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

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