A Generalized PI Sliding Mode and PWM Control of Switched Fractional Systems

The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.

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Stabilization of Fractional-Order Systems Subject to Saturation Element Using Fractional Dynamic Output Feedback Sliding Mode Control

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4035196 ◽

2016 ◽

Vol 12 (3) ◽

Cited By ~ 17

Author(s):

Esmat Sadat Alaviyan Shahri ◽

Alireza Alfi ◽

J. A. Tenreiro Machado

Keyword(s):

Fractional Order ◽

Output Feedback ◽

Sliding Mode ◽

Linear Matrix ◽

Linear Component ◽

Dynamic Output Feedback ◽

Closed Loop System ◽

Fractional Systems ◽

Dynamic Output ◽

System States

This paper addresses the design of a robust fractional-order dynamic output feedback sliding mode controller (FDOF-SMC) for a general class of uncertain fractional systems subject to saturation element. The control law is composed of two components, one linear and one nonlinear. The linear component corresponds to the fractional-order dynamics of the FDOF-SMC, while the nonlinear component is associated with the switching control algorithm. The closed-loop system exhibits asymptotical stability and the system states approach the sliding surface in a finite time. In order to design the controller, a linear matrix inequality (LMI)-based procedure is also derived. Simulation results demonstrate the feasibility of the FDOF-SMC strategy.

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Another Note on Stability of Sliding Mode Dynamics in Suppression of Fractional Chaotic Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.743.303 ◽

2015 ◽

Vol 743 ◽

pp. 303-306

Author(s):

J. Yuan ◽

B. Shi ◽

Yan Wang

Keyword(s):

Stability Analysis ◽

Chaotic Systems ◽

Sliding Mode ◽

Fractional Systems ◽

Infinite Dimensional ◽

Fractional Integrator ◽

Fractional Differential ◽

Continuous Frequency ◽

The Stability ◽

Sliding Mode Dynamics

This paper revisits the stability analysis of sliding mode dynamics in suppression of a classof fractional chaotic systems by a different approach. Firstly, we convert fractional differential equationsinto infinite dimensional ordinary differential equations based on the continuous frequency distributedmodel of the fractional integrator. Then we choose a Lyapunov function candidate to proposethe stability analysis. The result applies to both the commensurate fractional systems and the incommensurateones.

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Analysis of sliding-mode and PWM control for a DC motor

Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Control IEEE International Symposium on Computer-Aided Contro CCA-96 ◽

10.1109/cca.1996.558941 ◽

2002 ◽

Author(s):

M.K. Mudunuri ◽

D.A. Schoenwald

Keyword(s):

Sliding Mode ◽

Dc Motor ◽

Pwm Control

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Output feedback sliding mode control of fractional systems

10.1109/icecs.2005.4633576 ◽

2005 ◽

Cited By ~ 3

Author(s):

Reyad EL-Khazali

Keyword(s):

Sliding Mode Control ◽

Output Feedback ◽

Sliding Mode ◽

Fractional Systems ◽

Mode Control

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A sliding mode control for linear fractional systems with input and state delays

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2008.05.011 ◽

2009 ◽

Vol 14 (5) ◽

pp. 2310-2318 ◽

Cited By ~ 132

Author(s):

Amar Si-Ammour ◽

Said Djennoune ◽

Maamar Bettayeb

Keyword(s):

Sliding Mode Control ◽

Sliding Mode ◽

Fractional Systems ◽

Mode Control ◽

State Delays

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Simulated and experimental study of hydraulic anti-lock braking system using sliding-mode PWM control

Mechatronics ◽

10.1016/s0957-4158(01)00049-6 ◽

2003 ◽

Vol 13 (4) ◽

pp. 331-351 ◽

Cited By ~ 88

Author(s):

Ming-chin Wu ◽

Ming-chang Shih

Keyword(s):

Experimental Study ◽

Sliding Mode ◽

Pwm Control ◽

Braking System

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Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems

Mathematical Problems in Engineering ◽

10.1155/2015/972914 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Jian Yuan ◽

Bao Shi ◽

Zhentao Yu

Keyword(s):

Chaotic Systems ◽

Sliding Mode ◽

Adaptive Sliding Mode Control ◽

External Disturbances ◽

Fractional Systems ◽

Sliding Control ◽

Sliding Manifold ◽

The Stability ◽

Adaptation Law ◽

Sliding Dynamics

This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented.

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