Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

This paper presents a new fractional-order sliding mode controller (FOSMC) for disturbance rejection and stabilization of a class of fractional-order systems with mismatched disturbances. To design this control strategy, firstly, a fractional-order extended disturbance observer (FOEDO) is proposed to estimate the matched and mismatched disturbances and their derivatives. Then, according to the design procedure of the sliding mode controller and based on the designed FOEDO, a proper sliding mode surface is proposed. Subsequently, the proposed FOSMC is designed to guarantee that the system states reach the sliding surface and stay on it forever. The stability of the controlled fractional-order systems is proved via fractional-order Lyapunov stability theory. The numerical examples are used to illustrate the effectiveness of the proposed fractional-order controller. The simulation results of the proposed FOSMC are compared with the results of some other researchers’ works to show the superiority of the proposed control method. The new approach displays some attractive features such as fast response, the chattering reduction, robust stability, less disturbance estimation error, the mismatched disturbance, noise rejection, and better control performance.

[1]  Shabnam Pashaei,et al.  A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances. , 2016, ISA transactions.

[2]  Rachid Mansouri,et al.  Fractional sliding mode control of wind turbine for maximum power point tracking , 2019, Trans. Inst. Meas. Control.

[3]  H. Delavari,et al.  Fractional-Order Backstepping Sliding-Mode Control Based on Fractional-Order Nonlinear Disturbance Observer , 2018, Journal of Computational and Nonlinear Dynamics.

[4]  Mohammad Pourmahmood Aghababa,et al.  Chaos in a fractional-order micro-electro-mechanical resonator and its suppression , 2012 .

[5]  Fuchun Sun,et al.  Disturbance Observer Based Composite Learning Fuzzy Control of Nonlinear Systems with Unknown Dead Zone , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[6]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .

[7]  Mignon Park,et al.  Design of sliding-mode control based on fuzzy disturbance observer for minimization of switching gain and chattering , 2015, Soft Comput..

[8]  Reza Ghaderi,et al.  Fuzzy fractional order sliding mode controller for nonlinear systems , 2010 .

[9]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[10]  Mohammad Ali Badamchizadeh,et al.  Design Fractional-Order Terminal Sliding Mode Control for Synchronization of a Class of Fractional-Order Chaotic Systems with Uncertainty and External Disturbances , 2017 .

[11]  Mehdi Dalir,et al.  Applications of Fractional Calculus , 2010 .

[12]  Mohammad Pourmahmood Aghababa,et al.  A switching sliding mode control technique for chaos suppression of fractional-order complex systems , 2019, Trans. Inst. Meas. Control.

[13]  Guichao Yang,et al.  Output feedback control of electro-hydraulic servo actuators with matched and mismatched disturbances rejection , 2019, J. Frankl. Inst..

[14]  P. D. Shendge,et al.  Disturbance observer based sliding mode control of nonlinear mismatched uncertain systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[15]  Konstantinos Michail,et al.  An optimum sensor selection design framework applied to an electro-magnetic suspension system , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[16]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[17]  Farzad Hashemzadeh,et al.  A New Fractional-order Control Method for Robust Synchronization Between Fractional-order Uncertain Permanent Magnet Synchronous Motors , 2019, 2019 27th Iranian Conference on Electrical Engineering (ICEE).

[18]  P. D. Shendge,et al.  Sliding Mode Control for Mismatched Uncertain Systems Using an Extended Disturbance Observer , 2014, IEEE Transactions on Industrial Electronics.

[19]  M. P. Aghababa.  Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller , 2012 .

[20]  Fuchun Sun,et al.  Composite Intelligent Learning Control of Strict-Feedback Systems With Disturbance , 2018, IEEE Transactions on Cybernetics.

[21]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[22]  Yoichi Hori,et al.  Vibration Suppression Using Single Neuron-Based PI Fuzzy Controller and Fractional-Order Disturbance Observer , 2007, IEEE Transactions on Industrial Electronics.

[23]  Mehmet Önder Efe,et al.  Fractional Fuzzy Adaptive Sliding-Mode Control of a 2-DOF Direct-Drive Robot Arm , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Shrivijay B. Phadke,et al.  State and Extended Disturbance Observer for Sliding Mode Control of Mismatched Uncertain Systems , 2015 .

[25]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[26]  Kouhei Ohnishi,et al.  Microprocessor-Controlled DC Motor for Load-Insensitive Position Servo System , 1985, IEEE Transactions on Industrial Electronics.

[27]  Peyman Bagheri,et al.  Parallel cascade control of dead time processes via fractional order controllers based on Smith predictor. , 2020, ISA transactions.

[28]  Abolfazl Ranjbar Noei,et al.  Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance , 2018, Trans. Inst. Meas. Control.