A new optimal sliding mode controller design using scalar sign function

Mithun Singla; Leang-San Shieh; Gangbing Song; Linbo Xie; Yongpeng Zhang

doi:10.1016/j.isatra.2013.09.007

A new optimal sliding mode controller design using scalar sign function

ISA Trans. 2014 Mar;53(2):267-79. doi: 10.1016/j.isatra.2013.09.007. Epub 2013 Oct 10.

Authors

Mithun Singla¹, Leang-San Shieh², Gangbing Song³, Linbo Xie⁴, Yongpeng Zhang⁵

Affiliations

¹ Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, United States. Electronic address: mithunsingla@gmail.com.
² Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, United States.
³ Department of Mechanical Engineering, University of Houston, Houston, TX 77204, United States.
⁴ Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi, Jiangsu 214122, China.
⁵ Department of Engineering Technology, Prairie View A & M University, Prairie View, TX 77446, United States.

PMID: 24119760
DOI: 10.1016/j.isatra.2013.09.007

Abstract

This paper presents a new optimal sliding mode controller using the scalar sign function method. A smooth, continuous-time scalar sign function is used to replace the discontinuous switching function in the design of a sliding mode controller. The proposed sliding mode controller is designed using an optimal Linear Quadratic Regulator (LQR) approach. The sliding surface of the system is designed using stable eigenvectors and the scalar sign function. Controller simulations are compared with another existing optimal sliding mode controller. To test the effectiveness of the proposed controller, the controller is implemented on an aluminum beam with piezoceramic sensor and actuator for vibration control. This paper includes the control design and stability analysis of the new optimal sliding mode controller, followed by simulation and experimental results. The simulation and experimental results show that the proposed approach is very effective.

Keywords: Chattering; Optimal control; Scalar sign function; Sliding mode control.