Prediction Error Identification Method for Continuous-time Systems Having Multiple Unknown Time Delays
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Prediction Error Identification Method for Continuous-time Systems Having Multiple Unknown Time Delays Yamna Ghoul Abstract: This paper shows a continuous-time prediction error method for the identification of Multiple Input Single Output (MISO) Continuous-Time (CT) systems with multiple unknown time delays. The proposed algorithm entails the simultaneous estimation of both process parameters and multiple unknown time delays. Indeed, it minimizes the prediction error using the Levenberg-Marquardt (LM) optimization method with derivatives of the objective function with respect to the parameters including the multiple unknown time delays. An analysis is then presented which proves the convergence of the algorithm, and robustness issues are discussed as well. Finally, to verify the analysis and to demonstrate the feasibility of the algorithm, we present some of the simulation results which were carried out. Keywords: Continuous-time, convergence, Levenberg-Marquardt method, multiple unknown time delays, prediction error method.
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INTRODUCTION
Several researches have been presented involving control of systems [1]. As known, systems control methods are important not only for the property that they can be computed in real time, but they may be combined with identification strategies. Accordingly, a number of attempts of dealing with systems identification has been reported in the literature [2–4]. Meanwhile, we realize that the Levenberg-Marquardt (LM) method is a useful optimization algorithm widely existed in system identification [5–8]. On the other hand, it is well known that a board class of industrial processes includes time delay phenomena in their dynamics. As a consequence, the identification of time delay models is indeed a problem of considerable importance. In fact, according to the used time, the developed approaches can be classified into two classes of models: continuous-time (CT) models identification and discrete-time (DT) models identification. In fact, it is advised to use continuous-time approaches under certain circumstances. First, conforming to models used in nature like pressure, temperature, etc., we should use continuoustime approaches because the physical signal is always a continuous-time signal rather than a discrete-time signal from a zero-order holder. Second, when we need to estimate physical parameters for the purposes of analysis and system design, continuous-time approaches are recommended. Third, data do not need to be sampled equidis-
tantly. Existing methods, however, have mainly treated the problem of the identification of SISO time-delay systems. Nevertheless, for MISO systems with multiple unknown time delays, the problem is much more difficult. Such systems are often more challenging to model. A basic reason for the difficulties is that the couplings between several inputs and an output lead to more complex models. A second reason for studying the MISO systems with multiple unknown time delays is the presence of
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