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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.