Control of nonlinear two-tank hybrid system using sliding mode controller with fractional-order PI-D sliding surface

2018 ◽  
Vol 71 ◽  
pp. 953-965 ◽  
Author(s):  
Govinda Kumar E. ◽  
Arunshankar J.
Keyword(s):  
Fractional Order ◽  
Hybrid System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Sliding Surface

scholarly journals Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Jiacai Huang ◽  
Hongsheng Li ◽  
YangQuan Chen ◽  
Qinghong Xu
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
The State ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
State Variables ◽  
Nonlinear Load ◽  
Special Case

A new robust fractional-order sliding mode controller (FOSMC) is proposed for the position control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties and load disturbances, is studied widely in the application of PMSM drive. In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. The performance and robustness of the proposed method are analyzed and tested for nonlinear load torque disturbances, and simulation results show that the proposed algorithm is more robust and effective than the conventional SMC method.

scholarly journals Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chenhui Wang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Numerical Examples ◽  
Mode Synchronization ◽  
Fractional Order Integral

Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods.

Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Sara Dadras ◽  
Soodeh Dadras ◽  
HamidReza Momeni
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Sliding Mode ◽  
Superior Performance ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Matrix Inequality ◽  
Sliding Surface ◽  
Switching Law

A design of linear matrix inequality (LMI)-based fractional-order surface for sliding-mode controller of a class of uncertain fractional-order nonlinear systems (FO-NSs) is proposed in this paper. A new switching law is achieved guaranteeing the reachability condition. This control law is established to obtain a sliding-mode controller (SMC) capable of deriving the state trajectories onto the fractional-order integral switching surface and maintain the sliding motion. Using LMIs, a sufficient condition for existence of the sliding surface is derived which ensures the t−α asymptotical stability on the sliding surface. Through a numerical example, the superior performance of the new fractional-order sliding mode controller is illustrated in comparison with a previously proposed method.

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

2020 ◽  
Vol 42 (16) ◽  
pp. 3196-3215
Author(s):  
Osman Eray ◽  
Sezai Tokat
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Sliding Mode Controller ◽  
Sigmoid Function ◽  
Time Varying ◽  
Sliding Surface ◽  
Parameter Uncertainties ◽  
Improved Performance ◽  
System States

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.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

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