How Can Robust Control of Nonlinear Systems be Achieved? Examining Optimization Techniques

Table of Contents

1. Introduction

1.1 Background

1.2 Literature Survey

1.3 Motivation

1.4 Objectives of the Thesis Work

1.5 Thesis Outline

1.6 Summary

2. Feedback Linearization based Fixed Structure Robust H∞ loop shaping control of CSTR

2.1 Feedback Linearization

2.1.1 Input-Output linearization for SISO systems

2.2 Robust design specifications

2.3 Robust feedback linearization

2.4 H∞ Control design

2.4.1 H∞ loop-shaping controller design for CSTR

2.5 H∞ loop shaping control

2.6 Linear Matrix Inequality (LMI)

2.6.1 LMI formulation for LQR

2.6.2 YALMIP and CVX

2.6.3 Simulation Results

2.7 Summary

3. Structured H∞ design based on non-smooth optimization

3.1 Introduction

3.2 Non-smooth loop shaping design using HINFSTRUCT

3.3 HIFOO

3.4 Stability analysis of CSTR using Kharitonov theorem

3.5 Summary

4. Backstepping Control

4.1 Introduction

4.2 Feedback Linearization based on Back-stepping

4.2.1 Magnetic levitation system

4.2.2 Dynamics of MLS

4.2.3 Design Example

4.3 Summary

5. Nonlinear disturbance observer based control

5.1 Introduction

5.1.1 NDOBC for MIMO nonlinear systems

5.2 Nonlinear disturbance observer based SMC (NDOSMC)

5.2.1 Variable structure system and sliding mode

5.2.2 Stability of the sliding mode

5.2.3 Chattering

5.2.4 Design Example

5.3 Sliding Mode Control with NDOBC using optimization with GA

5.4 Summary

6. A Novel chattering free NDO based SMC for Inverted Pendulum with mismatched disturbances

6.1 Introduction

6.2 Methodology

6.3 Design Example

6.4 Summary

7. Conclusions and Future Scope

7.1 Conclusions

7.2 Contributions

7.3 Directions for future work

Objectives & Themes

The primary research objective of this thesis is to develop robust control methodologies for nonlinear systems, specifically addressing challenges related to parametric uncertainties, external disturbances, and chattering phenomena inherent in traditional control methods. The research explores hybrid control structures combining feedback linearization with optimization techniques, observers, and sliding mode strategies.

• Design of robust controllers for nonlinear systems utilizing evolutionary optimization and Linear Matrix Inequalities (LMI).
• Development of chattering-free sliding mode control strategies through nonlinear disturbance observers (NDO).
• Performance analysis of proposed controllers on complex engineering benchmarks like CSTR, magnetic levitation systems, and inverted pendulums.
• Comparative studies of control performance, tracking accuracy, and robustness against model uncertainties and external perturbations.

Excerpt from the Book

Summary of Chapters

1. Introduction: This chapter provides an overview of the research, defining the motivation for developing robust control methods for nonlinear systems, and outlines the objectives and organization of the thesis.

2. Feedback Linearization based Fixed Structure Robust H∞ loop shaping control of CSTR: This chapter covers feedback linearization concepts for SISO and MIMO systems and designs a fixed-structure robust H∞ loop shaping controller for a CSTR, employing LMI-based optimization.

3. Structured H∞ design based on non-smooth optimization: This chapter focuses on structured and fixed-order controller synthesis using non-smooth optimization solvers (HIFOO, HINFSTRUCT) and utilizes the Kharitonov theorem for robust stability analysis.

4. Backstepping Control: This chapter introduces backstepping as a recursive design methodology, combining it with feedback linearization to design robust controllers for a magnetic levitation system.

5. Nonlinear disturbance observer based control: This chapter explores NDO-based robust control for reference tracking and develops various NDO-based sliding mode control strategies to mitigate mismatched disturbances.

6. A Novel chattering free NDO based SMC for Inverted Pendulum with mismatched disturbances: This chapter proposes a novel chattering-free design for NDO-based SMC by incorporating a distance function instead of the traditional sign function to enhance robustness in an inverted pendulum system.

7. Conclusions and Future Scope: This chapter summarizes the contributions of the thesis, provides final conclusions on the effectiveness of the developed control strategies, and suggests directions for future research.

Keywords

Nonlinear Control, Feedback Linearization, H∞ Control, Sliding Mode Control, Nonlinear Disturbance Observer, Robust Stability, Evolutionary Optimization, LMI, Chattering, Inverted Pendulum, CSTR, Magnetic Levitation, Backstepping, Trajectory Tracking.

Frequently Asked Questions

What is the fundamental problem addressed in this research?

The research focuses on the limitations of traditional linear and feedback linearization controllers when applied to nonlinear systems in the presence of parametric uncertainties and external disturbances.

Which specific control design methods are the focus of this work?

The primary methods explored include feedback linearization, H∞ loop shaping, backstepping, sliding mode control (SMC), and nonlinear disturbance observer (NDO) based control.

What is the primary objective of the proposed control techniques?

The main objective is to achieve robust stability and high-performance reference tracking for nonlinear systems while overcoming practical challenges like model inaccuracies, mismatched disturbances, and controller-induced chattering.

What role do optimization techniques play in this thesis?

Optimization methods such as Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and LMI solvers are utilized to tune controller parameters and solve non-convex design problems effectively.

How is the chattering problem in sliding mode control addressed?

Chattering is mitigated through various approaches, including the development of NDO-based schemes, the use of distance functions to replace discontinuous sign functions, and optimization-based parameter tuning.

What defines the effectiveness of the proposed control methodologies?

The effectiveness is demonstrated through rigorous theoretical analysis and extensive simulation studies applied to specific engineering benchmarks like CSTRs, magnetic levitation systems, and inverted pendulums.

What is the significance of the Kharitonov theorem in Chapter 3?

The Kharitonov theorem is employed to verify the robust stability of the controllers synthesized for uncertain systems by checking a finite set of extreme polynomials.

How does the NDO-SMC approach perform compared to traditional SMC?

The NDO-SMC approach significantly reduces chattering and enhances disturbance attenuation, providing superior tracking performance under mismatched uncertainties compared to conventional SMC or I-SMC methods.