Roy T., Barai R.K. Robust Control-Oriented Linear Fractional Transform Modelling: Applications for the µ-Synthesis Based H∞ Control

Singapore: Springer, 2023. — 166 p.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
About the Authors
Introduction
Motivation
Organization of This Book
References
Mathematical Modelling of Real Physical Systems
Introduction
Mathematical Modelling of Real Physical Systems
Model-Based Control System
Uncertainty Modelling
Linear Fractional Transformation Modelling
Important Observations
Chapter Summary
References
Control-Oriented Linear Fractional Transformation
Introduction
Control-Oriented Modelling
Uncertainty Modelling
Unstructured Uncertainties
Parametric Uncertainty
Structured Uncertainty
Linear Fractional Transformation
Basic Principles
State-Space Realization of LFT Modelling
Interconnection of LFT
Reasons for Adopting LFT Model for Control-Oriented Modelling
Chapter Summary
References
μ-Synthesis-Based H∞ Control Theory
Introduction
Small-Gain Theorem
H∞ Optimization
H∞ Sub-optimal Controller Design
H∞ Control Problem
μ-Synthesis
Chapter Summary
References
Generalized Control-Oriented LFT Modelling of a Coupled Uncertain MIMO System
Introduction
Generalized Control-Oriented LFT Modelling of Linear MIMO System
Problem Formulation
Control-Oriented LFT Modelling Approach for Multiplicative Uncertainty Structure
Generalized Control-Oriented LFT Modelling of Nonlinear MIMO System
Problem Formulation
Control-Oriented LFT Modelling Approach for Polytopic Uncertainty Structure
Chapter Summary
References
Control-Oriented LFT Modelling of a Two-DOF Spring–Mass–Dashpot Dynamic System
Introduction
Mathematical Modelling of DOF SMD System
LFT Modelling
Control-Oriented Linear Fractional Transformation Modelling of Two-DOF Spring–Mass–Dashpot Dynamic System
H∞ Controller Design
Weighting Function
System Interconnection
Simulation Results
Chapter Summary
References
Control-Oriented LFT Modelling and H∞ Control of Twin Rotor MIMO System
Introduction
Mathematical Modelling of Twin Rotor MIMO System
Lagrangian Model of Twin Rotor MIMO System
Control-Oriented LFT Modelling of Twin Rotor MIMO System
Design Specifications
Weighting Function
System Structure
H∞ Controller Design
Simulation Results
Chapter Summary
Notation
References
Control-Oriented LFT Modelling and H∞ Control of Differentially Driven Wheeled Mobile Robot
Introduction
Mathematical Modelling of Differentially Driven Wheeled Mobile Robot
Kinematic Modelling
Dynamic Modelling
Control-Oriented LFT Modelling of Differentially Driven Wheeled Mobile Robot
Design Specifications
Weighting Functions
System Interconnections
H∞ Controller Design
Simulation Results
Chapter Summary
Notation
References
Control-Oriented LFT Modelling and H∞ Control of Differentially Driven Wheeled Mobile Robot with Slip Dynamics
Introduction
Differently Driven Wheeled Mobile Robot with Slip Dynamics
Control-Oriented LFT Modelling of Differentially Driven Wheeled Mobile Robot with Slip Dynamics
Design Specifications
Weighting Function
System Interconnections
H∞ Controller Design
Simulation Results
Comparison of the Performance of WMR Without and with Slip Dynamics
Chapter Summary
Notation
References
Index