Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode

Abstract

This paper proposes a novel recursive terminal sliding mode structure for tracking control of third-order chained–form nonholonomic systems in the presence of the unknown external disturbances. Finite-time convergence of the disturbance approximation error is guaranteed using the designed disturbance observer. Under the proposed terminal sliding model tracking control technique, the finite-time convergence of the states of the closed-loop system is guaranteed via Lyapunov analysis. A new reaching control law is proposed to guarantee the existence of the sliding mode around the recursive TSM surface in a finite-time. Simulation results are illustrated on a benchmark example of third-order chained-form nonholonomic systems: a wheeled mobile robot. The results demonstrate that the proposed control technique achieves promising tracking performance for nonholonomic systems.

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

“…Sliding mode control (SMC) as an effective robust control technique that has been successfully applied to control or track certain linear and nonlinear systems such as robotic manipulators [11], nonholonomic systems [12], aircraft [13], underwater vehicles [14], spacecraft [15], flexible space structures [16], chaotic systems [17], electrical motors [18] and power systems [19]. The significant features of SMC are the fast response, robustness against uncertainties, insensitivity to the bounded disturbances, good transient performance and computational easiness with respect to other robust control methods [20][21][22]. The procedure of SMC design can be divided into two phases, namely, the sliding phase and the reaching phase.…”

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

“…A recursive FTSMC technique for tracking control of nonholonomic systems in the chained form is proposed in [29], where the tracking errors are allowed to decay to the origin in the nite time with an exponential decay rate. A disturbance-observer-based recursive TSMC tracker is presented in [30] for the nite-time tracking control of third-order non-holonomic systems with unknown external disturbances. An adaptive FTSMC technique combined with GSM scheme is suggested in [31] for the tracking problem of uncertain nonlinear third-order systems.…”

“…A Linear Matrix Inequalities (LMI)-based second-order FTSMC method is investigated in [32] for the tracking control of nonlinear uncertain systems with matched and mismatched uncertainties. However, the singularity problem is not fully resolved in [26][27][28][29][30]. In [33], the robust synchronization problem of disturbed chaotic systems is investigated, where, using an LMI-based disturbance observer, the boundedness conditions of disturbance errors are satis ed.…”

A New Fuzzy Sliding Mode Controller with a Disturbance Estimator for Robust Vibration Control of a Semi-Active Vehicle Suspension System

“…The ability to reach the sliding surface and keep system states on this surface indicates the performance quality of the SMC. In various systems, this ability can be accomplished by integrating the SMC with the FL, named, a fuzzy sliding mode controller (FSMC) [27][28][29][30][31]. As is well known, the fuzzy system is a kind 2 of 20 of approximated function with a high degree of flexibility.…”

“…For example, the fuzzy system is used to approximate unknown functions, while the sliding mode approach adds the possibility of establishing stable adaptation laws [32]. Therefore, as a type of robust controller with strong points, FSMC has been widely used in many application fields [27][28][29][30][31]. In addition, the design of a FSMC and estimator (or observer) for external disturbances can be independently carried out [15,33].…”