Plant Friendly Input Design for Parameter Estimation in an Inertial System with Respect to D-Efficiency Constraints

• Main Author: Wiktor Jakowluk
• Format: Article
• Language: English
• Published: MDPI AG 2014-11-01
• Series: Entropy
• Subjects: plant-friendly identification; D-optimality; D-efficiency; ellipsoidal confidence region
• Online Access: http://www.mdpi.com/1099-4300/16/11/5822

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.