scholarly journals Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Wang ◽  
Lin Yin ◽  
Shaojie Wang ◽  
Shirui Miao ◽  
Tantan Du ◽  
...  
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Distributed Model ◽  
Finite Time Stability ◽  
Time Control ◽  
Governing System ◽  
Terminal Sliding Surface ◽  
Frequency Distributed Model

This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS). Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

scholarly journals Design of a Finite-Time Terminal Sliding Mode Controller for a Nonlinear Hydro-Turbine Governing System

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 634
Author(s):  
Tianyu Yang ◽  
Bin Wang ◽  
Peng Chen
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Nonlinear Mathematical Model ◽  
Terminal Sliding Mode ◽  
Finite Time Stability ◽  
Hydro Turbine ◽  
Time Control ◽  
Governing System ◽  
Mathematical Derivation

We focus on the finite-time control of a hydro-turbine governing system (HGS) in this paper. First, the nonlinear mathematical model of the hydro-turbine governing system is presented and is consistent with the actual project. Then, based on the finite-time stability theory and terminal sliding mode scheme, a new finite-time terminal sliding mode controller is designed for the hydro-turbine governing system and a detailed mathematical derivation is given. Only three vector controllers are required, which is less than the HGS equation dimensions and is easy to implement accordingly. Furthermore, numerical simulations for the proposed scheme and an existing sliding mode control are presented to verify the validity and advantage of improving transient performance. The approach proposed in this paper is simple and provides a reference for relevant hydropower systems.

Finite Time Control of a Fractional Order Hydro-Turbine Governing System With Load Rejection

2021 ◽  
Author(s):  
Peng Chen ◽  
Bin Wang
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Servo System ◽  
The State ◽  
Hydro Turbine ◽  
Time Control ◽  
Governing System ◽  
Hydraulic Servo ◽  
Hydraulic Servo System

Abstract This study focuses on the finite time control of a fractional order hydro-turbine governing system (HGS) with load rejection. First, the hydraulic servo system has significant historical reliance. Since it is a powerful advantage for fractional calculus to describe the function which has significant historical reliance, the fractional order hydraulic servo system is adopted and the more actual fractional order hydro-turbine governing system is presented. Second, some definitions and properties are given, and the state trajectories of HGS with load rejection is observed. The simulation results show that the state trajectory of the system is not stable, so it is necessary to design a controller with better control effect. Third, based on the frequency distribution model, the equivalent transformation model of HGS is presented. A new finite time sliding mode control scheme is proposed for the stability control of the HGS with load rejection. Furthermore, the no chattering sliding mode controller and its detailed mathematical derivation are given. The system stability is proved, and the upper limit of HGS finite time stability is given. Finally, numerical simulations have verified the theoretical results. The controller can make the state trajectories of the HGS converge to zero in a finite time, and the control time is very short.

scholarly journals Finite-time control for uncertain systems and application to flight control

2020 ◽  
Vol 25 (2) ◽  
Author(s):  
Fang Wang ◽  
Jianmei Wang ◽  
Kun Wang ◽  
Changchun Hua ◽  
Qun Zong
Keyword(s):  
Flight Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Closed Loop System ◽  
Finite Time Stability ◽  
Time Control ◽  
Control Scheme ◽  
Mismatched Uncertainty

In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller.

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.

Super-twisting integral-sliding-mode guidance law considering autopilot dynamics

2017 ◽  
Vol 232 (9) ◽  
pp. 1787-1799 ◽  
Author(s):  
Kezi Meng ◽  
Di Zhou
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Guidance System ◽  
Integral Sliding Mode ◽  
Finite Time Stability ◽  
Guidance Law ◽  
Chattering Free ◽  
Twisting Algorithm

A new guidance law considering missile autopilot dynamics is established via integrating a smooth super-twisting algorithm with nonlinear integral sliding mode. In this guidance law, a finite-time disturbance observer is introduced to estimate mismatched and matched disturbances resulting from target maneuvers. Based on Lyapunov stability theory, the finite-time stability of the closed-loop guidance system under this law is analyzed using a finite-time bounded function. The super-twisting algorithm guarantees that the proposed guidance law is chattering-free and the disturbance observer does not depend on the prior knowledge of target acceleration. So the proposed guidance law is easy to be implemented in practice. The finite-time convergence and robustness of the proposed guidance law are demonstrated via numerical simulations accounting for missile autopilot dynamics.

scholarly journals Robust Finite-Time Control Algorithm Based on Dynamic Sliding Mode for Satellite Attitude Maneuver

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 111
Author(s):  
You Li ◽  
Haizhao Liang
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Control ◽  
Satellite Attitude ◽  
Attitude Maneuver ◽  
Mode Parameter ◽  
Fixed Axis ◽  
System Robustness

Robust finite-time control algorithms for satellite attitude maneuvers are proposed in this paper. The standard sliding mode is modified, hence the inherent robustness could be maintained, and this fixed sliding mode is modified to dynamic, therefore the finite-time stability could be achieved. First, the finite -time sliding mode based on attitude quaternion is proposed and the loose finite-time stability is achieved by enlarging the sliding mode parameter. In order to get the strict finite-time stability, a sliding mode based on the Euler axis is then given. The fixed norm property of the Euler axis is used, and a sliding mode parameter without singularity issue is achieved. System performance near the equilibrium point is largely improved by the proposed sliding modes. The singularity issue of finite-time control is solved by the property of rotation around a fixed axis. System finite-time stability and robustness are analyzed by the Lyapunov method. The superiority of proposed controllers and system robustness to some typical perturbations such as disturbance torque, model uncertainty and actuator error are demonstrated by simulation results.

Chattering-Free Finite-Time Stability of a Class of Fractional-Order Nonlinear Systems

2019 ◽  
Author(s):  
Bin Wang ◽  
Yangquan Chen ◽  
Ying Yang
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Stability ◽  
External Disturbances ◽  
Finite Time Stability ◽  
Mode Control ◽  
Chattering Free

Abstract This paper studies the chattering-free finite-time control for a class of fractional-order nonlinear systems. First, a class of fractional-order nonlinear systems with external disturbances is presented. Second, a new finite-time terminal sliding mode control method is proposed for the stability control of a class of fractional-order nonlinear systems by combining the finite-time stability theory and sliding mode control scheme. Third, by designing a controller with a differential form and introducing the arc tangent function, the chattering phenomenon is well suppressed. Additionally, a controller is developed to resist external disturbances. Finally, numerical simulations are implemented to demonstrate the feasibility and validity of the proposed method.

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.

Finite-Time Tracker Design for Uncertain Nonlinear Fractional-Order Systems

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Tahereh Binazadeh
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Reference Signal ◽  
Convergence Time ◽  
Time Varying ◽  
Terminal Sliding Mode ◽  
Output Tracking ◽  
Time Control ◽  
Sliding Manifold

This paper considers the problem of finite-time output tracking for a class of nonautonomous nonlinear fractional-order (FO) systems in the presence of model uncertainties and external disturbances. The finite-time control methods indicate better properties in terms of robustness, disturbance rejection, and settling time. Thus, design of a robust nonsingular controller for finite-time output tracking of a time-varying reference signal is considered in this paper, and a novel FO nonsingular terminal sliding mode controller (TSMC) is designed, which can conquer the uncertainties and guarantees the finite-time convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate nonsingular terminal sliding manifold is designed, where maintaining the system's states on this manifold leads to finite-time vanishing of error signal (i.e., ensures the finite-time occurrence of both reaching and sliding phases). Moreover, by tacking the fractional derivative of the sliding manifold, the convergence of system's trajectories into the terminal sliding manifold in a finite time is proven, and the convergence time is estimated. Finally, in order to verify the theoretical results, the proposed method is applied to an FO model of a horizontal platform system (FO-HPS), and the computer simulations show the efficiency of the proposed method in finite-time output tracking.

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