A New Sliding Function for Discrete Predictive Sliding Mode Control of Time Delay Systems

Abstract

The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities (LMIs). Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.

Sliding mode predictive vibration control of a piezoelectric flexible plate

“…where c should be chosen to ensure cH ≠ 0 , and c 1 can be confirmed specifically according to (Nizar et al, 2013). x ( k ) is the state system vector of the k th sampling time, including the measured displacements using laser displacement sensors, and their derivative with respect to time.…”

“…x(k) is the state system vector of the kth sampling time, including the measured displacements using laser displacement sensors, and their derivative with respect to time. Then, the value of the sliding mode function on time k + p is (Nizar et al, 2013)…”

Second order sliding mode control for discrete decouplable multivariable systems via input-output models

“…In this case, we assumed that condition (6) was satisfied. The simulation results of the system controlled by the controller defined in (6) are shown in Figs. 6−8.…”

Robust Sliding Mode Predictive Control of Uncertain Networked Control System with Random Time Delay

“…In the first step, a sliding surface is designed, to which the plants dynamics is restricted during the sliding phase. In the second step, a control law is designed so that the system trajectory can converge to the sliding surface in finite time [10]. However, because of the existence of inertia and the limitation of control force, when system state reaches the designed sliding surface, it will not slide stably on the sliding surface as expected, but 2 Discrete Dynamics in Nature and Society will move in a zigzag path along the sliding surface, which is known as chattering.…”