Finite-time hybrid motion/deformation terminal control for rigid/compliant systems using acceleration-based quadratic objective function

Abstract

Nowadays, new concepts of active compliant structures employing smart materials are receiving increasing attention to design high-precision lightweight mechanisms, however, bring a new challenge to deformation control system design, especially considering the coupling with rigid motion control. An important issue for such a rigid/compliant system is to realize a fast, smooth hybrid motion/deformation control effect with minimized structural vibration in a given time interval. A rotating compliant manipulator actuated by an electric motor and distributed piezocomposite patches is utilized for investigation towards motion/deformation control. Open-loop simulations imply that structural vibration can be excited by both rigid motion control and deformation control. A finite-time terminal control design approach is developed using a new quadratic objective function which is formulated by (generalized) acceleration, instead of the state (composed of generalized displacement and velocity) and input of the system in regular formulation, to improve the terminal control effect without sharp change in the input profiles. The time-varying control law is obtained by solving a set of DREs. Pure and hybrid motion/deformation control with conventional and new objective functions are presented and discussed. The results imply that more smooth dynamic responses for hybrid motion/deformation control performance with minimized residual vibration can be obtained by using the new acceleration-based objective function, while the state and input at the terminal point are the approximate analytical steady-state. The new objective function also has unique merit in that the associated weighting matrix can be intuitively chosen with better robustness. Hybrid objective functions with a combination of the conventional and new acceleration-based terms can be employed to obtain favorable comprehensive control performance and bring a wider margin for the designers.