Identification of parametric models with a priori knowledge of process properties

Abstract An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived and combined with a recursive scheme determined for minimization of the sum of absolute model errors. The estimation problem of a model with known static gains of inputs is discussed and proper formulas are derived. This approach can overcome the non-identifiability problem which has been observed during estimation based on measurements recorded in industrial closed-loop control systems. The application of the proposed approach to estimation of a model for an industrial plant (a water injector into the steam flow in a power plant) is presented and discussed.

[1]  N. Draper,et al.  Applied Regression Analysis. , 1967 .

[2]  Håkan Hjalmarsson,et al.  The fundamental role of general orthonormal bases in system identification , 1999, IEEE Trans. Autom. Control..

[3]  Kazuhiko Hayakawa.  The Effects of Dynamic Feedbacks on LS and MM Estimator Accuracy in Panel Data Models: Some Additional Results , 2010 .

[4]  Maurice J.G Bun,et al.  Bias-Corrected Estimation in Dynamic Panel Data Models , 2005 .

[5]  Rolf Isermann,et al.  Identifikation dynamischer Systeme , 1988 .

[6]  Graham C. Goodwin,et al.  Bias issues in closed loop identification with application to adaptive control , 2002, Commun. Inf. Syst..

[7]  Zdzislaw Kowalczuk,et al.  Continuous-time approaches to identification of continuous-time systems , 2000, Autom..

[8]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[9]  Rik Pintelon,et al.  An Introduction to Identification , 2001 .

[10]  Krzysztof Janiszowski.  Towards Estimation in the Sense of the Least Sum of Absolute Errors , 1998 .

[11]  Lennart Ljung,et al.  Adaptation and tracking in system identification - A survey , 1990, Autom..

[12]  Karl Johan Åström,et al.  Theory and applications of adaptive control - A survey , 1983, Autom..

[13]  Donggyu Sul,et al.  Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence , 2003 .

[14]  Krzysztof B. Janiszowski,et al.  Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error , 2014, Int. J. Appl. Math. Comput. Sci..

[15]  P. Eykhoff.  System Identification Parameter and State Estimation , 1974 .

[16]  Riccardo Scattolini,et al.  Recursive estimation of time delay in sampled systems , 1991, Autom..

[17]  T. Söderström,et al.  Least squares parameter estimation of continuous-time ARX models from discrete-time data , 1997, IEEE Trans. Autom. Control..

[18]  L. A. Aguirre,et al.  Imposing steady-state performance on identified nonlinear polynomial models by means of constrained parameter estimation , 2004 .

[19]  Lennart Ljung,et al.  Bias, Variance and Optimal Experiment Design: Some Comments on Closed Loop Identification , 1998 .

[20]  William P. Heath,et al.  Bias of indirect non-parametric transfer function estimates for plants in closed loop , 2001, Autom..

[21]  Christian Gourieroux,et al.  Indirect Inference for Dynamic Panel Models , 2006 .

[22]  Karl Johan Åström,et al.  Theory and Applications of Adaptive Control , 1981 .

[23]  Jan F. Kiviet,et al.  On bias, inconsistency and efficiency of various estimators in dynamic panel data models , 1995 .

[24]  Sébastien Briot,et al.  New method for global identification of the joint drive gains of robots using a known payload mass , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.