Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

Abstract

This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

Repetitive Control based on Integral Sliding Mode Control of Matched Uncertain Systems

“…The linear repetitive process in (10) is stable along the pass if and only if there exist two symmetric positive definite matrices P and Q such that ( ) 0 k Vt  . The main goal of this paper is to make an ISMC law for the uncertain repetitive system described in (1). Details of the design process will be formulated in the next sections.…”

“…The next step consists to study the stability along the pass of the sliding mode process in (24) by designing gains controller 1 K and 2 K . Therefore, to achieve the design process, the following theorem gives a sufficient condition for the stability along the pass of the sliding mode process in (24) by using the LMI method and the 2D system theory.…”

“…Repetitive Control (RC) has been applied to many engineering applications, such as robot manipulators, rotary systems, power supply systems, computer disk drives, etc. [1]- [4]. Based on the error signals in previous periods, the basic idea of RC is to improve transient responses on each pass by refining the control inputs in tracking problems for periodic operated dynamic systems.…”

Variable-structure repetitive control for discrete-time linear systems with multiple-period exogenous signals

“…The RC method has successfully been implemented to cope with such periodic signals found in various applications, e.g., hard-disk-drive systems (Chen and Tomizuka, 2014), piezo-actuated nano-positioning systems (Li et al, 2017), robotic arm manipulators (Muramatsu and Katsura, 2018), and power electronic systems (Lorenzini et al, 2018). * Corresponding author This shows that the RC method is applicable for different classes of single-input single-output (SISO) and multi-input multi-output (MIMO) linear and nonlinear systems (Flores et al, 2012;Kurniawan et al, 2014;2016a;Tomei and Verrelli, 2015;Zhou et al, 2016;Sun et al, 2018;Sakthivel et al, 2020).…”

Laplace-type integral transform for time-varying periodic repetitive controller design

“…In Chen et al, 10 an optimal modified repetitive controller for a strictly proper plant with time-varying uncertainties is proposed to reject position-dependent disturbances, where the repetitive controller inserted by a low-pass filter and an adjustable parameter is developed. In literatures, [11][12][13][14][15] an equivalent-input-disturbance-based robust output-feedback modified repetitive control system is given to provide aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. Repetitive controllers are usually designed assuming a fixed fundamental frequency for the signals to be tracked/rejected and its main drawback being a dramatic performance decay when this frequency varies.…”