A new control method for global stabilisation of translational oscillator with rotational actuator. Issue 5 (4th April 2019)

• Record Type: Journal Article
• Authors: Zhang, Ancai; She, Jinhua; Qiu, Jianlong; Yang, Chengdong; Alsaadi, Fawaz
• Is Part Of: International journal of systems science. Volume 50:Issue 5(2019)
• Page Start: 954
• Page End: 960
• Publication Date: 2019-04-04
• Subjects: Translational oscillator with a rotational actuator (TORA) -- underactuated system -- Lyapunov function -- Lasalle invariance principle -- global stabilisation; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2019.1586000
• Languages: English
• ISSNs: 0020-7721

Abstract

ABSTRACT: A translational oscillator with a rotational actuator (TORA) is an underactuated mechanical system with two degrees of freedom. This paper presents a new method to solve the global stabilisation control problem for this underactuated system. First, a set of suitable state variables is chosen for the TORA. It transforms the system into a cascade affine nonlinear system. Then, a positive-definite Lyapunov function is constructed based on the structural characteristics of the system. A control law is designed to guarantee that the derivative of the Lyapunov function is non-positive. Finally, the global stability of the closed-loop control system is analysed using the Lasalle invariance principle. The condition on the control parameters is presented to globally stabilise the TORA at the origin. The effectiveness and robustness of the method are verified by a numerical example.