Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.

A new design of sliding mode control systems

A new sliding mode control technique for a class of SISO dynamic systems is presented in this chapter. It is seen that the stability status of the closed-loop system is first checked, based on the approximation of the most recent information of the first-order derivative of the Lyapunov function of the closed-loop system, an intelligent sliding mode controller can then be designed with the following intelligent features: (i) If the closed-loop system is stable, the correction term in the controller will continuously adjust control signal to drive the closed-loop trajectory to reach the sliding mode surface in a finite time and the desired closed-loop dynamics with the zero-error convergence can then be achieved on the sliding mode surface. (ii) If, however, the closed-loop system is unstable, the correction term is capable of modifying the control signal to continuously reduce the value of the derivative of the Lyapunov function from the positive to the negative and then drives the closed-loop trajectory to reach the sliding mode surface and ensures that the desired closed-loop dynamics can be obtained on the sliding mode surface. The main advantages of this new sliding mode control technique over the conventional one are that no chattering occurs in the sliding mode control system because of the recursive learning control structure; the system uncertainties are embedded in the Lipschitz-like condition and thus, no priori information on the upper and/or the lower bounds of the unknown system parameters and uncertain system dynamics is required for the controller design; the zero-error convergence can be achieved after the closed-loop dynamics reaches the sliding mode surface and remains on it. The performance for controlling a third-order linear system is evaluated in the simulation section to show the effectiveness and efficiency of the new sliding mode control technique.

Exact-estimator-based terminal sliding mode control system design

This paper investigates an estimator-based terminal sliding mode control system. An exact estimator is proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic levitation system to implement the control performance.

Robust fault-tolerant leader-follower control of four-wheel-steering mobile robots using terminal sliding mode

This paper addresses the actuator failure compensation problem of non-linear fourwheel-steering mobile robots based on vehicle kinematics, undergoing both known and unknown failures causing degenerated steering performance or wheels stuck at some observable angles. Terminal sliding mode control technique is used to guarantee the tracking stability infinite time with the presence of actuator fault. Simulation results are given to illustrate the effectiveness of the proposed control scheme. © Institution of Engineers Australia 2012.

DSP-based sliding-mode control for electromagnetic-levitation precise position system

This paper investigates the robust tracking control problem for a bipolar electromagnetic-levitation precise-position system. The dynamic model of the precise-position device is derived by conducting a thorough analysis on the nonlinear electromagnetic forces. Conventional sliding-mode control and terminal sliding-mode control strategies are developed to guarantee asymptotic and finite-time tracking capabilities of the closed-loop system. A lumped uncertainty estimator is proposed to estimate the system uncertainties. The estimated information is then used to construct a smooth uniformly ultimately bounded sliding-mode control. An exact estimator is also proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding-mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic-levitation system to validate the analysis.

Integral terminal sliding mode cooperative control of multi-robot networks

This paper studies the integral terminal sliding mode cooperative control of multi-robot networks. Here, we first propose an integral terminal sliding mode surface for a class of first order systems. Then, we prove that finite time consensus tracking of multi-robot networks can be achieved on this integral terminal sliding mode surface. Simulation results are presented to validate the analysis.

Dynamic output feedback sliding-mode control using pole placement and linear functional observers

This paper presents a methodological approach to design dynamic output feedback sliding-mode control for a class of uncertain dynamical systems. The control action consists of the equivalent control and robust control components. The design of the equivalent control and the sliding function are based on the pole-placement technique. Linear functional observers are developed to implement the sliding function and the equivalent control. Stability of the resulting system under the proposed control scheme is guaranteed. A numerical example is given to demonstrate its efficacy.

Estimator-based sliding mode control strategy design

This study addresses the design and properties of serial sliding mode control (SMC) systems for an induction servo motor drive to track periodic commands. It contains a SMC, an adaptive SMC (ASMC) and an estimator-based SMC (ESMC). The effectiveness of the proposed control systems is verifi ed by numerical simulations, and the superiority of the ESMC system is indicated in comparison with the SMC and ASMC systems.

A sliding-mode-control-based adaptive cruise controller

This paper presents an alternative solution to the conventional cruise controller of a hybrid electric vehicle based on the sliding mode control approach. The mathematical model of a hybrid electric vehicle cruise control system is developed. Then, the sliding mode control approach is applied as the controller. The sliding mode control stability is investigated and demonstrated. Thereafter, the system is simulated and the results are presented. © 2014 IEEE.

Navigation of four-wheel-steering mobile robots using robust fault-tolerant sliding mode control

This paper addresses the leader-follower tracking problem of a four-wheel-steering robot subjected to nonlinear uncertainties. Two control laws have been developed, based on the adaptive sliding mode method and the adaptive input-output feedback linearization method. The proposed control schemes have been tested by means of simulations.

Fast finite-time consensus of a class of high-order uncertain nonlinear systems

This paper poses and solves a new problem of consensus control where the task is to make the fixed-topology multi-agent network, with each agent described by an uncertain nonlinear system in chained form, to reach consensus in a fast finite time. Our development starts with a set of new sliding mode surfaces. It is proven that, on these sliding mode surfaces, consensus can be achieved if the communication graph has the proposed directed spanning tree. Next, we introduce the multi-surface sliding mode control to drive the sliding variables to the sliding mode surfaces in a fast finite time. The control Lyapunov function for fast finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surface. A recursive design procedure is provided, which guarantees the boundedness of the control input.

Finite-time consensus algorithm of multi-agent networks

This paper is concerned with leader-follower finite-time consensus control of multi-agent networks with input disturbances. Terminal sliding mode control scheme is used to design the distributed control law. A new terminal sliding mode surface is proposed to guarantee finite-time consensus under fixed topology, with the common assumption that the position and the velocity of the active leader is known to its neighbors only. By using the finite-time Lyapunov stability theorem, it is shown that if the directed graph of the network has a directed spanning tree, then the terminal sliding mode control law can guarantee finite-time consensus even under the assumption that the time-varying control input of the active leader is unknown to any follower.