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.
Author(s): Tamal Roy, Ranjit Kumar Barai
Series: Studies in Systems, Decision and Control, 453
Publisher: Springer
Year: 2023
Language: English
Pages: 165
City: Singapore
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
