Continuous Finite-time Control Research Articles

Finite-Time Terminal Sliding Mode Tracking Control for Piezoelectric Actuators

This paper proposes a continuous finite-time control scheme using a new form of terminal sliding mode (TSM) combined with a sliding mode disturbance observer (SMDO). The proposed controller is applied for nanopositioning of piezoelectric actuators (PEAs). Nonlinearities, mainly hysteresis, can drastically degrade the system performance. Same as the model imperfection, hysteresis can also be treated as uncertainties of the system. These uncertainties can be addressed by terminal sliding mode control (TSMC) for it is promising for positioning and tracking control. To further improve the robustness of the TSM controller, the SMDO is employed to estimate the bounded disturbances and uncertainties. The robust stability of the TSMC is proved through a Lyapunov stability analysis. Simulation results demonstrate the effectiveness of the proposed TSM/SMDO controller for both positioning and tracking applications. The fast response, few chattering, and high precision positioning and tracking performances can be achieved in finite time by the proposed controller.

Continuous finite-time anti-disturbance control for a class of uncertain nonlinear systems

The continuous finite-time anti-disturbance control problem for a class of nonlinear system under external disturbances and parameter uncertainties is investigated in this article. First, a continuous terminal sliding mode control (CTSMC) is introduced to stabilize the nominal system dynamics. Concerning the unsatisfying performance of the CTSMC in the presence of severe external disturbances and parameter uncertainties, a finite-time disturbance observer (FTDO) is employed to estimate the uncertainties to its nominal dynamics. By integrating the CTSMC method with the FTDO technique, a composite controller is presented for such kind of nonlinear system under external disturbances and parameter uncertainties. The composite controller obtains finite-time convergence property in the presence of disturbances and also nominal control performance recovery in the absence of disturbances. Moreover, compared with conventional sliding mode control, the proposed control law is continuous and no chattering phenomenon exists. The property of stability and the finite-time convergence of the closed-loop system under the proposed controller is guaranteed by means of Lyapunov stability criteria. The proposed control method is finally applied for the tracking control problem of robotic manipulators. Simulation results show that the proposed method exhibits promising control performance in the presence of severe external disturbances and parameter uncertainties.

Finite‐Time Tracking Control for Nonholonomic Mobile Robots Based on Visual Servoing

AbstractThis paper investigates the finite‐time tracking problem of nonholonomic mobile robots in kinematic models via visual servoing in the presence of parametric uncertainties associated with the camera system. First of all, a camera‐objective visual kinematic model is introduced by utilizing the pinhole camera model. Second, a unified tracking error system between the camera‐objective visual servoing model and the desired reference trajectory is introduced. Third, based on the unified error dynamics and by using the finite‐time control method, continuous finite‐time controller laws are designed to solve the finite‐time tracking problem for the mobile robot in the presence of parametric uncertainties associated with the camera system. Rigorous proof shows that the desired reference trajectory can be tracked in finite time. Finally, an example is employed to verify the efficiency of the proposed methods.

Composite control method for stabilizing spacecraft attitude in terms of Rodrigues parameters

In this paper, the attitude stabilization problem of a rigid spacecraft described by Rodrigues parameters is investigated via a composite control strategy, which combines a feedback control law designed by a finite time control technique with a feedforward compensator based on a linear disturbance observer (DOB) method. By choosing a suitable coordinate transformation, the spacecraft dynamics can be divided into three second-order subsystems. Each subsystem includes a certain part and an uncertain part. By using the finite time control technique, a continuous finite time controller is designed for the certain part. The uncertain part is considered to be a lumped disturbance, which is estimated by a DOB, and a corresponding feedforward design is then implemented to compensate the disturbance. Simulation results are employed to confirm the effectiveness of the proposed approach.

Decentralized Finite Time Attitude Synchronization Control of Satellite Formation Flying

This paper investigates a quaternion-based finite time attitude synchronization and stabilization problem for satellite formation flying. Sufficient conditions are presented for finite time boundness and stability of this distributed consensus problem. More specifically, a nonlinear control law based on a finite time control technique is developed such that the attitude of the rigid spacecraft will coordinate and converge to the attitude of the leader, while the angular velocity will converge to zero in finite time. The associated stability proof is constructive and accomplished by adding a power integrator term in the Lyapunov function. Furthermore, to reduce the heavy communication burden, a modified control law is then designed by introducing a finite time sliding-mode estimator such that only one satellite has to communicate with the leader. Simulation results are presented to demonstrate the effectiveness of the designed scheme, especially the potential advantages derived through the inclusion of the continuous finite time control method, such as the fast convergent rate and the alleviation of chattering.

Composite controller design for an airbreathing hypersonic vehicle

In this paper, a tracking control problem for the longitudinal model of an airbreathing hypersonic vehicle subject to external disturbances is investigated. Based on the characteristics of the longitudinal model, the model is divided into two subsystems, including an altitude subsystem and a velocity subsystem. A novel ideal is that, for each subsystem, some nonlinear coupling terms are considered to be parts of lumped disturbances, which are estimated by a nonlinear disturbance observer, and a corresponding feedforward design is then implemented to compensate the lumped disturbances. Meanwhile, by using a finite time control technique, a continuous finite time control law is introduced in the feedback control design. Then, a composite control scheme is obtained, which consists of a feedback control law based on the finite time control technique and a feedforward compensator based on the nonlinear disturbance observer technique. This scheme can guarantee stable tracking of the reference trajectories of velocity and altitude. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method. The results show that the control performance of the proposed method in terms of both tracking and disturbance rejection are considerably better than the traditional method.

Finite-time attitude stabilization for a rigid spacecraft using homogeneous method

AbstractThis paper investigates the finite-time attitude stabilization problem for a rigid spacecraft with an unknown inertia matrix. By using homogeneous approach, a local continuous finite-time controller is first designed such that the attitude can be stabilized to the equilibrium in finite time. Then, to solve global attitude stabilization problem, a modified finite-time controller is proposed. Rigorous proof shows that the attitude can be stabilized to the equilibrium in finite time. Finally, a simulation example is given to demonstrate the efficiency of the proposed method.

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.

Stabilization of the attitude of a rigid spacecraft with external disturbances using finite-time control techniques

In this paper, we consider the attitude stabilization problem for a rigid spacecraft with external disturbances. To obtain a better disturbance rejection property, we employ finite-time control techniques. In the absence of disturbances, by employing continuous finite-time control method, a continuous finite-time controller is designed such that the attitude of the rigid spacecraft will converge to the origin in finite time. In the presence of disturbances, by employing terminal sliding mode method, a discontinuous finite-time control law is proposed such that the states will eventually converge to a small region of the origin, which can be rendered as small as desired. Numerical simulation results show the effectiveness of the method.

A NEW APPROACH TO TERMINAL SLIDING MODE CONTROL DESIGN

In this paper, terminal sliding mode control design is considered. A control method, different from many existing terminal sliding model control design methods, is proposed based on a new switching law and continuous finite-time control ideas. Then terminal sliding mode control laws are constructed for some classes of nonlinear systems.

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.

Continuous finite-time control for robotic manipulators with terminal sliding mode

A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method.