Intelligent measurement and compensation of linear motor force ripple: a projection-based learning approach in the presence of noise

Due to their structural simplicity, linear motors are increasingly receiving attention for use in high velocity and high precision applications. The force ripple, as a space-periodic disturbance, however, would deteriorate the achievable dynamic performance. Conventional force ripple measurement approaches are time-consuming and have high requirements on the experimental conditions. In this paper, a novel learning identification algorithm is proposed for force ripple intelligent measurement and compensation. Existing identification schemes always use all the error signals to update the parameters in the force ripple. However, the error induced by noise is non-effective for force ripple identification, and even deteriorates the identification process. In this paper only the most pertinent information in the error signal is utilized for force ripple identification. Firstly, the effective error signals caused by the reference trajectory and the force ripple are extracted by projecting the overall error signals onto a subspace spanned by the physical model of the linear motor as well as the sinusoidal model of the force ripple. The time delay in the linear motor is compensated in the basis functions. Then, a data-driven approach is proposed to design the learning gain. It balances the trade-off between convergence speed and robustness against noise. Simulation and experimental results validate the proposed method and confirm its effectiveness and superiority.