The optimal design of repetitive controllers based on inverse frequency response

Abstract

AbstractThis article presents a complete design of non‐causal finite impulse response (FIR) and infinite impulse response (IIR) compensators for repetitive control. The concept of repetitive controllers involves imitating the inverse frequency response of the feedback control system by minimizing the amplitude of error propagation from one period to the next in the frequency domain. The FIR compensator design has already been presented in our previous work. However, it was not complete since some parameters, such as the number of causal gains and total number of gains were still left open for the designers to select. This work provides a reasonable suggestion on how to choose parameters based on the steepest descent method. In addition, an IIR compensator is further developed based on the designed FIR design. The gains of the IIR compensator are adjusted by aiming to minimize the cost function using the steepest descent. As can be observed from the results, the IIR compensator developed from the FIR compensator cannot overcome the original FIR compensator since its learning performance is relatively slow and the extra gains added to the denominator increase memory usage when executing.