The design of a fractional-order sliding mode controller with a time-varying sliding surface

Abstract

The novelty of this paper is the usage of a time-varying sliding surface with a fractional-order sliding mode controller. The objective of the controller is to allow the system states to move to the sliding surface and remain on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the controller. Firstly, by using the geometric coordinate transformation that is formerly defined for conventional sliding mode controller, a novel fractional-order sliding surface is defined. The time-varying fractional-order sliding surface is then rotated in the region in which the system state trajectories are stable. The adjustment of the sliding surface slope on the new coordinate axes is achieved by tuning a parameter defined as a sigmoid function. Then, a new control rule is derived. Numerical simulations are performed on the nonlinear mass-spring-damper and 2-DOF robot manipulator system models with parameter uncertainties and bounded external disturbances. The proposed controller is compared with the conventional sliding mode controller with a constant sliding surface and the fractional-order sliding mode controller with a constant sliding surface. Simulation results have shown improved performance of the proposed controller in terms of a decrease in the reaching and settling time, and robustness to disturbances as compared with the related controllers. Moreover, it is seen that the designed controller provides an improvement in the error state trajectories.

Fractional-Order Sliding Mode Guidance Law for Intercepting Hypersonic Vehicles

“…Currently, different definitions related to the fractional-order calculus operation have been studied. The Riemann-Liouville (R.L), Grunwald-Letnikov (G.L) and Caputo definitions are the essential definitions in this area [27,28], and the Caputo definition has been utilized in practical applications. In this paper, we will mainly consider the Caputo definition.…”

“…Thus, based on the existence and accessibility condition of the reaching law for continuous systems [34], it is easy to find that, by selecting k 1 , k 2 > 0, for arbitrary V(t 0 ) ≥ 0, V(t) will converge to zero progressively, which, in turn, implies that the designed fractionalorder sliding surface (24) can reach the equilibrium state s = 0 under the action of the fast power reaching law (27).…”

“…Moreover, in order to vertify the superiority of the FOFPR, we design an integer-order fast power reaching (IOFPR) guidance law based on an integer-order sliding surface (44) and the reaching law in Equation (27). Comparative numerical simulations are conducted among the PN, IOFPR and FOFPR guidance laws, respectively.…”

Analysis of Fractional Order Sliding Mode Control in a D-STATCOM Integrated Power Distribution System

“…The most significant cause of model uncertainties includes variation in system parameters such as mechanical stresses, expansion, self-thermal alterations, load demand, a failure rate of transmission lines, generation output, line outage and generator outage [83] can significantly disrupt the system stability and reduces the system performance [84]. The influence of uncertain parameters is usually not substantial for unstressed systems.…”

Fault tolerant control in an unmanned bicycle robot via sliding mode theory

“…Thus, several studies have been conducted on non-linear control schemes for such systems. Among these methods, sliding mode control (SMC) is a well-known robust control technique that has been widely utilised in real applications due to its strong robustness against the uncertainties and disturbances [1][2][3][4][5]. Another controller is model-based predictive control (MPC) that is extensively used as an excellent option in the constrained, multivariable control problems.…”