Designing Robust Repetitive Controllers

Abstract

A method for designing repetitive feedback controllers using nonparametric frequency response plant models is developed. In comparison to the zero-phase-error (ZPE) controller (ASME J. Dyn. Syst. Meas. Control, 111, pp. 353–358), this method has the added benefit of providing improved transient performance when the plant inverse is unstable. In this controller design process, a connection is made between model uncertainty and the desired frequency response of the so-called q filter. Also, it will be shown that an optimal equiripple filter is useful when designing high-order q filters. The entire process was experimentally verified on an engine control application. A repetitive controller was used to determine the dynamic fueling requirements of a fuel injected, spark-ignition engine subjected to periodic changes in the throttle position. This fueling information is necessary when designing feedforward fueling algorithms.

Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

“…Welch's method is one of the most common methods for obtaining an ETFE for RC . The plant output data is usually generated using Gaussian white‐noise excitation, although more informative input signals can be generated by experiment design, if prior information about the plant is known .…”

Low-order continuous-time robust repetitive control: Application in nanopositioning

“…Although existing work on robust RC has dealt with both uncertainties in the signal period [30,17,31,32] and the plant [7,33,34,35], such works are not immediately applicable since this work considers a known reference period, and the chosen structure of the overall control scheme and type of uncertainty differs from what has been previously studied. A tuning method to ensure robust stability for the RC scheme is therefore proposed.…”

“…Steps to improve on this situation are discussed in Section 4.2.2. By implementing Q(s) as a linear-phase FIR filter, this problem can be avoided [43,34,19], but is not an option for an analog circuit. By inspection of Fig.…”

Guaranteed cost repetitive control for uncertain discrete-time systems

“…For the continuous-time case, Weiss and Häfele [2] discussed the repetitive control of MIMO systems using H∞ design; Tsai and Yao [3] derived upper and lower bounds of the repetitive controller parameters that ensure stability and desired performance. Doh and Chung [4] presented a linear matrix inequality (LMI)-based repetitive controller design method for systems with norm-bounded uncertainties, while for the discrete-time case, Osburn and Franchek [5] developed a method for designing repetitive controllers using nonparametric frequency response plant models; Freeman et al [6] proposed an optimality-based repetitive control algorithm for timeinvariant systems; Pipeleers et al [7] proposed a novel design approach for SISO high-order repetitive controllers; She et al [8] presented a new design method for repetitive control system by employing discrete-time variable structure control algorithm.…”