Non-linear composite control with applications to 3-DOF planar motor

Abstract

A 3-DOF (degree of freedom) planar motion motor using multiple linear motors as actuators is widely implemented in ultra-precision positioning systems. It is a multi-input multi-output (MIMO) system and requires an accurate decoupled model for controller design. In practice, there are modelling errors between the nominal model and the actual model, such as the force ripple, inhomogeneous air-gap thickness, measurement noise and uncertain disturbances. Due to the modelling errors, this MIMO system cannot be decoupled and the desired tracking performance specifications will not be achieved. In order to improve the servo performance of the planar motor with uncertainties, a non-linear composite controller consisting of u1 and u2 terms is proposed. u1 is designed to compensate for the modelling errors; therefore the coupling effects between multi-degrees of freedom are reduced and the robustness is improved. In order to reduce the large servo error amplitudes, which are caused by the low-frequency disturbances and high-frequency noise, an amplitude-based variable-gain function is applied in u2; thus the control action benefits from this operation by suppressing the low-frequency contribution and no extra control effect, to avoid the high-frequency noise. The convergence and stability of the control law are guaranteed by Lyapunov stability theory. The trajectory tracking experimental results show that the proposed control method has superior tracking performance and positioning ability compared with the well-known inverse dynamics controller. This indicates that the non-linear composite controller is an attractive approach to improve the servo performance of a system with uncertainties.