The following text examines the questions, how nonlinear system can better be controlled by new optimisation techniques such as feedback linearization.
Due to the inevitable nonlinearities in real systems, several nonlinear control methods like feedback linearization, sliding mode control, backstepping approach and further modes are described in detail in the literature. Due to limitations in application of well known classical methods, researchers have struggled for decades to realize robust and practical solutions for nonlinear systems by proposing different approaches or improving classical control methods.
The feedback linearization approach is a control method which employs feedback to stabilize systems containing nonlinearities. In order to accomplish this, it assumes perfect knowledge of the system model to linearize the input-output relationship. In the absence of perfect system knowledge, modelling errors inevitably affect the performanceof the feedback controller. Many researchers have come up with a new form of feedback linearization, called robust feedback. This method gives a linearizing control law that transforms the nonlinear system into its linear approximation around an operating point. Thus, it causes only a small transformation in the natural behavior of the system, which is desired in order to obtain robustness.
The controllers are required to provide various time domain and frequency domain performances while maintaining sufficient stability robustness. In this regard, the evolutionary optimization techniques provide better option as these are probabilistic search procedures and facilitate inclusion of wide variety of time and frequency domain performance functionals in the objective functions. A significant scope of work remains to be done which provides motivation for the research in the design of robust controllers using evolutionary optimization. Also, emerging techniques using LMI also find potential in controller design for feedback linearized systems.The thrust of the study here is to design robust controllers for nonlinear systems using Evolutionary optimization and LMI.
Furthermore, latest control methods for nonlinear system have been studied, deeply, in this thesis. Combining feedback linearization with non linear disturbance observer based control (NDOBC) obtains promising disturbance rejection and reference tracking performance as compared to other robust control methods.
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
1.1 Background
Researchers from various areas like robotics, biomedical engineering, mechatronics, process control and spacecraft control, have shown a great interest in developing the methodologies for nonlinear control. Most public method for nonlinear control is to use a linear controller for the nonlinear arrangement that is obtained by approximation concerning an operating point. But, this method of manipulation works merely in the tiny vicinity of the working point, as linear approximation is valid merely in this region. And, when the required operation range is large, a linear controller performs poorly because the nonlinearities in the arrangement are not compensated properly. The feedback linearization is the resolution to this setback, because the nonlinear arrangement gets transformed precisely into a linear arrangement (which is valid for the whole working region) employing feedback linearization and, hence, this combination of feedback linearization and a linear controller will work at all the points, not merely in a tiny area of the operating point. Feedback linearization is established on the cancellation of nonlinearities in the plant dynamics by the controller (Seo et al., 2007). But because of inaccurate measurements, plant uncertainties, and disturbances precise cancellation of these nonlinearities is impossible in practice. The linearized arrangement thus obtained, by using feedback linearization, has completely different dynamics and said to be in Brunovsky form (Hedrick and Girard, 2005; Isidori, 2013; Sastry, 2013), a non-robust form that is exceedingly sensitive to the uncertainties. (Franco, et al., 2006).
Thus a new idea of feedback linearization, shouted robust feedback linearization was given by researchers (Guillard & Bourles, 2000) that give a linearizing control law that transforms the nonlinear arrangement into its linear approximation concerning an operating point. The supremacy of this method is that merely a tiny makeover in the usual behavior of the system occurs, that is wanted so as to attain robustness.
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.
- Quote paper
- Bhawna Tandon (Author), 2019, How Can Robust Control of Nonlinear Systems be Achieved? Examining Optimization Techniques, Munich, GRIN Verlag, https://www.grin.com/document/495757
