1 CHAPTER 1 INTRODUCTION 1.1 Motivation The presence of uncertainties and disturbances has always been a vital issue in the control of dynamic systems. The classical linear controllers, PI and PID controllers designed based on the mathematical model of real systems fail to give a good response in the presence of uncertainties and disturbances and can even cause system instability due to the discrepancies or mismatches between the actual plant and its mathematical model which arise from plant parameters, external disturbances and unmodeled dynamics like unpredictable faults. In the present scenario, it is required to have automatic control with good performance over a wide operating range with simple design and implementation. How to deal with the inevitable uncertainties to achieve increasingly demanding control design requirements has been the central topic of recent research in Control Engineering. As a result, significant advances have been achieved in robust control approaches such as model predictive control, non-linear adaptive control, back-stepping control, sliding mode control and others. These control approaches are capable of guaranteeing the control objectives in the presence of modeling errors, parameter uncertainties and external disturbances. Among the existing robust control techniques, sliding mode control approach is characterized by high simplicity, high robustness, reduced order compensated dynamics, finite time convergence and inherent stability. In the last decades, the ideas of sliding mode control have been
2 successfully applied to the practical industrial systems, for example, mobile robots, electric drives, underwater ships, spacecrafts and many other systems. However, sliding mode control uses infinite gain to force the trajectories of a dynamic system to slide along the restricted sliding mode subspace. Hence, sliding mode control must be applied with much care for the systems that have moderate control action. In particular, because actuators have delays and other imperfections, sliding mode control action can lead to high frequency oscillations called chattering that may result in the excitation of unmodeled dynamics and may even damage the plant. Second order sliding mode control is one of the most recent and successful approaches for the reduction of chattering. However, the conventional second order sliding mode control requires increased information in the form of the knowledge of the value of the time derivative of the sliding variable compared with the conventional sliding mode control. This prevents the conventional second order sliding mode control from being used extensively. Super-twisting sliding mode controller is the most recent type of second order sliding mode controller which maintains the distinctive robust features of sliding mode control techniques, while providing a control signal smoother than that obtained through the conventional sliding mode controller. Hence, super-twisting sliding mode control has the advantage of less chattering compared with the conventional sliding mode control. Moreover, super-twisting sliding mode control method offers a simple algorithm for the easy implementation as it does not require the derivative of the sliding variable compared with the conventional second order sliding mode controllers. However, the performance of super-twisting sliding mode
3 control heavily depends on the sliding surface. If the sliding surface is designed properly, super-twisting sliding mode control can eliminate chattering effect without degrading the transient response, steady-state response and robustness. If the sliding surface is not designed properly, it may lead to adverse effects in the response which are not desirable. However, finding the optimum sliding surface is a tedious task. A successful sliding surface design method for improving the controller performance is to use time-varying sliding surface instead of constant one. 1.2 Problem Statement The aim of this research work is to propose a super-twisting sliding mode control scheme using time-varying sliding surface to improve the dynamic performance of the conventional super-twisting sliding mode control scheme. The adjustment of the sliding surface should be achieved by a simple mechanism without affecting the simplicity and stability of the conventional super-twisting sliding mode control scheme. The proposed scheme should be robust, stable and should be able to exhibit good transient and steady-state responses. 1.3 Solution to the Problem In this research work, a novel super-twisting sliding mode control scheme with a simple single input-single output fuzzy logic control based time-varying sliding surface is proposed. The idea behind this control scheme is to utilize a time-varying slope in the sliding surface of super-twisting sliding mode controller using a simple Mamdani-type single input-single
4 output fuzzy logic controller so that the sliding surface can be rotated in such a direction that the dynamic performance of the system can be improved. The fuzzy logic controller is designed such that the sliding surface slope is always positive to ensure the stability and robustness. 1.4 Objectives of the Research Work The objectives of this research work are: 1. To propose a novel super-twisting sliding mode control scheme using a simple single input-single output fuzzy logic control based time-varying sliding surface. 2. To study the effectiveness of the proposed control scheme in comparison with the conventional super-twisting sliding mode controller with a fixed sliding surface through Matlab/Simulink based simulations for a system with uncertain parameters and disturbances. 3. To verify the robustness of the proposed control scheme for parametric variations and disturbances. 4. To illustrate the application of the proposed control scheme for Electronic throttle control system. 1.5 Methodology for Solving the Problem The effect of the sliding surface on the performance of the conventional super-twisting sliding mode control scheme is studied. The observations are verified by Matlab/Simulink based simulation. Based on the observations, the rules to adjust the sliding surface online to improve the dynamic performance of the controller are formulated. Based on these rules,
5 a fuzzy logic controller to adjust the sliding surface online is designed. The performance of the proposed super-twisting sliding mode control scheme using fuzzy logic control based time-varying sliding surface is studied in comparison with the conventional super-twisting sliding mode control scheme with a fixed sliding surface using Matlab/Simulink based simulations for a system with uncertainties and disturbances. The application of the proposed control scheme is illustrated for Electronic throttle control system. 1.6 Merits of the Proposed Work The proposed super-twisting sliding mode control scheme with a single input-single output fuzzy logic controller based time-varying sliding surface is a powerful robust control scheme for dynamic uncertain systems. The proposed scheme is free from chattering effect compared with the conventional sliding mode control. The elimination of the chattering is achieved without sacrificing the tracking performance and accuracy. The proposed scheme does not require the information of the time derivative of the sliding variable compared with the conventional second order sliding mode control scheme. As the sliding surface slope adjustment is done by a Mamdani-type single input-single output fuzzy inference system, the scheme is simple and computationally efficient. Moreover, the proposed scheme is very easy to implement.
6 1.7 Thesis Organization The thesis is organized as follows: CHAPTER 2: LITERATURE REVIEW. In this chapter, the literature review conducted for the research work is presented. The literature review includes surveys on sliding mode control, chattering reduction techniques, second order sliding mode control and super-twisting sliding mode control. CHAPTER 3: SLIDING MODE CONTROL. In this chapter, the basic principles and design procedure of sliding mode control are presented. The stability analysis and the chattering effect of sliding mode control are discussed. The Matlab/Simulink based simulation of sliding mode control is discussed. CHAPTER 4: SUPER-TWISTING SLIDING MODE CONTROL. In this chapter, an introduction of second order sliding mode control and supertwisting sliding mode control are presented. The effects of the sliding surface on the performance of super-twisting sliding mode control is discussed. The Matlab/Simulink based simulation of super-twisting sliding mode control is discussed. The comparison of the performance of super-twisting sliding mode control and the conventional first order sliding mode control are presented. The simulation results for confirming the effects of the sliding surface on the performance of super-twisting sliding mode control are presented. CHAPTER 5: FUZZY LOGIC CONTROL. This chapter deals with the basics of Fuzzy logic control. The basic theory of fuzzy logic and the basic
7 components of fuzzy logic based control system are discussed. The advantages of fuzzy logic based control are highlighted. CHAPTER 6: FUZZY LOGIC BASED SUPER-TWISTING SLIDING MODE CONTROLLERS. In this chapter, a novel adaptive super-twisting sliding mode controller with a fuzzy logic control based time-varying sliding surface is proposed for the control of dynamic uncertain systems. The stability and robustness of the proposed control scheme are discussed. CHAPTER 7: PERFORMANCE ANALYSIS OF FUZZY LOGIC BASED SUPER-TWISTING SLIDING MODE CONTROLLERS. In this chapter, Matlab/Simulink based simulations conducted for studying the performance of the proposed fuzzy logic control based super-twisting sliding mode controllers are discussed. The comparison of the performance of the proposed control scheme and the conventional super-twisting sliding mode control with a fixed sliding surface is presented. CHAPTER 8: APPLICATION OF FUZZY LOGIC BASED SUPER- TWISTING SLIDING MODE CONTROLLERS FOR ELECTRONIC THROTTLE CONTROL. In this chapter, the application of the proposed fuzzy logic based super-twisting sliding mode control scheme for Electronic throttle control system is presented. CHAPTER 9: CONCLUSION AND FUTURE SCOPE. In this chapter, the conclusion of the research work and scope for the future work are presented.