Modified Artstein Predictor for LTI Systems with Dead Time and Unkown Disturbances
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Modified Artstein Predictor for LTI Systems with Dead Time and Unkown Disturbances Tito L. M. Santos1
Received: 1 October 2015 / Revised: 29 November 2015 / Accepted: 22 February 2016 / Published online: 14 March 2016 © Brazilian Society for Automatics–SBA 2016
Abstract This paper presents a modified Artstein-based predictor for the control of LTI systems with dead time and bounded disturbances. A generalized condition is presented in order to achieve null prediction error in the presence of constant disturbances. The proposed predictor can also be explored to achieve null prediction error in the presence of sinusoidal disturbances or to improve disturbance rejection for processes with long dead time. Comparative simulation examples are used to illustrate the usefulness of the proposed approach. Keywords Input delay · Linear time-invariant systems · Prediction · Unknown disturbances · Disturbance rejection
1 Introduction Since Smith’s seminal article (Smith 1957), several works have been presented in order to control processes with time delay. It is well known that the Smith predictor cannot be used to control open-loop unstable processes because predictor structure is not internally stable (Normey-Rico and Camacho 2007). Several strategies have been presented to deal with open-loop unstable systems as Manitius and Olbrot (1979), Kwon and Pearson (1980) and Artstein (1982), which consider state-space representation, and Normey-Rico and Camacho (2009) and Albertos and García (2009), which are based on transfer function description. Actually, for LTI systems with single-input delay, state-space-based predictor
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Tito L. M. Santos [email protected] Electric Engineering Department (DEE), Federal University of Bahia (UFBA), Rua Aristides Novis, N.02, Salvador, BA 40210-630, Brazil
and transfer function-based dead-time compensators can be related as discussed in Mirkin and Raskin (2003). Time delay systems with input delay is an active research topic with several open problems. For example, robustness in terms of closed-loop stability with respect to delay uncertainty has been analyzed in several works (Krstic 2008; Karafyllis and Krstic 2013; Li et al. 2014). Timevarying input delay is treated by using adaptive schemes in Loreto et al. (2012) and Zhu et al. (2015) and truncationbased predictors are considered for systems with single- and multiple-input delays in Zhou et al. (2012) and Zhou and Lin (2014). Robustness of nonlinear input delay predictors is also an important research topic (Krstic 2010; Limon et al. 2011; Bekiaris-Liberis and Krstic 2013; Santos et al. 2014). However, it is interesting to note that null prediction error in the presence of unknown disturbance is not discussed in most of these works. Actually, some of them guarantee disturbance rejection in the presence of deterministic disturbance models, such as constant or sinusoidal unknown disturbances, but the performance with respect to prediction error response is not analyzed in these works. It was recently pointed out in Léchappé et al. (2015)
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