A Frequency-Dependent Filter Design Approach for Norm-Optimal Iterative Learning Control and Its Fundamental Trade-Off Between Robustness, Convergence Speed, and Steady-State Error

This paper focuses on norm-optimal iterative learning control (NO-ILC) for single-input-single-output (SISO) linear time invariant (LTI) systems and presents an infinite time horizon approach for a frequency-dependent design of NO-ILC weighting filters. Because NO-ILC is a model-based learning algorithm, model uncertainty can degrade its performance; hence, ensuring robust monotonic convergence (RMC) against model uncertainty is important. This robustness, however, must be balanced against convergence speed (CS) and steady-state error (SSE). The weighting filter design approaches for NO-ILC in the literature provide limited design freedom to adjust this trade-off. Moreover, even though qualitative guidelines to adjust the trade-off exist, a quantitative characterization of the trade-off is not yet available. To address these two gaps, a frequency-dependent weighting filter design is proposed in this paper and the robustness, convergence speed, and steady-state error are analyzed in the frequency domain. An analytical expression characterizing the fundamental trade-off of NO-ILC with respect to robustness, convergence speed, and steady-state error at each frequency is presented. Compared to the state of the art, a frequency-dependent filter design gives increased freedom to adjust the trade-off between robustness, convergence speed, and steady-state error because it allows the design to meet different performance requirements at different frequencies. Simulation examples are given to confirm the analysis and demonstrate the utility of the developed filter design technique.