The paper presents the identification issues and a parameters’ identification algorithm that separates the system parameters from the time-delays for the class of single input single output (SISO) linear time delay systems (LTDS). The presence of the unknown time delay greatly complicates the parameter estimation problem, because the parameters of the model are not linear with respect to the time-delay. However, once the time delay is determined, the model becomes linear for the other coefficient parameters and hence the common least square method can be utilized directly. This problem is solved in the paper [12]. Solution presented in the previous mentioned paper is based on the nonlinear least square problem developed in the paper [3]. The hybrid method based on the Genetic algorithm and the Nelder-Mead technique is used for the minimization of variable projection functional. The both techniques use a little local information and don’t require the derivation of the cost function. According to this fact the both previous mentioned techniques have a problem with the reliability and convergence rate. The convergence rate is smaller than the optimization techniques of the first order which use more local information including the gradient of cost function. In order to achieve the better convergence rate, the Quasi-Newton optimization method is used instead of the Nelder-Mead method. The special Broyden-Fletcher-Goldfarb-Shanno (BFGS) Quasi-Newton algorithm, which involves the several initial conditions treated at the same time developed by [8], is applied here. This approach is illustrated by a particular application in the field of the heat transfer, concretely on the time-delay model of the recuperative plate heat exchanger.

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