Abstract
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.
Highlights
System identification is typically carried out by perturbing processes or plants under operation and use experimental data to construct the model of the dynamic system
Constrained optimal inputs for the first-order, linear time-invariant (LTI) model of the system were computed for the assumed initial values of parameters: a = −1, b = 1, and nominal time duration t = [0, 10] s, using sequential quadratic programming (SQP) algorithm
The novelty of this work was to design the free final time input signals, with constraints on input move size and D-efficiency value which are used in the system identification experiments
Summary
System identification is typically carried out by perturbing processes or plants under operation and use experimental data to construct the model of the dynamic system. The fundamental task in system identification is to excite the system of interest using an informative input and build the model of the system with maximum pertinence [2,3]. The problem of the optimal input signal design is typically solved by minimizing an a priori selected norm of the Fisher information matrix with respect to an appropriate experimental setup [4]. The identification experiment can be executed in both closed and open loop conditions and could be utilized for arbitrary model parameterizations. Improper experiment conditions can cause performance degradation of the control loop. It has been reported that about 80% of the designed control loops do not guarantee the acceptable performance assessment [5]
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