Title: Sliding mode control with PI-based saturation for nano-positioning

Authors: Liu Yang; Donghao Xu

Addresses: College of Automation, Harbin University of Science and Technology, Heilongjiang Sheng, China ' College of Automation, Harbin University of Science and Technology, Heilongjiang Sheng, China

Abstract: This paper proposes a modified sliding mode controller with proportion-integral (Pl)-based saturation (PISSMC) for nano-positioning of Piezoelectric Actuators (PEAs). Based on the sliding mode theory, the controller can consider hysteresis as the uncertainty of the system, which the non-linearities of hysteresis and model imperfection can be processed to achieve precise positioning and tracking control. The PI term of this controller can decrease the steady-state error of the system and alleviate the chattering of the discontinuous part of the Sliding Mode Controller (SMC). Further, as the only measurable information is the position state, a high-gain observer is adopted to estimate the other states. The designed controller employs a linear PEA system as parameters estimation of the model to estimate the control gain and compensate for the process non-linearity. The robust stability of the PISSMC is proved through a Lyapunov stability analysis. Experimental results demonstrate that compared with the traditional SMC, the proposed controller can accomplish better control performance, such as more accurate resolution, less steady-state error and slighter chattering.

Keywords: sliding mode control; PEAs; piezoelectric actuators; hysteresis; nano-positioning; non-linear system.

DOI: 10.1504/IJWMC.2019.099859

International Journal of Wireless and Mobile Computing, 2019 Vol.16 No.3, pp.204 - 210

Received: 25 Apr 2018
Accepted: 26 Aug 2018
Published online: 24 May 2019 *

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