Abstract
A kind of incremental sliding mode control (SMC) approach in connection with the well-known composite nonlinear feedback (CNF) control strategy is newly considered in this research to deal with the nonlinear magnetic ball suspension and inverted pendulum systems, as well. The incremental SMC approach is in fact proposed to handle the aforementioned underactuated systems under control, which have a lower number of actuators than degrees of freedom. Based on the outcomes of the investigation presented here, the small overshoot and short settling time of the system response are fulfilled. In fact, the proposed CNF control strategy comprises two parts: the first term assures the stability of the closed-loop nonlinear system and provides a fast convergence response. The second term reduces its overshoot. The genetic-cuckoo hybrid algorithm is designed to minimize tracking errors for the purpose of finding the most suitable sliding surface coefficients. Finally, the finite time stability for the closed-loop system is proved, theoretically.
Highlights
The system uncertainty or mismatch is considered as one of the most important challenges in the area of nonlinear systems
The selection of all the tuning parameters regarding the aforementioned sliding mode control (SMC)-based composite nonlinear feedback (CNF) strategy is turned into a minimization problem and solved automatically by the GC algorithm
It should be noted that the Lyapunov stability theory is used to prove the finite time closed-loop stability of the magnetic ball suspension system and the inverted pendulum system
Summary
The system uncertainty or mismatch is considered as one of the most important challenges in the area of nonlinear systems . This paper proposes the SMC based on CNF approach for tracking control of a nonlinear magnetic ball suspension system and stabilization of an inverted pendulum system. The idea of the CNF controller to the inverted pendulum system and nonlinear magnetic ball suspension system has been extended by the SMC and GC algorithm [14,15,16,17]. The rest of the paper is organized as follows: the formulation and preliminary concerning the incremental SMC-based CNF strategy is first studied and subsequently the genetic-cuckoo (GC) algorithm has been introduced to minimize tracking errors for the purpose of finding the suitable sliding surface coefficients. The main results regarding this research including the stability of the closed-loop system for magnetic ball suspension and inverted pendulum systems are proposed. In the section before the conclusion, the simulation results are carried out and in last section, concluding remarks are provided
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