for controller design. This book covers the generalized robust control-oriented LFT modeling representation of the MIMO system depending upon the uncertainty structure, system dynamics, and the dimensions of the input–output. The modeling framework results into a compact and manageable representation of uncertainty modeling in the form of feedback-like structure that is suitable for design and implementation of the robust control technique like μ-synthesis-based H∞ control theory. This book also describes the application of the proposed methodology in a variety of advanced mechatronic systems like the Twin Rotor MIMO system, wheeled mobile robot, and an industrial robot arm. Preface Contents About the Authors 1 Introduction 1.1 Motivation 1.2 Organization of This Book References 2 Mathematical Modelling of Real Physical Systems 2.1 Introduction 2.2 Mathematical Modelling of Real Physical Systems 2.3 Model-Based Control System 2.4 Uncertainty Modelling 2.5 Linear Fractional Transformation Modelling 2.6 Important Observations 2.7 Chapter Summary References 3 Control-Oriented Linear Fractional Transformation 3.1 Introduction 3.2 Control-Oriented Modelling 3.3 Uncertainty Modelling 3.3.1 Unstructured Uncertainties 3.3.2 Parametric Uncertainty 3.3.3 Structured Uncertainty 3.4 Linear Fractional Transformation 3.4.1 Basic Principles 3.4.2 State-Space Realization of LFT Modelling 3.4.3 Interconnection of LFT 3.5 Reasons for Adopting LFT Model for Control-Oriented Modelling 3.6 Chapter Summary References 4 μ-Synthesis-Based H∞ Control Theory 4.1 Introduction 4.2 Small-Gain Theorem 4.3 H∞ Optimization 4.4 H∞ Sub-optimal Controller Design 4.5 H∞ Control Problem 4.6 μ-Synthesis 4.7 Chapter Summary References 5 Generalized Control-Oriented LFT Modelling of a Coupled Uncertain MIMO System 5.1 Introduction 5.2 Generalized Control-Oriented LFT Modelling of Linear MIMO System 5.2.1 Problem Formulation 5.2.2 Control-Oriented LFT Modelling Approach for Multiplicative Uncertainty Structure 5.3 Generalized Control-Oriented LFT Modelling of Nonlinear MIMO System 5.3.1 Problem Formulation 5.3.2 Control-Oriented LFT Modelling Approach for Polytopic Uncertainty Structure 5.4 Chapter Summary References 6 Control-Oriented LFT Modelling of a Two-DOF Spring–Mass–Dashpot Dynamic System 6.1 Introduction 6.2 Mathematical Modelling of 2DOF SMD System 6.3 LFT Modelling 6.3.1 Control-Oriented Linear Fractional Transformation Modelling of Two-DOF Spring–Mass–Dashpot Dynamic System 6.4 H∞ Controller Design 6.4.1 Weighting Function 6.4.2 System Interconnection 6.4.3 Simulation Results 6.5 Chapter Summary References 7 Control-Oriented LFT Modelling and H∞ Control of Twin Rotor MIMO System 7.1 Introduction 7.2 Mathematical Modelling of Twin Rotor MIMO System 7.2.1 Lagrangian Model of Twin Rotor MIMO System 7.3 Control-Oriented LFT Modelling of Twin Rotor MIMO System 7.4 Design Specifications 7.4.1 Weighting Function 7.4.2 System Structure 7.5 H∞ Controller Design 7.6 Simulation Results 7.7 Chapter Summary 7.8 Notation References 8 Control-Oriented LFT Modelling and H∞ Control of Differentially Driven Wheeled Mobile Robot 8.1 Introduction 8.2 Mathematical Modelling of Differentially Driven Wheeled Mobile Robot 8.2.1 Kinematic Modelling 8.2.2 Dynamic Modelling 8.3 Control-Oriented LFT Modelling of Differentially Driven Wheeled Mobile Robot 8.4 Design Specifications 8.4.1 Weighting Functions 8.4.2 System Interconnections 8.5 H∞ Controller Design 8.6 Simulation Results 8.7 Chapter Summary 8.8 Notation References 9 Control-Oriented LFT Modelling and H∞ Control of Differentially Driven Wheeled Mobile Robot with Slip Dynamics 9.1 Introduction 9.2 Differently Driven Wheeled Mobile Robot with Slip Dynamics 9.3 Control-Oriented LFT Modelling of Differentially Driven Wheeled Mobile Robot with Slip Dynamics 9.4 Design Specifications 9.4.1 Weighting Function 9.4.2 System Interconnections 9.5 H∞ Controller Design 9.6 Simulation Results 9.7 Comparison of the Performance of WMR Without and with Slip Dynamics 9.8 Chapter Summary 9.9 Notation References Index