scholarly journals Fixed-Time Stability of the Hydraulic Turbine Governing System

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Caoyuan Ma ◽  
Chuangzhen Liu ◽  
Xuezi Zhang ◽  
Yongzheng Sun ◽  
Wenbei Wu ◽  
...  
Keyword(s):  
Control Strategy ◽  
Finite Time ◽  
Initial Conditions ◽  
Hydraulic Turbine ◽  
Fixed Time ◽  
Time Stability ◽  
Initial State ◽  
Time Control ◽  
Governing System ◽  
Water Turbine

This paper studies the problem of fixed-time stability of hydraulic turbine governing system with the elastic water hammer nonlinear model. To control and improve the quality of hydraulic turbine governing system, a new fixed-time control strategy is proposed, which can stabilize the water turbine governing system within a fixed time. Compared with the finite-time control strategy where the convergence rate depends on the initial state, the settling time of the fixed-time control scheme can be adjusted to the required value regardless of the initial conditions. Finally, we numerically show that the fixed-time control is more effective than and superior to the finite-time control.

Sub-fixed-time control for a class of second order system

2020 ◽  
pp. 014233122092100
Author(s):  
Boyan Jiang ◽  
Hua Chen ◽  
Bo Li ◽  
Xuewu Zhang
Keyword(s):  
Initial Conditions ◽  
Equilibrium Points ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
Time Stability ◽  
Time Control ◽  
Initial States ◽  
The Stability

In this paper, a new concept “sub-fixed-time stability” (SFTS) is proposed and studied, which means the states can converge to a region of equilibrium points in a fixed time for any initial states’ values. Then, a sufficient condition for it is given and proven. Though SFTS is similar to “practical fixed-time stability” (PFTS), they are not the same, and the sufficient condition for SFTS is much clearer and simpler than PFTS. Next, a sub-fixed-time controller is proposed for a class of second order system. The stability analyses are given in the case without disturbance and with disturbance, respectively. Finally, to illustrate the robustness of the proposed sub-fixed-time controller to different initial conditions, 100 numerical simulations are conducted for 100 initial states’ values.

scholarly journals Fixed-Time Feedback Control of the Hydraulic Turbine Governing System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Caoyuan Ma ◽  
Chuangzhen Liu ◽  
Xuezi Zhang
Keyword(s):  
Numerical Simulation ◽  
Hydraulic Turbine ◽  
Fixed Time ◽  
Convergence Time ◽  
Backstepping Method ◽  
Initial State ◽  
Feedback Controllers ◽  
Sign Function ◽  
Governing System ◽  
Simulation Results

Dealing with convergence time and dealing with steady state are two of the most challenging problems in the field of stability of the hydraulic turbine governing system. In this paper, we solve these two challenging problems by designing fixed-time feedback controllers. The design of the controllers is based on the fixed-time theory and backstepping method. Compared with the existing controllers for fixed-time, finite-time, and other techniques, the designed controllers make the maximum convergence time of the system unaffected by the initial state. The convergence time is also shorter. Meanwhile, they are continuous and do not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome via nonchattering control. In addition, they give the system better stability and robustness to disturbances. Finally, the numerical simulation results in this paper will contribute to a better understanding of the effectiveness and superiority of the proposed controllers.

scholarly journals Fixed-time control of delayed neural networks with impulsive perturbations

2018 ◽  
Vol 23 (6) ◽  
pp. 904-920 ◽  
Author(s):  
Jingting Hu ◽  
Guixia Sui ◽  
Xiaoxiao Lv ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Initial Conditions ◽  
Fixed Time ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Time Control ◽  
Analysis Technique ◽  
Lyapunov Function Method ◽  
Impulsive Perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis.

Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: An linear matrix inequalitie approach

2021 ◽  
pp. 107754632199759
Author(s):  
Peng Chen ◽  
Bin Wang ◽  
Yuqiang Tian ◽  
Ying Yang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Hydraulic Turbine ◽  
System Stability ◽  
Linear Matrix ◽  
Time Control ◽  
Governing System ◽  
The Stability

This article mainly studies the Mittag–Leffler stability and finite-time control of a time-delay fractional-order hydraulic turbine governing system. First, properties of the Riemann–Liouville derivative and some important lemmas are introduced. Second, considering the mechanical time delay of the main servomotor, the mathematical model of a fractional-order hydraulic turbine governing system with mechanical time delay is presented. Then, based on Mittag–Leffler stability theorem, a suitable sliding surface and finite-time controller are designed for the hydraulic turbine governing system. The system stability is confirmed, and the stability condition is given in the form of linear matrix inequalities. Finally, the traditional proportional–integral–derivative control method and an existing sliding mode control method are selected to verify the effectiveness and robustness of the proposed method. This study also provides a new approach for the stability analysis of the time-delay fractional-order hydraulic turbine governing system.

scholarly journals Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Maoxing Liu ◽  
Jie Wu ◽  
Yong-zheng Sun
Keyword(s):  
Stability Analysis ◽  
Permanent Magnet ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Stability Control ◽  
Time Stability ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

Event-triggered integral sliding mode fixed time control for trajectory tracking of autonomous underwater vehicle

2021 ◽  
pp. 014233122199438
Author(s):  
Bo Su ◽  
Hongbin Wang ◽  
Ning Li
Keyword(s):  
Trajectory Tracking ◽  
Control Strategy ◽  
Autonomous Underwater Vehicle ◽  
Sliding Mode ◽  
Fixed Time ◽  
Underwater Vehicle ◽  
Reference Trajectory ◽  
Integral Sliding Mode ◽  
Time Control ◽  
Event Triggered

In this paper, an event-triggered integral sliding mode fixed-time control method for trajectory tracking problem of autonomous underwater vehicle (AUV) with disturbance is investigated. Initially, the global fixed time stability is ensured with conventional periodic sampling method for reference trajectory tracking. By introducing fixed time integral sliding mode manifold, fixed time control strategy is expressed for the AUV, which can effectively eliminate the singularity. Correspondingly, in order to reduce the damage caused by chattering phenomenon, an adaptive fixed-time method is proposed based on the designed continuous integral terminal sliding mode (ITSM) to ensure that the trajectory tracking for AUV is achieved in fixed-time with external disturbance. In order to reduce resource consumption in the process of transmission network, the event-triggered sliding mode control strategy is designed which condition is triggered by an event. Also, Zeno behavior is avoided by proof of theoretical. It is shown that the upper bounds of settling time are only dependent on the parameters of controller. Theoretical analysis and simulation experiment results show that the presented methods can realize the control object.

scholarly journals Finite-Time H-Infinity Control of a Fractional-Order Hydraulic Turbine Governing System

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 57507-57517 ◽  
Author(s):  
Le Liu ◽  
Bin Wang ◽  
Sijie Wang ◽  
Yuantai Chen ◽  
Tasawar Hayat ◽  
...  
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Hydraulic Turbine ◽  
H Infinity ◽  
Governing System ◽  
H Infinity Control

Fixed-time trajectory tracking control for multiple nonholonomic mobile robots

2020 ◽  
pp. 014233122096641
Author(s):  
Meiying Ou ◽  
Haibin Sun ◽  
Zhenxing Zhang ◽  
Lingchun Li
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Initial Conditions ◽  
Fixed Time ◽  
Nonholonomic Mobile Robots ◽  
Trajectory Tracking Control ◽  
Adding A Power Integrator ◽  
Time Control ◽  
Power Integrator

This paper investigates the fixed-time trajectory tracking control for a group of nonholonomic mobile robots, where the desired trajectory is generated by a virtual leader, the leader’s information is available to only a subset of the followers, and the followers are assumed to have only local interaction. According to fixed-time control theory and adding a power integrator technique, distributed fixed-time tracking controllers are developed for each robot such that all states of each robot can reach the desired value in a fixed time. Moreover, the settling time is independent of the system initial conditions and only determined by the controller parameters. Simulation results illustrate and verify the effectiveness of the proposed schemes.

scholarly journals Research on trajectory tracking control of manipulator based on modified terminal sliding mode with double power reaching law

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141984789 ◽  
Author(s):  
Yan Xia ◽  
Wei Xie ◽  
Jiachen Ma
Keyword(s):  
Control Strategy ◽  
Finite Time ◽  
Sliding Mode ◽  
Practical Implementation ◽  
Sliding Surface ◽  
Initial State ◽  
Trajectory Tracking Control ◽  
Terminal Sliding Mode ◽  
Reaching Law ◽  
Terminal Sliding Surface

This article proposes a control strategy that combines the double power reaching law with the modified terminal sliding mode for tracking tasks of rigid robotic manipulators quickly and accurately. As a significant novelty, double power reaching law can reach the sliding surface in finite time when the system is in any initial state. At the same time, modified terminal sliding surface guarantees the system that position and velocity error converge to be zero approximately. In other words, the control law is able to make the system slip to the equilibrium point in a finite time and improves the speed of the system approaching and sliding modes. The simulation results demonstrate the practical implementation of the control strategy, verify its robustness of more accurate tracking and faster disturbance rejection, and weaken the chattering phenomenon more effectively compared with the conventional terminal sliding mode 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.

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