Free Final Time Input Design Problem for Robust Entropy-Like System Parameter Estimation

Jakowluk, Wiktor

doi:10.3390/e20070528

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…System identification relies on an accurate mathematical model built using experimental data and a priori knowledge of the plant [20]. The accuracy of the model to be estimated is deeply related to an excitation signal [1,12]. To design an optimal input signal, an adequate scalar norm of the Fisher information matrix (FIM) should be used.…”

Section: Optimal Pump Control Signal Designmentioning

confidence: 99%

“…input energy, experiment duration), the experiment cost includes the input design problem through the objective function [10]. Another method used to experiment with cost minimization is called plant-friendly system identification [11,12]. The plant-friendly input signal design is related to the application-oriented system identification method.…”

Section: Introductionmentioning

confidence: 99%

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Bulletin of the Polish Academy of Sciences: Technical Sciences

Jakowluk,

Jaszczak

2022

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The main goal of estimating models for industrial applications is to guarantee the cheapest system identification. The requirements for the identification experiment should not be allowed to affect product quality under normal operating conditions. This paper deals with ensuring the required liquid levels of the cascade system tanks using the model predictive control (MPC) method. The MPC strategy was extended with the Kalman filter (KF) to predict the system's succeeding states subject to a reference trajectory in the presence of both process and measurement noise covariances. The main contribution is to use the application-oriented input design to update the parameters of the model during system degradation. This framework delivers the least-costly identification experiment and guarantees high performance of the system with the updated model. The methods presented are evaluated both in the experiments on a real process and in the computer simulations. The results of the robust MPC application for cascade system water levels control are discussed.

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Section: Optimal Pump Control Signal Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Jakowluk,

Jaszczak

2022

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“…Such a closed-loop experiment should be stable and have a short duration [13,14]. Another important thing is to ensure that the identification experiment is plant-friendly and meets industrial demands [15][16][17]. The spectrum of the excitation signal affects the model parameters to be estimated during the identification experiment.…”

Section: Introductionmentioning

confidence: 99%

Application-Oriented Input Spectrum Design in Closed-Loop Identification

Jakowluk

Swiercz

2023

Applied Sciences

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In the paper, a problem of real-time input design, where the spectral characteristic of the external excitation signal is optimized considering the fixed bound on the ellipsoidal constraint applied to the quality measure of the estimated model, has been presented. We designed a compensator close to the complementary sensitivity function such that the resulting closed-loop system is stable and guarantees robust performance. The contribution of this work comprises a comparison of the KYP and frequency grid methods for the worst-case minimization between the identified plant and all models in the uncertainty region. It has been noted that the input design problem considering the frequency grid is far more numerically robust than the KYP method and guarantees that more than 90% of the estimated model parameters are clustered inside the assumed confidence region. The proposed approach is verified by numerical examples, and the sensitivity of the input spectrum design to the estimates of model parameters is discussed.

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“…The Maximum Likelihood (ML), Minimum Entropy (ME), and Generalized Maximum Entropy (GME) methods for robust parameter estimation, which guarantee robustness subject to regression models, are proposed in [ 19 ]. Another prediction error estimation method called the Least Entropy-Like (LEL) estimator is described in [ 20 , 21 ]. This method is based on properly established penalty function and is developed based on the Gibbs entropy definition.…”

Section: Introductionmentioning

confidence: 99%

Robustness Analysis of the Estimators for the Nonlinear System Identification

Jakowluk

Godlewski

2020

Entropy

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The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from normal working conditions during the identification task is minimized. In this paper, the adaptive filtering (AF) scheme for plant model parameter estimation is proposed. The experimental results are obtained using the nonlinear interacting water tanks system. The adaptive filtering is expressed by minimizing the error between the system and the plant model outputs subject to the white noise signal affecting system output. This measurement error is quantified by the comparison of Minimum Error Entropy Renyi (MEER), Least Entropy Like (LEL), Least Squares (LS), and Least Absolute Deviation (LAD) estimators, respectively. The plant model parameters were obtained using sequential quadratic programming (SQP) algorithm. The robustness tests for the double-tank water system parameter estimators are performed using the ellipsoidal confidence regions. The effectiveness analysis for the above-mentioned estimators relies on the total number of iterations and the number of function evaluation comparisons. The main contribution of this paper is the evaluation of different estimation methods for the nonlinear system identification using various excitation signals. The proposed empirical study is illustrated by the numerical examples, and the simulation results are discussed.

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Free Final Time Input Design Problem for Robust Entropy-Like System Parameter Estimation

Cited by 6 publications

References 29 publications

Bulletin of the Polish Academy of Sciences: Technical Sciences

Bulletin of the Polish Academy of Sciences: Technical Sciences

Application-Oriented Input Spectrum Design in Closed-Loop Identification

Robustness Analysis of the Estimators for the Nonlinear System Identification

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