Design of Fractional-order Sliding Mode Controller (FSMC) for a class of Fractional-order Non-linear Commensurate Systems using a Particle Swarm Optimization (PSO) Algorithm

Abstract

In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional calculus, in many areas of science and engineering. In most cases, the objective of using fractional calculus is to apply the fractional order control (FOC) to enhance the system control quality performance and robustness. Research activities are focused on developing new analysis and design methods for fractional order controllers which may involve fractional integration, fractional differentiation and/or fractional systems in their structure or implementation. The aim of this paper is to develop a fractional-order sliding mode control (FSMC) and to compare its application with the conventional sliding mode control (SMC) for a class of fractional-order non-linear commensurable systems using particle swarm optimization (PSO) algorithm which calculates optimum saturation gain ???? and the parameter ???? of the sliding surface. According to the obtained results from the two used systems for these applications, it‘s clearly shown that the stability and the robustness issues using FSMC are more enhanced than those obtained using SMC. This robustness is also depending on the nature of the chosen sliding surface.