Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

Binazadeh, Tahereh; Shafiei, Mohammad Hossein

doi:10.1016/j.mechatronics.2013.04.009

Cited by 49 publications

(32 citation statements)

References 22 publications

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“…Proof. Let the Lyapunov function be defined as (19). Taking derivative of (19) with respect to time and using (41) yieldṡ…”

Section: Fractional-order Nonsingular Fast Terminal Sliding-mode Controlmentioning

confidence: 99%

“…For the fractionalorder systems with time-delay, Wang and Gao designed a fractional-order proportional-derivative (PD) controller with H ∞ performance [18]. Most recently, a novel fractionalorder sliding mode controller for output tracking of a time-varying reference signal is designed and the proposed method is applied to a fractional-order gyroscope model [19]. Consensus problems of fractional-order systems with nonuniform input and communication delays over directed static networks are studied based on a frequency-domain approach and generalized Nyquist stability criterion; some results are obtained to ensure the consensus of the fractionalorder systems [20].…”

Section: Introductionmentioning

confidence: 99%

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Fractional-Order Fast Terminal Sliding Mode Control for a Class of Dynamical Systems

Zhao

2013

Mathematical Problems in Engineering

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This paper introduces a novel fractional fast terminal sliding mode control strategy for a class of dynamical systems with uncertainty. In this strategy, a fractional-order sliding surface is proposed, the corresponding control law is derived based on Lyapunov stability theory to guarantee the sliding condition, and the finite time stability of the closeloop system is also ensured. Further, to achieve the equivalence between convergence rate and singularity avoidance, a fractional-order nonsingular fast terminal sliding mode controller is studied and the stability is presented. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.

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“…Proof. Let the Lyapunov function be defined as (19). Taking derivative of (19) with respect to time and using (41) yieldṡ…”

Section: Fractional-order Nonsingular Fast Terminal Sliding-mode Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional-Order Fast Terminal Sliding Mode Control for a Class of Dynamical Systems

Zhao

2013

Mathematical Problems in Engineering

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“…Azarmi et al [6] demonstrated and proved FOPID controller for a CE 150 type laboratory helicopter model is better than PID and FOPI controller under change in disturbance. Moreover, the flexibility of handling uncertainties, robustness, sinking undesired oscillations and fast change of control signal makes requirement of fractional order controller concepts into many advanced control strategies such as phase lead lag compensator [7,8], sliding mode control based FOC [9,10], quadratic regulator based FOC [11,12], smith predictor based FOC [13], internal model based FOC [14,15], H∞ norm based FOC [16,17], set-point weighted FOC [18], FOC with pre-filter [19] and Loop shaping method [20]. From the above literature clearly shows FOPID controller is better than other integer order controller.…”

Section: Introductionmentioning

confidence: 99%

Optimal tuning of FOPID controller based on PSO algorithm with reference model for a single conical tank system

Rajesh¹

2019

SN Appl. Sci.

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The fractional order proportional integral derivative controller (FOPID) replaces the conventional PID controller for its immense merits such as its simple structure, better set point tracking, high disturbance rejection, higher capability of handling model uncertainties in nonlinear and real time applications. This paper addresses the effectiveness of the FOPID controller on a level control of single conical system in real time. It is one of the classical nonlinear control problem and its shape not only contributes the proper mixing of liquids and also guarantee to drainage of solid wastes. This study, a dual loop controller is proposed and constructed with a master process and slave process for a level control of a single conical tank system. In the slave process, the output response obtained by the traditional PID controller combined with the conical tank reference model and compared with the output response of the master process. The obtained error signal is used to dynamically correct the parameters of the FOPID controller in the master process. The tuning of FOPID controller is a challenging task due to its presence of extra parameters and it efficiently carried out by particle swarm optimization (PSO) algorithm. The obtained result reveals that the Proposed PSO optimized FOPID controller with reference model demonstrated the better set point tracking, smooth controller response than other conventional integer order controllers.

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“…In addition, dynamical behavior like chaos and hyperchaos were generated in fractional-order systems and its complex properties were also considered [1,6,11,15]. At the same time, many control methods were used to control uncertainties using sliding control, fuzzy control and boundary control for nonlinear fractional-order systems [3,17,29].…”

Section: Introductionmentioning

confidence: 99%

Full state hybrid projective synchronization of variable-order fractional chaotichyperchaotic systems with nonlinear external disturbances and unknown parameters

Zhang¹,

Liu²

2016

J. Nonlinear Sci. Appl.

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The full state hybrid projective synchronization (FSHPS) definition for variable-order fractional chaotic/hyperchaotic systems with nonlinear external disturbances and unknown parameters is firstly presented. Then by introducing a compensator and a nonlinear controller, the FSHPS scheme is generated to eliminate the influence of nonlinear external disturbances effectively. Moreover, the parameters are estimated validly. Based on these control methods, appropriate parameters and controller to achieve FSHPS for the variable-order fractional chaotic/hyperchaotic systems are chosen impactfully. Simulations of variable-order fractional Chen and Lü system and fractional order hyperchaotic Lorenz system in the sense of FSHPS are performed and results show the effectiveness of our method.

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Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

Cited by 49 publications

References 22 publications

Fractional-Order Fast Terminal Sliding Mode Control for a Class of Dynamical Systems

Fractional-Order Fast Terminal Sliding Mode Control for a Class of Dynamical Systems

Optimal tuning of FOPID controller based on PSO algorithm with reference model for a single conical tank system

Full state hybrid projective synchronization of variable-order fractional chaotichyperchaotic systems with nonlinear external disturbances and unknown parameters

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