Design of Nonlinear Conformable Fractional-Order Sliding Mode Controller for a Class of Nonlinear Systems (original) (raw)
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In this article, a novel nonlinear sliding mode controller is proposed to control a class of nonlinear systems. The proposed control scheme is based on conformable fractional order operators. The stability analysis is performed using Lyapunov direct method. Simulation results show high convergence speed, chattering reduction and small control effort.
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International Journal of Industrial Electronics, Control and Optimization (IECO), 2019
In this paper, a novel conformable fractional order (FO) sliding mode control technique is studied for a class of FO chaotic systems in the presence of uncertainties and disturbances. First, a novel FO nonlinear surface based on conformable FO calculus is proposed to design the FO sliding mode controller. Then, asymptotic stability of the controller is derived by means of the Lyapunov direct method via conformable FO operators. The stability analysis is performed in the sliding and reaching phase. In addition, the realization of reaching phase is guaranteed in finite time and the reaching time is calculated analytically. The proposed control approach has some superiorities. Reduction of the chattering phenomenon, high robustness against the uncertainty and external disturbance, and fast convergence speed are the main advantages of the proposed control scheme. Moreover, it has simple calculations because of using conformable FO operators in the control design. The numerical simulations verify the efficiency of the proposed controller.
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This paper presents a new approach of fractional order sliding mode controllers (FOSMC) for a class of nonlinear systems which have a single input and two outputs (SITO). Firstly, two fractional order sliding surfaces S1 and S2 were proposed with an intermediate variable z transferred from S2 to S1 in order to hierarchy the two sliding surfaces. Secondly, a control law was determined in order to control the two outputs. A sliding control stability condition was obtained by using the properties of the fractional order calculus. Finally, the effectiveness and robustness of the proposed approach were demonstrated by comparing its performance with the one of the conventional sliding mode controller (SMC), which is based on integer order derivatives. Simulation results were provided for the case of controlling an inverted pendulum system.
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Transactions of the Institute of Measurement and Control, 2020
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 un...
International Journal of Robust and Nonlinear Control, 2010
Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional-order dynamics. After making a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The first one is based on the conventional discontinuous first-order sliding mode control technique. The second scheme is based on the chattering-free second-order sliding mode approach that leads to the same robust performance but using a continuous control action. Simple controller tuning formulas are constructively developed along the paper by Lyapunov analysis. The simulation results confirm the expected performance.
International Journal of Automation and Control, 2019
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International Journal of Systems Science, 2017
A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.
International Journal of Dynamics and Control, 2020
This study presents a novel fractional-order nonlinear sliding mode controller (FONSMC) based on an extended nonlinear disturbance observer (ENDOB) for a class of fractional order systems with matched and mismatched disturbances. Firstly, an ENDOB is introduced to estimate both the matched and mismatched disturbances. Then, the fractional-order nonlinear sliding surface is designed to satisfy the sliding condition in finite time. Accordingly, the corresponding FONSMC is proposed using the Lyapunov stability theorem. The proposed method shows an impressive disturbances rejection and also guarantees finitetime stability of closed-loop systems. Finally, the effectiveness of the proposed FONSMC-ENDOB structure is illustrated via numerical simulation. The simulation results exhibit the superiority of the proposed controlling method. Keywords Fractional-order systems • Nonlinear sliding mode control • Disturbance observer • Matched and mismatched disturbances • Finite-time stability B Amir Razzaghian