A low-pass filter is essential for stabilizing strictly proper repetitive-control systems, but it inevitably degrades steady-state tracking accuracy due to gain attenuation and phase lag. This article presents a new filter design and optimization method that improves both transient response and steady-state accuracy in continuous-time repetitive-control systems. First, the gain and phase characteristics of conventional filter-based repetitive controllers are rigorously analyzed to reveal the relationship between filter parameters and tracking performance. Based on this analysis, a new filter structure is designed to precisely compensate for gain attenuation and phase delay, specifically at the fundamental frequency, by minimizing the error term without increasing the filter bandwidth. A guideline for selecting the filter parameters for varying periodic trajectories is also provided. In addition, according to the one-to-one mapping between control and learning behaviors and their respective gains, dual performance indices are constructed to account for tracking error and control effort across multiple learning cycles. A multiobjective optimization framework is then developed to directly tune these gains subject to stability constraints, achieving an optimal balance between rapid transient convergence and control energy efficiency. Experimental results validate the effectiveness and superiority of the design.
Zhang et al. (Wed,) studied this question.