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.

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.

Hyperchaos synchronization of fractional-order arbitrary dimensional dynamical systems via modified sliding mode control

2014 ◽  
Vol 76 (4) ◽  
pp. 2059-2071 ◽  
Author(s):  
Ling Liu ◽  
Wen Ding ◽  
Chongxin Liu ◽  
Huigang Ji ◽  
Chuqing Cao
Keyword(s):  
Dynamical Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Mode Control

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

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Guoliang Zhao
Keyword(s):  
Dynamical Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Terminal Sliding Mode Control ◽  
Terminal Sliding Mode ◽  
Finite Time Stability ◽  
Mode Control ◽  
Fast Terminal Sliding Mode

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.

Synchronization of Fractional-Order Hyperchaotic Finance Systems Using Sliding Mode Control Techniques

2020 ◽  
pp. 133-152
Author(s):  
Sanjay Kumar ◽  
Ram Pravesh Prasad ◽  
Krishan Pal ◽  
Mahendra Pratap Pal ◽  
Ajeet Singh
Keyword(s):  
Dynamical Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Phase Portraits ◽  
Slide Mode Control ◽  
Finance System ◽  
Control Techniques ◽  
Mode Control ◽  
Basic Concepts

In this chapter, the basic concepts of fractional-order dynamical systems are presented, and the synchronization methodologies of fractional order chaotic dynamical systems are established using slide mode control techniques. Through observation of the different phase portraits and time-series graphs of fractional order finance systems through utilization of the fractional calculus and computer simulation, the authors have obtained that the lowest dimension of fractional order hyper chaotic finance system is 3.90, which is less than 4. Bifurcation diagrams and Lyapunov exponents of fractional order hyper chaotic finance system are calculated to justify the chaos in the systems. Synchronization of two identical fractional-order hyper chaotic finance systems are achieved using sliding mode control techniques.

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.

scholarly journals Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Bao Shi ◽  
Jian Yuan ◽  
Chao Dong
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Sliding Mode Control ◽  
Fractional Differential Equations ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Law ◽  
Mode Control ◽  
Fractional Differential ◽  
Control Methodology

This paper deals with the problem of pseudo-state sliding mode control of fractional SISO nonlinear systems with model inaccuracies. Firstly, a stable fractional sliding mode surface is constructed based on the Routh-Hurwitz conditions for fractional differential equations. Secondly, a sliding mode control law is designed using the theory of Mittag-Leffler stability. Further, we utilize the control methodology to synchronize two fractional chaotic systems, which serves as an example of verifying the viability and effectiveness of the proposed technique.

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