Control system design for a class of non-cascade nonlinear under-actuated systems with an application to a rotary crane system

Abstract

For cascade under-actuated systems, several effective control methods have been established. For non-cascade under-actuated systems with one under-actuation degree, several control methods, such as cascade transformation and energy-based control, have been studied. For non-cascade nonlinear under-actuated systems with two or more under-actuation degrees, approximate linearization is necessary to apply these methods, thus only stability at the equilibrium point has been guaranteed. In this paper, control system design and stability analysis are presented for a class of non-cascade nonlinear under-actuated systems with two or more under-actuated degrees. The stability condition obtained in the analysis is a conservative sufficient condition because norm estimation is used. Based on the sufficient condition, we propose a stabilization parameter search algorithm to numerically obtain the practical control parameters. The proposed algorithm is applied to a rotary crane system as one of the nonlinear systems with two under-actuated degrees. The effectiveness of the proposed control system design is verified by numerical simulations and experiments.