Design of Repetitive Control Systems Using a Delayed Control Input and a State Error
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Design of Repetitive Control Systems Using a Delayed Control Input and a State Error Tae-Yong Doh* and Jung Rae Ryoo Abstract: This paper presents a modified repetitive control scheme comprising of a state error and a control input via delayed feedback to track periodic reference trajectories and/or attenuate disturbances. The closed-loop state error dynamics can be represented using a typical neutral delay system with an exogenous input to be attenuated. The sufficient conditions to achieve overall stability and H∞ performance to minimize state error are derived by applying a Lyapunov-Krasovskii functional and a Hamiltonian, which are expressed as an algebraic Riccati inequality (ARI) and a linear matrix inequality (LMI). Based on the derived conditions, it is shown that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint to determine the state error feedback gain. Finally, a numerical example is presented to demonstrate the feasibility of the proposed method. Keywords: Algebraic Riccati inequality (ARI), delayed control input, H∞ performance, L2 norm, linear matrix inequality (LMI), neutral delay system, repetitive control, state error feedback.
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INTRODUCTION
Repetitive control is a specialized control scheme used to track periodic reference commands and/or attenuate periodic exogenous disturbances. Frequency domain analysis shows that its highly accurate tracking performance can be achieved using a periodic signal generator implemented in the repetitive controller. However, the positive feedback loop to generate the periodic signal decreases the stability margin of the system. Therefore, the tradeoff between stability and tracking performance can be considered as an important factor to design the control system. Hara et al. [1] derived the sufficient conditions for stability of original repetitive as well as modified repetitive control systems that sacrifice tracking performance at high frequencies in favor of system stability. Doh and Ryoo dealt with the problem of a robust repetitive controller design for an uncertain feedback control system using its explicit performance information [2]. To apply repetitive control to various types of systems, several theories have been developed for repetitive control in the state space. Doh et al. proposed a method for designing repetitive control systems that could ensure robust stability for linear systems with time-varying uncertainties [3] and applied this repetitive controller to the track-following servo system of an optical disk drive [4]. Lucibello showed that the repetitive control of positive
real systems via delayed feedback was Lyapunov asymptotically stable [5]. Q. Quan et al. developed a repetitive controller that was composed of a delayed control input and an output error multiplied by a time-varying gain and derived a sufficient condition for stability via a Lyapunov-Krasovskii functional and linear matrix inequalities (LMIs) [6]. Zh
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