Asymptotic Stabilization of Delayed Linear Fractional-Order Systems Subject to State and Control Constraints

In this paper, we investigate the problem of sliding mode control for singular fractional-order systems that have matched uncertainties. We design an innovative integral sliding mode function and controller based on the normalizable condition. A strict linear matrix inequality-based sufficient condition is obtained for the system’s stability. The normalizable condition is eliminated by updating and developing the control method, and a sufficient and necessary condition is developed for the admissibility of the system. Lastly, verification of our method’s effectiveness is numerically conducted in two instances.

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“…When α = 1 or E = I, Theorem 3 becomes an extension of the Lyapunov stability theory. K can be obtained according to the method in [27].…”

Section: Integral Smc Methodsmentioning

confidence: 99%

On Sliding Mode Control for Singular Fractional-Order Systems with Matched External Disturbances

2022

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“…Fractional calculus provides a feasible and effective method to solve the problems in a practical industrial process [30]. Compared with the control method based on integer order, the fractional order system model and control design can ensure that the system has good stability and can better adapt to the changes of the system in complex actual situations [31].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Distributed Model Predictive Control of Fast and Strong Interacting Systems

et al. 2022

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Fast and strong interacting systems are hard to control from both performance and control effort points of view. Moreover, multiple objective functions or objectives with various identifiers of varying weights can hold unfeasible solutions at times. A novel cost objective function is proposed here to overcome both feasibility set limitations and computational burdens. An application example is used to illustrate its added value, which is a fast and strong interacting multivariable system: a landscape office lighting regulatory problem. New lighting technology and an intelligent control system have been produced to improve control accuracy and reduce power consumption. While optimizing the hardware of the lighting system, the energy consumption can be further reduced by applying advanced control strategy in the lighting system. This paper designed a fractional order distributed model predictive control (FOMPC) scheme to realize the reference tracking and stability control of multiple illuminations at the same time. In order to test the efficiency of the control strategy, an experiment was carried out on the lighting setup based on the dSPACE control system. The FOMPC scheme was analyzed through simulation and lighting experiments based on the dSPACE control system. Through a comparison with the mode predictive control (MPC) scheme, the superiority of the FOMPC scheme for the dynamic behavior and control performance of multiple lighting systems was verified. The research results provide a basis for multiple lighting control and its application.

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“…The role of robust feedback control has very much importance in non-volatile fractional order systems [11][12][13]. A fractional-order controller for stabilizing an unstable open loop is proposed in [14][15][16]. In [17], adaptive fractional PID controller based on neural network is proposed.…”

Section: Introductionmentioning

confidence: 99%

Novel Robust Control Using a Fractional Adaptive PID Regulator for an unstable system

Bensafia

Idir

Khettab

et al. 2022

IJEEI

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Recent advances in fractional order calculus led to the improvement of control theory and resulted in the potential use of a fractional adaptive proportional integral derivative (FAPID) controller in advanced academic and industrial applications as compared to the conventional adaptive PID (APID) controller. Basically, a fractional order adaptive PID controller is an improved version of a classical integer order adaptive PID controller that outperformed its classical counterpart. In the case of a closed loop system, a minor change would result in overall system instability. An efficient PID controller can be used to control the response of such a system. Among various parameters of an instable system, the speed of the system is an important parameter to be controlled efficiently. The current research work presents the speed control mechanism for an uncertain, instable system by using a fractional-order adaptive PID controller. To validate the arguments, the effectiveness and robustness of the proposed fractional order adaptive PID controller have been studied in comparison to the classical adaptive PID controller using the criterion of quadratic error. Simulation findings and comparisons demonstrated that the proposed controller has superior control performance and outstanding robustness in terms of percentage overshoot, settling time, rising time, and disturbance rejection.

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Asymptotic Stabilization of Delayed Linear Fractional-Order Systems Subject to State and Control Constraints

Cited by 8 publications

References 35 publications

On Sliding Mode Control for Singular Fractional-Order Systems with Matched External Disturbances

On Sliding Mode Control for Singular Fractional-Order Systems with Matched External Disturbances

Fractional Order Distributed Model Predictive Control of Fast and Strong Interacting Systems

Novel Robust Control Using a Fractional Adaptive PID Regulator for an unstable system

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