Fractional order integral sliding mode control for PMSM based onfractional order sliding mode observer

In view of the variation of system parameters and external load disturbance affecting the high-performance control of permanent magnet synchronous motor(PMSM),a fractional order integral sliding mode control(FOISMC)strategy is developed for PMSM drive system by means of fractional order sliding mode observer(FOSMO).Based on FOISMC technology,a fractional order integral sliding mode regulator(FOISM-based regulator)is designed,and a global integral sliding mode surface design method is presented,which can guarantee the global robustness of the system.Combining fractional order theory and sliding mode control theory,the FOSMO is constructed to achieve better identification accuracy of the speed and rotor position.Meanwhile the sliding mode load observer is used to observe the load torque in real time,and the observed value is transmitted to speed regulator to improve the capability of accommodating the challenge of load disturbance.Simulation results validate the feasibility and effectiveness of the proposed scheme.

Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control

An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.

The stability control of fractional order unified chaotic system with sliding mode control theory

This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts： the continuous part and switching part. With Gronwall＇s inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.

Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance

This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.

Stabilization of Uncertain Fractional Memristor Chaotic Time⁃Delay System Based on Fractional Order Sliding Mode Control

Based on Lyapunov theorem and sliding mode control scheme,the chaos control of fractional memristor chaotic time⁃delay system was studied.In order to stabilize the system,a fractional sliding mode control method for fractional time⁃delay system was proposed.In addition,Lyapunov stability theorem was used to analyze the control scheme theoretically,which guaranteed the stability of commensurate and non⁃commensurate order systems with or without uncertainties and disturbances.Furthermore,to illustrate the feasibility of controller,the conditions for designing the controller parameters were derived.Finally,the simulation results presented the effectiveness of the designed strategy.

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

A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.

Constrained sliding mode control of nonlinear fractional order input affine systems

Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.

Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system

Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control （FASMC） method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are en- hanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.

Comparison between two different sliding mode controllers for a fractional-order unified chaotic system

Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.

Synchronization between a novel class of fractional-order and integer-order chaotic systems via a sliding mode controller

In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integer- order chaotic system, in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method. Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus. Moreover, three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results. Finally, results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.

Sliding Mode Control of Fractional-Order Memristive System

A sliding mode controller for a fractional-order memristor-based chaotic system is designed to address its problem in stabilization control.Firstly,aphysically realizable fractional-order memristive chaotic system was introduced,which can generate a complex dynamic behavior.Secondly,a sliding mode controller based on sliding mode theory along with Lyapunov stability theory was designed to guarantee the occurrence of the sliding motion.Furthermore,in order to demonstrate the feasibility of the controller,a condition was derived with the designed controller＇s parameters,and the stability analysis of the controlled system was tested.A theoretical analysis shows that,under suitable condition,the fractional-order memristive system with a sliding mode controller comes to a steady state.Finally,numerical simulations are shown to verify the theoretical analysis.It is shown that the proposed sliding mode method exhibits a considerable improvement in its applications in a fractional-order memristive system.

A Novel ANFIS Based SMC with Fractional Order PID Controller

Interacting The highest storage capacity of a circular tank makes it pop-ular in process industries.Because of the varying surface area of the cross-sec-tions of the tank,this two-tank level system has nonlinear characteristics.Controlling theflow rate of liquid is one of the most difficult challenges in the production process.This proposed effort is critical in preventing time delays and errors by managing thefluid level.Several scholars have explored and explored ways to reduce the problem of nonlinearity,but their techniques have not yielded better results.Different types of controllers with various techniques are implemented by the proposed system.Sliding Mode Controller(SMC)with Fractional Order PID Controller based on Intelligent Adaptive Neuro-Fuzzy Infer-ence System(ANFIS)is a novel technique for liquid level regulation in an inter-connected spherical tank system to avoid interferences and achieve better performance in comparison of rise time,settling time,and overshoot decrease.Evaluating the simulated results acquired by the controller yields the efficiency of the proposed system.The simulated results were produced using MATLAB 2018 and the FOMCON toolbox.Finally,the performance of the conventional controller(FOPID,PID-SMC)and proposed ANFIS based SMC-FOPID control-lers are compared and analyzed the performance indices.

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

基于分数阶滑模控制的无人机轨迹跟踪控制器设计

四旋翼无人机在农业、工业和国防等领域广泛应用,但其复杂的系统特性和对扰动的敏感性使得控制变得困难。首先,考虑分数阶方法具有良好的鲁棒性以及调节灵活性的优点,将整数阶积分滑模面和改进的分数阶指数趋近律相结合,设计出了一种新的分数阶积分滑模控制器。然后,将所设计的分数阶积分滑模控制器应用于四旋翼无人机轨迹跟踪控制问题。仿真结果表明,所提控制器作用下的四旋翼无人机进行轨迹跟踪时响应速度快、无超调,且对外界干扰具有较强的鲁棒性。

Sprott-D不确定分数阶混沌系统的自适应滑模同步

基于非线性混沌系统滑模方法,根据分数阶稳定性理论和同步控制方法研究Sprott-D不确定分数阶系统的滑模控制与同步,并用MATLAB仿真程序对结果进行验证.结果表明,在一定的假设下,Sprott-D不确定分数阶混沌系统对应的主从系统可取得自适应滑模同步.

分数阶Rucklidge不确定混沌系统的自适应滑模同步

研究具有模型不确定及外部扰动条件下,分数阶Rucklidge系统的自适应滑模同步问题,通过设计一个滑模函数,获得分数阶Rucklidge不确定混沌系统自适应滑模同步的两个充分条件,该滑模函数可以平推到整数阶Rucklige混沌系统.用数值仿真算例检验了所得结论.

压电平台高精度自适应分数阶滑模跟踪控制

为了实现压电平台高精度指令跟踪控制,针对其存在的严重迟滞问题,本文提出了一种自适应分数阶滑模跟踪控制方法。首先,根据Duhem模型结构将分数阶算子和自适应律引入到滑模面的设计过程中,增加滑模面的自由度可变性并实现了滑模面参数的自适应调节;其次,利用不确定和干扰估计方法代替传统的滑模控制器切换项,解决了滑模控制器存在的抖振问题并提高了控制器的鲁棒性。最后,通过压电平台指令跟踪控制实验结果表明:相较于PID和传统的滑模控制方法,提出的自适应分数阶滑模控制器的指令跟踪误差减小了80%以上,在50 Hz参考指令信号下自适应分数阶滑模控制器将压电平台的平均跟踪误差降低到0.41μm。因此,自适应分数阶滑模控制方法具有更加优越的跟踪性能。

Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractionalorder system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the noncommensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally,numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time.