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

Doctoral Thesis / Dissertation , 2019 , 170 Pages , Grade: A.00

Engineering - General

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.

ROBUST CONTROL OF NONLINEAR SYSTEMS USING OPTIMIZATION TECHNIQUES

Abstract

Due to the inevitable nonlinearities in real systems, several nonlinear control methods (e.g., feedback linearization, sliding mode control, backstepping approach etc.) 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 stabilizesystems containing nonlinearities. In order to accomplish this, it assumes perfectknowledge of the system model to linearize the input-output relationship.In the absenceof 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.

Sliding mode controller design provides a systematic approach to the problem of maintaining stability and consistent performance in the presence of modeling imprecision, for the class of systems to which it applies.Nonlinear disturbance observer (NDO) based sliding mode control (SMC) was proposed (Chen; 2004) in order to achieve better control performance by reducing chattering while maintaining the nominal performance in the presence of mismatched uncertainties. In this thesis, chattering and hitting time in NDO based SMC is reduced by obtaining the optimal controller parameters using optimization methods such as genetic algorithm (GA).

Also a novel and simple chattering free NDO based SMC methodology is proposed here for the robust tracking of nonlinear system with time varying mismatched uncertainties. The chattering alleviation is achieved by using a distance function which measures the distance between the sliding surface and trajectory of state errors as the remedial action in the control law instead of discontinuous sign function. Then Lyapunov method is used to prove the stability of the overall system.

List of Research Publications

1. Bhawna Tandon, Shiv Narayan, “Fixed Structure Robust H-infinity loop shaping of feedback linearized CSTR using PSO”, International Journal of Modeling, Identification and Control, Inderscience Publications, Vol. 22, No. 1, p.p. 33-40, 2014 (SCOPUS & WEB OF SCIENCE INDEXED).
2. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “LMI based control of feedback linearized CSTR using YALMIP and CVX- a comparative analysis”, International Journal of Automation and Control, Inderscience Publications, Vol. 9, No.1, 2015 (SCOPUS INDEXED).
3. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “Explicit Feedback Linearization of Magnetic Levitation System”,World Academy of Science, Engineering and Technology, International Journal of Computer, Information, Systems and Control Engineering Vol:8,No:10,Dec 2014.
4. Bhawna Tandon, Shiv Narayan, Jagdish Kumar, “Structured MIMO H∞ design for feedback linearized CSTR based on non-smooth optimization”, IEEE sponsored International Conference on Recent advances in Engineering and Computational Sciences (RAECS-2015) held on 21st – 22nd December 2015 at University Institute of Engineering & Technology, Punjab University, Chandigarh.
5. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “A simulation study of nonlinear disturbance observer based sliding mode control for inverted pendulum with mismatched disturbances”, International Journal of System Control and Information Processing (IJSCIP), Vol. 1, No. 4, 2015, Inderscience Publications.
6. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “Stability analysis of non-smooth optimisation based controller designs for CSTR using Kharitonov theorem”, International Journal of System Control and Communications, Vol. 7, No. 2, 2016, Inderscience Publications (SCOPUS INDEXED).
7. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “Design of a non-linear controller using Feedback Linearization based on back-stepping technique for Magnetic Levitation system”, International Journal of Applied Nonlinear Science, Vol. 2, No. 4, 2016,Inderscience Publications (WEB OF SCIENCE INDEXED).
8. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “Sliding mode control with nonlinear disturbance observer based on genetic algorithm for inverted pendulum with mismatched disturbances”, Indian Journal of Science and Technology, Vol. 10, Issue 30, August 2017 (WEB OF SCIENCE INDEXED).
9. Bhawna Tandon, Shiv Narayan and Jagdish Kumar, “Nonlinear disturbance observer based robust control for continuous stirred tank reactor”, ICIC (Innovative Computing, Information and Control) Express letters, Vol. 12, Issue1, pp. 1-7, Jan 2018. (SCOPUS INDEXED).
10. One paper titled “A Novel chattering free Nonlinear Disturbance Observer based Sliding Mode Control for Inverted Pendulum with mismatched disturbances” has been communicated to a SCI journal.

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• Grade: A.00
• Author: Bhawna Tandon (Author)
• Publication Year: 2019
• Pages: 170
• Catalog Number: V495757
• ISBN (eBook): 9783346038654
• ISBN (Book): 9783346038661
• Language: English
• Tags: robust, control, nonlinear, systems, achieved, examining, optimization, techniques