4C13 Realization of Giant Swing Motions of a two-link horizontal bar gymnastic robot Using Delayed Feedback Control

Abstract

This paper studies the behavior of the giant swing motions of a two-link horizontal bar gymnastic robot using chaos control. Until now, the generalized method of control on such systems with non-holonomic constraints has still not been established. The delayed feedback control (DFC) of chaos, proposed by Pyragas, is well known as an effective method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, the DFC has a limitation such that it can not stabilize any systems with an odd number of real eigenvalues greater than unity. The stability analysis of continuous systems like gymnastic robot by a modified DFC method called Prediction-based DFC (PDFC) is concentrated in this paper. Firstly, a Poincare section is defined to regard the target system as a discrete-time system so that the system stability can be evaluated easierly. Meanwhile, a way to calculate analytically the error transfer matrix and the input matrix which are necessary for discretization is proposed. Secondly, the stability of the gymnastic robot system controlled by the PDFC is discussed. Finally, some simulation results show that it is effective in the control of the giant swing motions with the proposed method.