No-chattering sliding mode control in a class of fractional-order chaotic systems

In gas turbine process, the axial compressor is subjected to aerodynamic instabilities because of rotating stall and surge associated with bifurcation nonlinear behaviour. This paper presents a Genetic Algorithm and Particle Swarm Optimization (GA/PSO) of robust sliding mode controller in order to deal with this transaction between compressor characteristics, uncertainties and bifurcation behaviour. Firstly, robust theory based equivalent sliding mode control is developed via linear matrix inequality approach to achieve a robust sliding surface, then the GA/PSO optimization is introduced to find the optimal switching controller parameters with the aim of driving the variable speed axial compressor (VSAC) to the optimal operating point with minimum control effort. Since the impossibility of finding the model uncertainties and system characteristics, the adaptive design widely considered to be the most used strategy to deal with these problems. Simulation tests were conducted to confirm the effectiveness of the proposed controllers.

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“…The sliding mode control law of (13), with LMI constraints (19) [28], [29]. The nonlinear part of the controller can be expressed as:…”

Section: Chattering Reductionmentioning

confidence: 99%

GA/PSO Robust Sliding Mode Control of Aerodynamics in Gas Turbine

Debbah

Kherfane

2018

Acta Universitatis Sapientiae Electrical and Mechanical Engineering

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“…To do a comparative study on the performance of the proposed chattering elimination technique, another well‐known existing method in the literature, namely the boundary layer method, which has been proposed in , is used here to attenuate the chattering. Based on the work , to prevent the chattering, the

sign

function in the control input is replaced by the

sat

function represented by (29). And an integral type fractional‐order sliding manifold similar to that of proposed in is adopted in the simulation.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Based on the work , to prevent the chattering, the

sign

function in the control input is replaced by the

sat

function represented by (29). And an integral type fractional‐order sliding manifold similar to that of proposed in is adopted in the simulation.

sat true(s true) = true{\begin{array}{l} sgn true(s true) | s | > 1 \\ s | s | \leq 1 \end{array}

…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Nevertheless, to our best knowledge, there is little work on the chattering elimination of fractional sliding mode controllers. The commonly applied method in the literature for chattering reduction is the fuzzy and/or crisp boundary layer method . In the boundary layer method, the

sign

function in the control input is approximated by a continuous function such as tanh or

sat

function to prevent chattering.…”

Section: Introductionmentioning

confidence: 99%

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Control of non‐integer‐order dynamical systems using sliding mode scheme

Aghababa

2015

Complexity

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This article deals with the problem of control of canonical non-integer-order dynamical systems. We design a simple dynamical fractional-order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering-free fractional-order sliding mode controller. V C 2015 Wiley Periodicals, Inc. Complexity 000: 00-00, 2015

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“…The results show that using sliding mode method can make the system track target orbit strictly and smoothly with short transition time. Chen et al [14] proposed a no-chattering sliding mode control strategy for a class of fractional-order chaotic systems. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function

Zhang

Chu

et al. 2014

Journal of Applied Mathematics

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A new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Hopf bifurcation of a new chaotic system with chaos entanglement function is studied. More precisely, we study the stability and bifurcations of equilibrium in the new chaotic system. Besides, we controlled the system to any fixed point to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller.

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No-chattering sliding mode control in a class of fractional-order chaotic systems

Cited by 17 publications

References 20 publications

GA/PSO Robust Sliding Mode Control of Aerodynamics in Gas Turbine

GA/PSO Robust Sliding Mode Control of Aerodynamics in Gas Turbine

Control of non‐integer‐order dynamical systems using sliding mode scheme

Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function

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