Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

2020 ◽  
Vol 42 (13) ◽  
pp. 2423-2439
Author(s):  
Shabnam Pashaei ◽  
Mohammad Ali Badamchizadeh
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Estimation Error ◽  
Design Procedure ◽  
Lyapunov Stability Theory ◽  
Fast Response ◽  
Sliding Mode Controller ◽  
Fractional Order Systems ◽  
Mismatched Disturbances

This paper presents a new fractional-order sliding mode controller (FOSMC) for disturbance rejection and stabilization of a class of fractional-order systems with mismatched disturbances. To design this control strategy, firstly, a fractional-order extended disturbance observer (FOEDO) is proposed to estimate the matched and mismatched disturbances and their derivatives. Then, according to the design procedure of the sliding mode controller and based on the designed FOEDO, a proper sliding mode surface is proposed. Subsequently, the proposed FOSMC is designed to guarantee that the system states reach the sliding surface and stay on it forever. The stability of the controlled fractional-order systems is proved via fractional-order Lyapunov stability theory. The numerical examples are used to illustrate the effectiveness of the proposed fractional-order controller. The simulation results of the proposed FOSMC are compared with the results of some other researchers’ works to show the superiority of the proposed control method. The new approach displays some attractive features such as fast response, the chattering reduction, robust stability, less disturbance estimation error, the mismatched disturbance, noise rejection, and better control performance.

Fixed-time fractional-order sliding mode control for nonlinear power systems

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1425-1434 ◽  
Author(s):  
Sunhua Huang ◽  
Jie Wang
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Fixed Time ◽  
Sliding Mode Controller ◽  
Mode Control ◽  
Time Control

In this study, a fractional-order sliding mode controller is effectively proposed to stabilize a nonlinear power system in a fixed time. State trajectories of a nonlinear power system show nonlinear behaviors on the angle and frequency of the generator, phase angle, and magnitude of the load voltage, which would seriously affect the safe and stable operation of the power grid. Therefore, fractional calculus is applied to design a fractional-order sliding mode controller which can effectively suppress the inherent chattering phenomenon in sliding mode control to make the nonlinear power system converge to the equilibrium point in a fixed time based on the fixed-time stability theory. Compared with the finite-time control method, the convergence time of the proposed fixed-time fractional-order sliding mode controller is not dependent on the initial conditions and can be exactly evaluated, thus overcoming the shortcomings of the finite-time control method. Finally, superior performances of the fractional-order sliding mode controller are effectively verified by comparing with the existing finite-time control methods and integral order sliding mode control through numerical simulations.

scholarly journals CentrifugationSynchronization Control of Fractional Order Chaotic Systems Based on Memristor and Its Hardware Implementation

2021 ◽  
pp. 289-297
Author(s):  
Zhaohan zhang, Huiling Jin
Keyword(s):  
Fractional Order ◽  
Hardware Implementation ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Controlled System ◽  
Integer Order ◽  
The Stability ◽  
Dynamic Phenomena

This paper studies the synchronization control of fractional order chaotic systems based on memristor and its hardware implementation. This paper takes the complex dynamic phenomena of memristor turbidity system as the research background. Starting with the integer order memristor system, the fractional order form is derived based on the integer order turbid system, and its dynamics is deeply studied. At the same time, the turbidity phenomenon is applied to the watermark encryption algorithm, which effectively improves the confidentiality of the algorithm. Finally, in order to suppress the occurrence of turbidity, a fractional order sliding mode controller is proposed. In this paper, the sliding mode controller under the function switching control method is established, and the conditions for the parameters of the sliding mode controller are derived. Finally, the experimental results analyze the stability of the controlled system under different parameters, and give the corresponding time-domain waveform to verify the correctness of the theoretical analysis.

Fractional-order adaptive controller for chaotic synchronization and application to a dual-channel secure communication system

2019 ◽  
Vol 33 (24) ◽  
pp. 1950290 ◽  
Author(s):  
Ye Li ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Fractional Order ◽  
Communication System ◽  
Secure Communication ◽  
Sliding Mode ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Sliding Mode Controller ◽  
Terminal Sliding Mode ◽  
Dual Channel

A novel fractional-order adaptive non-singular terminal sliding mode control (FONTSMC) method is investigated for the synchronization of two nonlinear fractional-order chaotic systems in the presence of external disturbance. The proposed controller consists of a fractional-order non-singular terminal sliding mode surface and an adaptive gain adjusted with sliding surface. Based on Lyapunov stability theory and stability theorem for fractional-order dynamic systems, the controlled system’s stable synchronization is guaranteed. A dual-channel secure communication system is presented to transmit useful signals based on the proposed synchronization controller. Finally, numerical simulations and comparison with fractional-order PID controller, fractional-order PD sliding mode controller and adaptive terminal sliding mode controller are given to demonstrate the effectiveness and the robustness of the proposed FONTSMC control. The application of the proposed synchronization method is studied in the dual-channel secure communication.

scholarly journals A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmadreza Haghighi ◽  
Roveida Ziaratban
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Controller Design ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Slip Surface ◽  
Direct Method ◽  
Distributed Model ◽  
Sliding Mode Controller

Abstract In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering and undesirable vibration effects. The advantages of the proposed control method are rapid convergence to the equilibrium point, the absence of chattering and unwanted oscillations, high resistance to uncertainties, and the possibility of applying this method to most fractional order chaotic systems. We applied the direct method of Lyapunov stability theory and the frequency distributed model to prove the stability of the slip surface and closed loop system. Finally, we simulated this method on two commonly used and practical chaotic systems and presented the results.

Continuous dynamic sliding mode control of converter-fed DC motor system with high order mismatched disturbance compensation

2020 ◽  
Vol 42 (14) ◽  
pp. 2812-2821 ◽  
Author(s):  
Arshad Rauf ◽  
Shihua Li ◽  
Rafal Madonski ◽  
Jun Yang
Keyword(s):  
High Performance ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
High Order ◽  
Engineering Practice ◽  
Sliding Mode Controller ◽  
Multiple Sources ◽  
Continuous Dynamic ◽  
Dynamic Sliding Mode

The combination of DC-DC buck power converters with DC motors for generating the so-called smooth start of drives has many advantages in engineering practice. Achieving high performance of such systems is, however, limited by the influence of disturbances/uncertainties of multiple sources. Some of the disturbances are mismatched, which makes them even more difficult to handle. Furthermore, the relatively high order of system dynamics makes the control design challenging. In this paper, a control structure with continuous dynamic sliding mode controller with a finite-time disturbance observer is proposed to address these practical issues. First, a special state transformation is applied, aggregating the acting disturbances/uncertainties in a sole perturbing term of the system expressed in new coordinates. Then, the observer estimates in real time the information about the lumped disturbances based on already available input/output signals and the obtained estimated signals (and their high order time-derivatives) are used to construct a sliding surface. Finally, the sliding mode controller is applied to achieve high performance of the resultant plant dynamics and to robustify the governing scheme against modelling discrepancies. The stability of the closed-loop system is proved here using Lyapunov stability theory and the efficiency of the proposed control method is validated through a multi-criteria numerical simulation.

scholarly journals Smooth Fractional Order Sliding Mode Controller for Spherical Robots with Input Saturation

2020 ◽  
Vol 10 (6) ◽  
pp. 2117
Author(s):  
Ting Zhou ◽  
Yu-gong Xu ◽  
Bin Wu
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Input Saturation ◽  
Sliding Mode Controller ◽  
Spherical Robot ◽  
Closed Loop System ◽  
Hierarchical Sliding Mode ◽  
Sliding Mode Controllers ◽  
Globally Stable

This study considers the control of spherical robot linear motion under input saturation. A fractional sliding mode controller that combines fractional order calculus and the hierarchical sliding mode control method is proposed for the spherical robot. Employing this controller, an auxiliary system in which a filter was used to gain smooth control performance was designed to overcome the input saturation. Based on the Lyapunov stability theorem, the closed-loop system was globally stable and the desired state was achieved using the fractional sliding mode controller. The advantages of the proposed controller are illustrated by comparing the simulation results from the fractional order sliding mode controllers and the integer order controller.

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