System identification, in practice, is carried out by perturbing processes or plants under operation. That is why in many industrial applications a plant-friendly input signal would be preferred for system identification. The goal of the study is to design the optimal input signal which is then employed in the identification experiment and to examine the relationships between the index of friendliness of this input signal and the accuracy of parameter estimation when the measured output signal is significantly affected by noise. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) expressed in conventional Bolza form. As setting such conditions of the identification experiment we can only talk about the D-suboptimality, we quantify the plant trajectories using the D-efficiency measure. An additional constraint, imposed on D-efficiency of the solution, should allow one to attain the most adequate information content from the plant which operating point is perturbed in the least invasive (most friendly) way. A simple numerical example, which clearly demonstrates the idea presented in the paper, is included and discussed.
In this paper, a novel method is proposed to design a free final time input signal, which is then used in the robust system identification process. The solution of the constrained optimal input design problem is based on the minimization of an extra state variable representing the free final time scaling factor, formulated in the Bolza functional form, subject to the D-efficiency constraint as well as the input energy constraint. The objective function used for the model of the system identification provides robustness regarding the outlying data and was constructed using the so-called Entropy-like estimator. The perturbation time interval has a significant impact on the cost of the real-life system identification experiment. The contribution of this work is to examine the economic aspects between the imposed constraints on the input signal design, and the experiment duration while undertaking an identification experiment in the real operating conditions. The methodology is applicable to the general class of systems and was supported by numerical examples. Illustrative examples of the Least Squares, and the Entropy-Like estimators for the system parameter data validation where measurements include additive white noise are compared using ellipsoidal confidence regions.
Part 5: Modelling and OptimizationInternational audienceSystem identification, in practice, is carried out by perturbing processes or plants under operation. That is why in many industrial applications an optimal input signal would be preferred for system identification. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) expressed in conventional Bolza form. As setting such conditions of the identification experiment we can only say about the D-suboptimality, we quantify the plant trajectories using the Defficiency measure. An additional constraint, imposed on D-efficiency of the solution, should allow to attain the most adequate contents of information from the plant which operating point is perturbed in the least invasive way. A simple numerical example, which clearly demonstrates the idea presented in the paper, is included and discussed
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