Delay-independent sliding mode control of time-delay linear fractional order systems

2016 ◽  
Vol 40 (4) ◽  
pp. 1212-1222 ◽  
Author(s):  
M Yousefi ◽  
T Binazadeh
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Control Law ◽  
State Delay ◽  
New Approach ◽  
Mode Control ◽  
Sliding Manifold ◽  
Theoretical Results

This paper considers the problem of delay-independent stabilization of linear fractional order (FO) systems with state delay. As in most practical systems in which the value of delay is not exactly known (or is time varying), a new approach is proposed in this paper, which results in asymptotic delay-independent stability of the closed-loop time-delay FO system. For this purpose, a novel FO sliding mode control law is proposed in which its main advantage is its independence to delay. Furthermore, a novel appropriate delay-independent sliding manifold is suggested. Additionally, two theorems are given and proved, which guarantee the occurrence of the reaching phase in finite time and the asymptotic delay-independent stability conditions of the dynamic equations in the sliding phase. Finally, in order to verify the theoretical results, two examples are given and simulation results confirm the performance of the proposed controller.

scholarly journals Fractional Order Adaptive Fast Super-Twisting Sliding Mode Control for Steer-by-Wire Vehicles with Time-Delay Estimation

Electronics ◽  
2021 ◽  
Vol 10 (19) ◽  
pp. 2424
Author(s):  
Yong Yang ◽  
Yunbing Yan ◽  
Xiaowei Xu
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Time Delay Estimation ◽  
Lyapunov Theory ◽  
Delay Estimation ◽  
Mode Control ◽  
Model Free ◽  
Steer By Wire

It is difficult to model and determine the parameters of the steer-by-wire (SBW) system accurately, and the perturbation is variable with complex and changeable tire–road conditions. In order to improve the control performance of the vehicle SBW system, an adaptive fast super-twisting sliding mode control (AFST-SMC) scheme with time-delay estimation (TDE) is proposed. The proposed scheme uses TDE to acquire the lumped dynamics in a simple way and establishes a practical model-free structure. Then, a fractional order (FO) sliding mode surface and a fast super-twisting sliding mode control structure were designed on the basic super-twisting sliding mode to ensure fast convergence and high control accuracy. Since the uncertain boundary information of the actual system is unknown, a novel adaptive algorithm is proposed to regulate the control gain based on the control errors. Theoretical analysis concerning system stability is given based on the Lyapunov theory. Finally, the effectiveness of the method is verified through comparative experiments. The results show that the proposed TDE-AFST-FOSMC control scheme has the advantages of model-free, fast response and high accuracy.

Fractional sliding mode control of wind turbine for maximum power point tracking

2018 ◽  
Vol 41 (2) ◽  
pp. 447-457 ◽  
Author(s):  
Aghiles Ardjal ◽  
Rachid Mansouri ◽  
Maamar Bettayeb
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Maximum Power Point Tracking ◽  
Control Law ◽  
Maximum Power Point ◽  
Mode Control ◽  
Point Tracking ◽  
Power Point Tracking ◽  
Power Point

This paper deals with a nonlinear control algorithm based on a sliding mode theory to reach the maximum power point tracking of a variable-speed wind energy conversion system. The proposed method allows us to combine the sliding mode and fractional-order theory. The fractional-order component of the control law is introduced by a sliding surface. In order to validate this controller, fractional and integer sliding modes are developed. The proposed fractional-order sliding mode control law is tested in a Simulink/Matlab environment. The simulation results show the effectiveness of the proposed scheme, suppression of the chattering phenomenon and robustness of the proposed controller compared to the integer sliding mode control law.

scholarly journals A Novel Compound Nonlinear State Error Feedback Super-Twisting Fractional-Order Sliding Mode Control of PMSM Speed Regulation System Based on Extended State Observer

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Peng Gao ◽  
Guangming Zhang ◽  
Xiaodong Lv
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Regulation System ◽  
Control Law ◽  
Error Feedback ◽  
Mode Control ◽  
Speed Regulation ◽  
Nonlinear State ◽  
State Error

In this article, a novel compound nonlinear state error feedback super-twisting fractional-order sliding mode control (NLSEF-STFOSMC) is proposed for the control of the permanent magnet synchronous motor (PMSM) speed regulation system. Firstly, a novel fractional-order proportion integration differentiation (FOPID) switching manifold is designed. A modified sliding mode control (SMC) is constructed by a super-twisting reaching law and the novel FOPID sliding surface. Secondly, the nonlinear state error feedback control law (NLSEF) has been widely used because of high control accuracy, fast convergence, and flexible operation. Therefore, combining the modified SMC with the NLSEF, the compound NLSEF-STFOSMC is proposed, which has an excellent performance. At the same time, the external disturbance of the system is observed by a novel extended state observer. Finally, the performance of the corresponding control law to the speed operation of the PMSM is fully investigated compared with other related algorithms to demonstrate the effectiveness. The comparison results show that the proposed compound control strategy has excellent dynamic and static performance and strong robustness.

A New Result on Fractional Differential Inequality and Applications to Control of Dynamical Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Ngo Van Hoa ◽  
Tran Minh Duc ◽  
Ho Vu
Keyword(s):  
Dynamical Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Differential Inequality ◽  
Sliding Mode ◽  
Control Law ◽  
Asymptotically Stable ◽  
Mode Control ◽  
Fractional Differential

In this work, we establish a new estimate result for fractional differential inequality, and this inequality is used to derive a robust sliding mode control law for the fractional-order (FO) dynamic systems. The sliding mode control law is provided to make the states of the system asymptotically stable. Some examples are given to illustrate the results.

scholarly journals Sliding Mode Control for a Class of Sub-Systems with Fractional Order Varying Trajectory Dynamics

2015 ◽  
Vol 18 (6) ◽  
Author(s):  
Clara Ionescu ◽  
Cristina Muresan
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Control Strategy ◽  
Sliding Mode ◽  
Control Law ◽  
Mode Control ◽  
Nonlinear Mechanical ◽  
Trajectory Dynamics

AbstractIn this paper, a sliding mode control strategy is discussed for a class of nonlinear mechanical sub-systems with varying trajectory dynamics. The proposed class of sub-systems are represented in this simulation example by a two link robot actuator/manipulator. The fractional order is introduced in the setpoint definition as to represent changes in the desired trajectory of this sub-system. Furthermore, the same order is used to adapt the control law to the new dynamics. Uncertainties are introduced in the model used for the control law, hence robustness is intrinsic.

scholarly journals Discrete-Time Sliding Mode Control for Uncertain Networked System Subject to Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Saulo C. Garcia ◽  
Marcelo C. M. Teixeira ◽  
José Paulo F. Garcia ◽  
Uiliam N. L. T. Alves ◽  
Jean M. S. Ribeiro
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Discrete Time ◽  
Uncertain Systems ◽  
Sliding Mode ◽  
Delay System ◽  
Control Law ◽  
Time Delay System ◽  
Mode Control ◽  
Uncertain Time

We deal with uncertain systems with networked sliding mode control, subject to time delay. To minimize the degenerative effects of the time delay, a simpler format of state predictor is proposed in the control law. Some ultimate bounded stability analyses and stabilization conditions are provided for the uncertain time delay system with proposed discrete-time sliding mode control strategy. A numerical example is presented to corroborate the analyses.

Sliding Mode Based LMI Criterion for Robust Stabilization of Uncertain Fractional Order Nonlinear Systems

2013 ◽  
Author(s):  
Sara Dadras ◽  
YangQuan Chen
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Control Technique ◽  
Control Law ◽  
Mode Control ◽  
Systems Model ◽  
Control Scheme

A robust sliding mode control (SMC) technique is introduced in this paper for a class of fractional order (FO) nonlinear dynamical systems. Using the sliding mode control technique, a sliding surface is determined and the control law is established. A new LMI criterion based on the sliding mode control law is derived to make the states of the FO nonlinear system asymptotically gravitate toward the origin which can work for any order of the system, 0<q<2. The designed control scheme can also control the uncertain FO nonlinear systems, i.e. the controller is robust against the system uncertainty and guarantees the property of asymptotical stability. The advantage of the method is that the control scheme does not depend on the order of systems model and it is fairly simple. So, there is no complexity in the application of our proposed method. An illustrative simulation result is given to demonstrate the effectiveness of the proposed robust sliding mode control design.

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