Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control

Abstract

A discrete-time integral sliding mode control scheme is proposed to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. It will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against system uncertainties and disturbances. Chattering phenomenon and reaching phase are eliminated. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme.

A new sliding mode-based learning control for uncertain discrete-time systems

“…It has been shown from the discussions above that the proposed DSMLC (7), whose parameters are designed as in (12), is capable of driving the sliding variable vector to converge to zero, thus the closed-loop dynamics can then asymptotically converge to zero in the sliding mode. It also ensures the stability of the closed-loop system in the sliding mode with a strong robustness with respect to the uncertainties.…”

“…Among these, [11] proposed adaptive output feedback multirate SMC using a dead-zone function to estimate the bounds of uncertainties, but the switching motion still exists in the sliding mode. In addition, [12] designed a robust output tracking control for uncertain systems via discrete-time integral sliding mode, yet the zero-error convergence is lost as one stepdelayed disturbance value used to estimate the lumped uncertainties can only guarantee the stability in the vicinity of the sliding surface. These above limitations in the conventional DSMC have raised a need for the development of DSMC in the perspective of handling uncertainties and removing the chattering phenomenon in DSMC systems.…”

Dynamic Integral Sliding Mode Tracking Control for Nonlinear Uncertain Systems

“…Of all the relevant researches on uncertain system control, sliding mode control (SMC) could overcome the undesirable influence of uncertain by the structure change of controller [3][4][5], which has overcome the quality restriction of traditional control theory. Compared with other sliding mode control methods, integral sliding mode control shows a lower demand for model accuracy, while the derivatives of system outputs and its errors are not essential known quantity and longer.…”

Model following control system with time delays

“…They belong to the class of functional differential equations which are infinite dimensional and dependent on the past history of the dynamics [25]. Design of MFCS for uncertain linear systems have been proposed in [9,11,12,13,23]. In [24] the model following control problem has been formulated as an eigenstructure assignment problem, tunable CGT design scheme substantially enhances the capability of the controller to optimise model-matching errors.…”