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250  Mathematical Techniques of Fractional Order Systems


            bounded input and bounded output (BIBO) stability of overall system. It is
            a high gain controller where output of system reaches the sliding surface
            very fast and tries to maintain its position on this surface (Liu and Wang,
            2012). This is a type of nonlinear variable order control scheme which is
            generally designed for nonlinear multiinput multioutput (MIMO) complex
            systems. In the present chapter, the design and analysis of the SMC control-
            ler, a nonlinear, coupled, MIMO complex system, two-link planar rigid
            robotic manipulator is considered. Nowadays, robotic manipulators are
            extensively used in hazardous areas like welding, assembling, manufactur-
            ing, painting, etc. in industries. Other applications of robotic manipulators
            are in the field of automobile industries, robotically assisted surgery, han-
            dling of radioactive and biohazardous materials etc. As a manipulator sys-
            tem is a nonlinear, coupled MIMO system where uncertainty can also be
            realized, it always makes a challenge for control engineers for automatic
            control purposes. Linear PID controllers fail to give satisfactory results in
            controlling such types of systems and due to that a robust controller like
            SMC is always suggested for suitable controlling (Sharma et al., 2014;
            Azar and Zhu, 2015). Several scientists have suggested classical SMC as
            well as hybrid of classical SMC with intelligent techniques for controlling
            the manipulator system. A detailed literature survey for different variants
            of SMC is presented in the section following.
               In this section, a comprehensive literature for controlling of nonlinear,
            coupled and complex systems by using different variations and modifications
            of SMC is presented. Starting from classical SMC, the modifications by
            incorporating soft computing techniques like fuzzy logic (FL), artificial
            neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS),
            etc., to the SMC are presented in this section.
               Despite the continuous research in the field of SMC over the last five
            decades, the significant technical problems such as effects of unmodeled
            dynamics, uncertainties of the system parameters, chattering, adaptive behav-
            ior etc. has attracted researchers and scientists. Out of these problems, SMC
            offered fast oscillations in the controller output, i.e., chattering which can
            harm the final control element part of the system. Various technical schemes
            have been developed and incorporated to the classical SMC to address these
            complications. An excellent survey on various aspects of SMC has been
            presented by Yu and Kaynak (2009) where it has been explored that although
            it has been used for the past half century, enhancements in this area are still
            required to design the control scheme for nonlinear complex processes.
            Some current research works explore the use of SMC in different areas like
            synchronization of chaotic system (Vaidyanathan et al., 2015a; Vaidyanathan
            and Azar, 2015a,b), control of Furuta pendulum (Azar and Serrano, 2015c),
            fault tolerance control (Mekki et al., 2015), continuous nonlinear switched
            systems (Azar and Serrano, 2016a), etc.
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