On the synthesis of a stable and causal compensator for discrete-time high-order repetitive control systems
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On the synthesis of a stable and causal compensator for discrete-time high-order repetitive control systems Edi Kurniawan1 · Hendra Adinanta1 · Hendra G. Harno2 · Jalu A. Prakosa1 · Suryadi Suryadi1 · Purwowibowo Purwowibowo1 Received: 21 April 2020 / Revised: 5 September 2020 / Accepted: 17 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents a novel methodology to design a discrete-time compensator for a high-order repetitive control system. An optimization-based approach is applied to design the compensator, which is required to be stable and causal. This methodology is applicable to both minimum and non-minimum phase systems, for which stability and tracking error convergence are ensured. The compensator is yielded in the form of a proper transfer function and can be implemented separately without being merged with a high-order internal model. The high-order internal model is used to provide robustness against period variations of the reference signal. Simulation and experimental results are provided to show the effectiveness of the compensator design methodology. Keywords High-order repetitive control · Causal compensator · Internal model · Minimum and non-minimum phase system · Optimization
List of Symbols P(z) Discrete-time plant model C(z) Conventional controller H (z) High-order repetitive controller r (k) Reference signal e(k) Tracking error High-order repetitive control signal u H (k) u(k) Control signal y(k) Plant output Q(z) Low pass filter D(z) Weighted delays L(z) Compensator N Number of samples per reference period Reference period Tr T Sampling time Stabilized plant model Ps (z) Repetitive control signal u R (k)
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Edi Kurniawan [email protected], [email protected]
1
Research Center for Physics, Indonesian Institute of Sciences (LIPI), Kawasan PUSPIPTEK Serpong, Tangerang Selatan 15314, Indonesia
2
Department of Aerospace and Software Engineering, Gyeongsang National University, 501 Jinju-daero, Jinju-si 52828, Gyeongsangnam-do, Republic of Korea
1 Introduction Repetitive control (RC) is a well-known control strategy for tracking and rejection of periodic signals. Recently, RC has been successfully applied to control various systems such as a leg exoskeleton [1], an industrial wide-format printing machine [2], a nanomanipulator of micro-stereolithography [3], a magnetically suspended rotor [4], a functional electrical stimulation cycling [5], and a liquid-level servomechanism [6]. The idea of RC was introduced by Francis and Wonham [7] where a model of reference and/or disturbance signals, referred as an internal model, was attached to a feedbackloop system in order to achieve a zero tracking error. The design of a discrete-time RC generally involves two main parts i.e the discrete-time internal model, also referred as a signal generator, and the compensator. The internal model is used to generate a periodic signal and is constructed from a discrete-time delay whose length is the period of the reference signal to be tracked o
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