Hybrid L1 Adaptive Control: Applications of Fuzzy Modeling, Stochastic Optimization and Metaheuristics

✍ Scribed by Roshni Maiti, Kaushik Das Sharma, Gautam Sarkar

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 263
• Series: Studies in Systems, Decision and Control, 422
• Category: Library

✦ Synopsis

This book details the designing of hybrid control strategies for practical systems containing time varying uncertainties, disturbances, nonlinearities, unknown parameters, unmodelled dynamics, delays, etc., concurrently. In this book, the advantages of different controllers will be brought together to produce superior control performance for the practical systems. Being aware of the advantages of adaptive controller to tackle unknown constant, time varying uncertainties and time varying disturbances, a variant of adaptive controller, namely L₁ adaptive controller, is hybridized with other strategies.

In this book, to facilitate optimal parameter setting of the basic L₁ adaptive controller, stochastic optimization technique will be hybridized with it. The stability of the optimization technique along with the controller will be guaranteed analytically with the help of spectral radius convergence. The proposed method exhibits satisfactory exploration and exploitation capabilities.

Again, this book will throw light on tackling nonlinearities along with uncertainties and disturbances by hybridizing fuzzy logic with L₁ adaptive controller. The performances of the designed controllers will be compared with different control methodologies to validate their effectiveness. The overall stability of the nonlinear system with the designed controller will be guaranteed with the help of fuzzy Lyapunov function to retain the zonal behaviour of the system. This fuzzy PDC-L₁ adaptive controller is efficient to tackle nonlinearities and at the same time cancels unknown constant, time varying uncertainties and time varying disturbances adequately.

This book will also contain four simulation case studies to validate fruitfulness of the designed controllers. To demonstrate the superior control ability of these controllers in tackling practical system, three experimental case studies will also be provided.

✦ Table of Contents

Preface
Part-I: Prologue
Part-II: Preliminaries
Part-III: Design of Hybrid L1 Adaptive Controller
Part-IV: Applications
Part-IV: Epilogue
Acknowledgements
Contents
About the Authors
Symbols
Acronyms
List of Figures
List of Tables
Part I Prologue
1 Introduction
1.1 Journey Towards Modern Control Theories
1.2 Overview of Modern Control Methodologies
1.2.1 Stochastic Optimization and Metaheuristics Techniques
1.2.2 Fuzzy Logic Systems
1.2.3 L1 Adaptive Control Methodologies
1.3 State of the Art of Hybrid L1 Adaptive Control Methodologies
1.4 Overview of Stability Conditions
1.5 Aims and Scopes of the Book
1.5.1 Aims
1.5.2 Scopes
1.6 Summary
References
Part II Preliminaries
2 Basic L1 Adaptive Controller: A State of the Art Study
2.1 Introduction
2.2 Motivation of Designing L1 Adaptive Controller
2.2.1 Proportional Integral Derivative Controller
2.2.2 Linear Quadratic Gaussian
2.2.3 Model Reference Adaptive Controller
2.3 Architecture of Basic L1 Adaptive Controller
2.4 Stability Analysis of Basic L1 Adaptive Controller
2.5 Transient and Steady State Performance Analysis of Basic L1 Adaptive Controller
2.6 Simulation Case Studies
2.6.1 Case Study-I: Duffing’s Oscillatory System
2.6.2 Case Study-II: Nonlinear Spring Mass Damper System
2.6.3 Case Study III: Inverted Pendulum with Cart
2.6.4 Case Study-IV: Twin Rotor MIMO System
2.7 Summary
References
Part III Design of Hybrid L1 Adaptive Controller
3 Hybrid L1 Adaptive Controller-I: Stochastic Optimization and Metaheuristics Based Approach
3.1 Introduction
3.2 Description of Optimization Techniques Used in This Book
3.2.1 Particle Swarm Optimization: A Stochastic Optimization Approach
3.2.2 Harmony Search Algorithm: A Metaheuristics Approach
3.2.3 Local Best Harmony Search Algorithm: An Advanced Metaheuristics Approach
3.3 Designing of Lbest HS-L1 Adaptive Controller
3.4 Stability Analysis of Lbest HS-L1 Adaptive Controller
3.5 Transient and Steady State Performance Analysis of Lbest HS-L1 Adaptive Controller
3.6 Simulation Case Studies
3.6.1 Case Study-I: Duffing’s Oscillatory System
3.6.2 Case Study-II: Nonlinear Spring Mass Damper System
3.6.3 Case Study-III: Inverted Pendulum with Cart
3.6.4 Case Study-IV: Twin Rotor MIMO System
3.7 Summary
References
4 Hybrid L1 Adaptive Controller-II: Fuzzy Parallel Distributed Compensation Based Approach
4.1 Introduction
4.2 Linear Consequence Rule Based T-S Fuzzy System Design
4.2.1 Nonlinear System Approximation Utilizing T-S Fuzzy System with Linear Consequence
4.2.2 Fuzzy Parallel Distributed Compensation (PDC) Controller Design
4.3 Linear Consequence Rule Based Fuzzy PDC-L1 Adaptive Controller Design
4.3.1 Fuzzy Logic Based Predictor Design
4.3.2 Fuzzy Logic Based Adaptive Laws Formulation for Unknown Constant, Time Varying Uncertainties and Time Varying Disturbances
4.3.3 Fuzzy Logic Based Control Law Design
4.3.4 Fuzzy Logic Based Filter Design
4.4 Stability Analysis of Fuzzy PDC-L1 Adaptive Controller
4.5 Transient and Steady State Performance Analysis of Fuzzy PDC-L1 Adaptive Controller
4.6 Simulation Case Studies
4.6.1 Case Study-I: Duffing’s Oscillatory System
4.6.2 Case Study-II: Nonlinear Spring Mass Damper System
4.6.3 Case Study-III: Inverted Pendulum with Cart
4.6.4 Case Study-IV: Twin Rotor MIMO System
4.7 Summary
References
Part IV Applications
5 Speed Control of Electrical Actuator
5.1 Introduction
5.2 Dynamical Model of Electrical Actuator
5.3 Description of Experimental Setup of Electrical Actuator
5.4 System Identification of Electrical Actuator
5.5 Experimental Case Study of Electrical Actuator
5.6 Summary
References
6 Angular Position Control of Two Link Robot Manipulator
6.1 Introduction
6.2 Dynamical Model of TLRM
6.3 Description of Experimental Setup of TLRM
6.4 System Identification of TLRM
6.5 Experimental Case Study of TLRM
6.6 Summary
References
7 Temperature Control of Air Heater System
7.1 Introduction
7.2 Dynamical Model of Air Heater System
7.2.1 Padé Approximation Based Delay Modelling
7.2.2 Fuzzy Linear Consequence Rule Based Delay Modelling
7.3 Description of Experimental Setup of Air Heater System
7.4 System Identification of Air Heater System
7.5 Experimental Case Study of Air Heater System
7.5.1 Experiment-I
7.5.2 Experiment-II
7.6 Summary
References
Part V Epilogue
8 Future Research Directions of Hybrid Controller
8.1 Significance of the Methodologies Presented in This Book
8.2 Future Research Directions
References
Appendix A Norms of Vector and Matrix
A.1 Vector Norms
A.2 Matrix Norms
Appendix B Spectral Radius Convergence
Index