Abstract
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.
Highlights
The choice of an input signal used for actuation of the system is critical in the task of model building and parameter identification
A plant-friendly input signal design problem for system identification was formulated in the paper and the method of the problem solution was outlined
In the presented approach the input signal is a solution of a dynamic optimisation problem, where the plant friendliness index is maximised, at the same time providing a guaranteed level of D-efficiency
Summary
The choice of an input signal used for actuation of the system is critical in the task of model building and parameter identification. It is a common practice to perturb the system of interest and use the resulting data to build the model [1,2,3]. The accuracy of parameter estimates is increased by the use of optimal excitation signals [4,5]. The pertinence of a model is the critical factor for proper tuning of a controller, usually performed as a model-based optimisation task. An inaccurate model can significantly influence the performance of the control loop, and deteriorate the quality of the plant product. The control performance assessment has a large impact on the economic aspect of the production process. It was found that about 66%–80% of the advanced control systems are not able to achieve the desired performance [6]
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