Fuzzy Lyapunov synthesis control of an underactuated 2DTORA system

Article type: Research Article

Authors: Gao, Bingtuan^; | Ye, Fei

Affiliations: School of Electrical Engineering, Southeast University, Nanjing, China | Jiangsu Key Laboratory of Smart Grid Technology and Equipment, Zhenjiang, China

Note: [] Corresponding author. Bingtuan Gao, School of Electrical Engineering, Southeast University, Nanjing 210096, China. E-mail: [email protected]

Abstract: The underactuated 2-dimensional translational oscillator with rotational actuator (2DTORA) system consisting of an rotational proof-mass and two unactuated translational carts is an extension version TORA which is a well-known benchmark for nonlinear control design. In this paper, dynamics of 2DTORA system is modeled and written in general affine form. And we apply fuzzy Lyapunov synthesis to design a state feedback controller to stabilize the system with partial information about dynamics by using only a linguistic description. The designed state feedback controller is nonlinear which can be simplified as the classic linear state feedback controller. The globally stability of the closed-loop system is proofed according to the second Lyapunov theorem and LaSalle's stability theorem. Simulation results demonstrate the effectiveness of the designed controller and advantages in comparison with a previously designed linear controller for the 2DTORA system.

Keywords: Underactuated systems, 2-dimensional translational oscillator with rotational actuator (2DTORA), fuzzy Lyapunov synthesis, state feedback controller

DOI: 10.3233/IFS-141337

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 581-589, 2015