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.

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 Optimal New Sliding Mode Controller Combined with Modified Supertwisting Algorithm for a Perturbed Quadrotor UAV

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yassine El Houm ◽  
Ahmed Abbou ◽  
Moussa Labbadi ◽  
Mohamed Cherkaoui
Keyword(s):  
Sliding Mode ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Sliding Surface ◽  
State Variables ◽  
Quadrotor Uav ◽  
The Stability ◽  
Quadrotor System

This paper deals with the design of a novel modified supertwisting fast nonlinear sliding mode controller (MSTFNSMC) to stabilize a quadrotor system under time-varying disturbances. The suggested control strategy is based on a modified supertwisting controller with a fast nonlinear sliding surface to improve the tracking performance. The paper suggests a simple optimization tool built-in MATLAB/Simulink to tune the proposed controller parameters. Fast convergence of state variables is established by using a nonlinear sliding surface for rotational and translational subsystems. The modified supertwisting controller is developed to suppress the effect of chattering, reject disturbances, and ensure robustness against external disturbance effect. The stability of the proposed controller (MSTFNSMC) is proved using the Lyapunov theory. The performance of the proposed MSTFNSMC approach is compared with the supertwisting sliding mode controller (STSMC) by numerical simulations to verify its effectiveness.

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.

scholarly journals H∞Control for Stochastic Systems with Markovian Switching and Time-Varying Delay via Sliding Mode Design

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Lijun Gao ◽  
Yuqiang Wu
Keyword(s):  
Stochastic Systems ◽  
Sliding Mode ◽  
Nonlinear Function ◽  
Markovian Switching ◽  
Time Varying ◽  
Sliding Surface ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Integral Sliding Surface ◽  
The Given

This paper addresses the problem ofH∞control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method.

Asymptotic stabilization of a class of uncertain nonlinear time-delay fractional-order systems via a robust delay-independent controller

2017 ◽  
Vol 24 (19) ◽  
pp. 4541-4550 ◽  
Author(s):  
T. Binazadeh ◽  
M. Yousefi
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Delay Systems ◽  
Time Varying ◽  
State Variables ◽  
Parameter Uncertainties ◽  
External Disturbances ◽  
Sliding Manifold

This paper studies the robust stabilization for a class of nonlinear time-delay fractional order (FO) systems in the presence of some practical aspects. The considered aspects in the FO system include: nonlinear Lipschitz functions; time-varying norm-bounded uncertain terms; and time-delays in the state variables. A major challenge in the control of time-delay systems is that the value of delay is usually not perfectly known or it may be even time-varying. In this paper, a novel asymptotic stabilizing control law is proposed which is delay independent and also has a robust manner in the presence of uncertain terms in the model which may be due to model uncertainties (parameter uncertainties or model simplification) and/or external disturbances. The proposed controller is a FO sliding mode controller that is designed such that the closed-loop system is asymptotically delay-independent stable. For this purpose, a FO sliding manifold is introduced and the occurrence of the reaching phase in a finite time is proved. Finally, in order to validate the theoretical results, an example is given and simulation results confirm the appropriate performance of the proposed controller.

Multiloop state-dependent nonlinear time-varying sliding mode control of unmanned small-scale helicopter

2019 ◽  
Vol 234 (3) ◽  
pp. 585-606 ◽  
Author(s):  
Sinan Ozcan ◽  
Metin U Salamci ◽  
Volkan Nalbantoglu
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Operating Conditions ◽  
Small Scale ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Step ◽  
Mode Control ◽  
State Dependent ◽  
Improved Performance

Time delays, parameter uncertainties, and disturbances are the fundamental problems that hinder the stability and reduce dramatically the tracking performance of dynamical systems. In this paper, a new state-dependent nonlinear time-varying sliding mode control autopilot structure is proposed to cope with these dynamical and environmental complexities for an unmanned helicopter. The presented technique is based on freezing the nonlinear system equations on each time step and designing a controller using the frozen system model at this time step. The proposed method offers an improved performance in the presence of major disturbances and parameter uncertainties by adapting itself to possible dynamical varieties without a need of trimming the system on different operating conditions. Unlike the existing linear cascade autopilot structure, this study also proposes a nonlinear cascade state-dependent coefficient helicopter autopilot structure consisting of four separate nonlinear sub-systems. The proposed method is tested through the real time and PC-based simulations. To show the performance of the proposed robust method, it is also bench-marked against a linear sliding control control in PC-based simulations.

Finite-time H∞ sliding mode control of uncertain T-S fuzzy system with time-varying delay based on observer

2021 ◽  
Vol 40 (1) ◽  
pp. 983-999
Author(s):  
Huan Li ◽  
Pengyi Tang ◽  
Yuechao Ma
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Time Interval ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Sliding Surface ◽  
State Estimator ◽  
Mode Control

In this paper, a class of observer-based sliding mode controller is designed, and the finite-time H∞ control problem of uncertain T-S fuzzy systems with time-varying is studied. Firstly, an integral-type sliding surface function with time-delay is devised based on the state estimator, and sufficient criteria of finite-time bounded and finite-time H∞ bounded can be obtained for the T-S systems. Moreover, the proposed sliding mode control law is integrated to ensure the dynamics of controlled system into the sliding surface in a finite-time interval. Then, according to the linear matrix inequalities (LMIs), the desired gain matrices of fuzzy sliding mode controller and state estimator are derived. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.

scholarly journals Efficient Control of a Non-Linear System Using a Modified Sliding Mode Control

2019 ◽  
Vol 9 (7) ◽  
pp. 1284 ◽  
Author(s):  
Saad Abbasi ◽  
Karam Kallu ◽  
Min Lee
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Sliding Surface ◽  
Parameter Uncertainties ◽  
Pass Filter ◽  
Mode Control ◽  
Efficient Control ◽  
Non Linear ◽  
Non Linear System

Trajectory tracking is an essential requirement in robot manipulator movement and localization applications. It is a current research topic of interest, and several researchers have proposed different schemes to achieve the task accurately. This research proposes efficient control of a hydraulic non-linear robot manipulator using a modified sliding mode control, named proportional derivative sliding mode control with sliding perturbation observer (PDSMCSPO), to overcome parameter uncertainties and non-linearity. The proposed new control strategy achieves higher accuracy and better time convergence than the previous one. A positive derivative gain, which has a value less than one, is multiplied with the velocity error term of the sliding surface. The proposed control (PDSMCSPO) also achieves robustness. Results show that by introducing the derivative gain, the chattering from the system has been reduced more than classical sliding mode control (SMC). The reason is that during reaching phase this small gain multiplies with the perturbation and minimizes the effect of perturbation on the system. A smaller value of switching gain K is required as compared to SMC, and the transfer function between sliding surface and perturbation in proportional derivative sliding mode control (PDSMC)has low pass filter characteristics. The proposed PDSMCSPO has a faster response than previous sliding mode control with sliding perturbation observer (SMCSPO), and the output and sliding surface convergence to the desired value is much quicker than conventional logic. Some other characteristics such as error in the output are small because of more attenuation of the perturbation signal. Simulation and experimental results are presented for a link between the hydraulic robot manipulator and the mass damper system.

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

2016 ◽  
Vol 40 (1) ◽  
pp. 49-60 ◽  
Author(s):  
Iman Ghasemi ◽  
Abolfazl Ranjbar Noei ◽  
Jalil Sadati
Keyword(s):  
Fractional Order ◽  
Iterative Learning Control ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Learning Control ◽  
Iterative Learning ◽  
Control Law ◽  
Sliding Mode Controller ◽  
Text Type ◽  
Single Link

In this paper a new type of sliding mode based fractional-order iterative learning control (ILC) is proposed for nonlinear systems in the presence of uncertainties. For the first time, a sliding mode controller is combined with fractional-order ILC. This sliding mode based [Formula: see text] and [Formula: see text]-type ILC is applied on a nonlinear robot manipulator. Convergence of the proposed method is investigated when the stability is also proved. In this method, the control signal at any iteration is generated in two parts. The first section comes from the sliding mode controller while the second part is output of the fractional-order ILC. The latter signal is assessed using its previous amount and the sliding mode error signal. The achieved control law is capable of controlling nonlinear iterative processes, perturbed by bounded disturbances with high accuracy. The same frequent disturbance is eliminated by the iterative learning part, while the effect of nonrepetitive uncertainty is improved by the sliding mode part. The sliding mode based [Formula: see text]-type ILC (as an adaptive control law) is proposed to control a single-link arm robot. The controller is then improved to sliding mode based [Formula: see text]-type ILC. The effectiveness of the proposed method is again investigated on a single-link robot manipulator through a simulation approach. It is shown that the controller for [Formula: see text] provides performance by means of faster response together with more accuracy with respect to a conventional ILC.

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