Design of Fractional Order Odd-Harmonics Repetitive Controller for Discrete-Time Linear Systems with Experimental Validations

Abstract

This paper presents a simple and straightforward design of a discrete-time fractional-order odd-harmonics repetitive controller (RC). Unlike general RC designs, the proposed method utilizes an internal model with a half-period delay and a stabilizing controller with a fractional phase lead compensator. First, the odd-harmonics internal model representing odd-harmonics frequencies is constructed by using the information of the reference’s basis period and the preferred tracking bandwidth. Secondly, an optimization problem synthesized from the stability condition of the RC closed-loop system is solved to obtain the fractional phase lead compensator. Finally, the fractional term of the stabilizing controller is realized by using a causal and stable infinite impulse response (IIR) filter, where the filter coefficients are computed by applying the Thiran formula. Simulation and experimental validation on a servomotor system are conducted to verify the effectiveness of the proposed design.

A Performance Evaluation of Repetitive and Iterative Learning Algorithms for Periodic Tracking Control of Functional Electrical Stimulation System

“…For stable minimum phase plant, the learning function is simply the inverse of 𝑃(𝑧) in (2), 𝐿(𝑧) = 1/𝑃(𝑧), as its inverse will have stable poles. Some other learning function designs can also be found in [86], [88]. Phase lead-based learning function has been proposed in [88].…”

“…Some other learning function designs can also be found in [86], [88]. Phase lead-based learning function has been proposed in [88]. Meanwhile, the work [86] introduces IIR filter-based learning functions.…”