Adaptive repetitive control of a linear oscillating motor under periodic hydraulic step load

A linear oscillating motor has a direct and efficient linear motion output and is widely used in linear actuation systems. The motor is often applied to compact hybrid electrohydraulic actuators to drive a linear pump. However, the periodic switch of the rectification valve in the pump brings the hydraulic step load to the linear motor, which causes periodic oscillation waveform distortions. The distortion results in the reduction of pumping capacity. The conventional feedback proportional-integral-derivative control is applied to the pump, however, this solution cannot handle the step load as well as resolving nonlinear properties and uncertainties. In this paper, we introduce a nonlinear model to identify periodic hydraulic load. Then, the loads are broken up into a set of simple terms by Fourier series approximation. The uncertain terms and other modeling uncertainties are estimated and compensated by the practical adaptive controller. A robust control term is also developed to handle uncertain nonlinearities. The controller overcame drawbacks of conventional repetitive controllers, such as heavy memory requirements and noise sensitivity. The controller can achieve a prescribed final tracking accuracy under periodic hydraulic load via Lyapunov analysis. Finally, experimental results on the linear oscillating motor-pump are provided for validation of the effectiveness of the scheme.