This paper investigates fast finite-time control of nonlinear dynamics using terminal sliding-mode (TSM) scheme. Some new norms of fast TSM strategies are proposed, and a faster convergence rate is established in comparison with the conventional fast TSM. A novel concept of nonsingular fast TSM, which is able to avoid the possible singularity during the control phase, is adopted in the robust high-precision control of uncertain nonlinear systems. Numerical simulation on a two-link rigid robot manipulator demonstrates the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley & Sons, Ltd.

Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems

Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty

Traffic problems such as pollution and congestion are becoming more and more serious in urban areas. A potential solution to these problems is to develop narrow vehicles that occupy less space and have lower emissions. There has been increasing interest in underactuated mechanical systems, i.e., mobile wheeled inverted pendulum (MWIP) models, which are widely used in the field of autonomous robotics and intelligent narrow vehicles. A novel narrow vehicle based on an MWIP and a movable seat, called UW-Car, is investigated in this paper. The dynamic model of the underactuated vehicle system running on flat ground is derived by Lagrange's equation of motion. Based on the dynamic model and terminal sliding mode control method, two terminal sliding mode controllers are designed to control velocity and braking of the UW-Car. The first one is used to control the forward speed to a desired value while keeping the body upright and the seat on some fixed position. The second one is a switching sliding mode controller, composed of three terminal sliding mode controllers that quickly brakes the system according to an optimal braking scheme. All the control algorithms are tested in both Matlab simulation and a UW-Car experiment. The simulation and experimental results demonstrate the efficiency of the model and controllers.

Modeling and Velocity Control for a Novel Narrow Vehicle Based on Mobile Wheeled Inverted Pendulum

Payload variations, friction, and external disturbances deteriorate the control performance of linear motor (LM) positioners. To provide high-speed and high-precision performance for the LM, an adaptive recursive terminal sliding-mode (ARTSM) controller is proposed in this article. For the controller, a fast nonsingular terminal sliding function and a recursive integral terminal sliding function are developed in a recursive structure such that the sliding surfaces are arrived successively and ultimately the tracking error can converge to zero in a finite time. Furthermore, by setting an appropriate initial value for the integral element of the ARTSM controller, the control system is enforced to start on the sliding surface at the initial time such that the reaching time is reduced. Stability analysis is presented to prove the finite-time convergence and zero tracking error of the closed-loop system under the proposed ARTSM controller. Experimental results also demonstrate the effectiveness of the controller in terms of significantly reduced tracking errors and faster disturbance rejection in comparison with a recently reported fast nonsingular terminal sliding-mode (FNTSM) controller for the LM positioner.

Finite-Time Control of a Linear Motor Positioner Using Adaptive Recursive Terminal Sliding Mode

A new dynamic terminal sliding mode control (DTSMC) technique is proposed for a class of single-input and single-output (SISO) uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.

A novel dynamic terminal sliding mode control of uncertain nonlinear systems

In this paper, a terminal sliding mode control scheme is proposed for second-order nonlinear uncertain systems. By using a function augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. In addition, the proposed scheme eliminates the reaching phase problem so that the closed-loop system always shows the invariance property to parameter uncertainties. Copyright © 1999 John Wiley & Sons, Ltd.

Kang-Bark Park

Papers

Terminal sliding mode control of second‐order nonlinear uncertain systems