Enhanced discrete‐time sliding mode strategy with application to piezoelectric actuator control

Abstract

This study presents a new discrete-time sliding mode control (DSMC) scheme with applications to precise motion control of piezoelectric actuators. Different from existing DSMC algorithms whose implementations rely on the construction of state observers for providing the state feedback, a simple yet effective DSMC strategy is developed based on a discrete-time model without using the state observer. Hence, one distinctive feature of the proposed DSMC lies in that it is very easy to implement. Only a second-order plant model is needed whereas the modelling of piezoelectric non-linearities is not required, which further simplifies the practical implementation process. The local stability of the closed-loop system is proved in theory and the effectiveness of the DSMC is demonstrated by several experimental studies. Results show that the DSMC strategy is superior to proportional-integral-derivative control in terms of transient response speed, positioning accuracy and robustness against external disturbances. The reported method can be extended for precise motion control of other second-order systems as well.

Discrete Sliding Mode Control Design for Piezoelectric Actuator

“…x(t) = 1 where k represents the kth time step. Therefore, substituting the equations (3), (4) into equation 2, we have the equivalent discrete time dynamics equation [30] mx…”

A new LMI-based robust Sliding Mode Control for the uncertain discrete-time systems

“…Note that in [26] another framework is used to deal with the uncertain inequality in (9) and convert it to an LMI. Here, our proposed method removed the stability assumption in [26] and also improved the conservatism of the control method in [26].…”

Validation of an integral sliding mode control for optimal control of a three blade variable speed variable pitch wind turbine

“…SMC and ISMC are implemented based on single mass WT model. Discrete time sliding mode control (DSMC) is applied to precise motion of piezoelectric actuators [23]. Without using the state observer model DSMC is developed.…”