Observability of reduced order models - application to a model for control of alpha process

This paper describes the theoretical basis and some applications of a identifiability/observability test for state-space models based on the recursive calculation of the numerical condition of the observability matrix. This test evaluates the possibility of estimating the unknown states and parameters of a mathematical model under defined experimental conditions and available information. The numerical value of the proposed “observability parameter” is also an index of uncertainty propagation through the model. As examples of the utility of the proposed test, the paper presents the analysis of a reduced-order model for two wastewater treatment plant configurations (D-N and Alpha process), evaluating the on-line information that is theoretically indispensable in distinguishing each one of the unknown states and parameters under steady or dynamic conditions.

[1]  Niels Kjølstad Poulsen,et al.  Grey box modelling in two time domains of a wastewater pilot scale plant , 1993 .

[2]  M. B. Beck.  Understanding Uncertain Environmental Systems , 1994 .

[3]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[4]  Andrea G. Capodaglio,et al.  Wastewater Treatment Plants under Transient Loading – Performance, Modelling and Control , 1993 .

[5]  Axel Munack,et al.  Optimal Feeding Strategy for Identification of Monod-Type Models by Fed-Batch Experiments , 1989 .

[6]  E. Ayesa,et al.  Evaluation of Sensitivity and Observability of the State Vector for System Identification and Experimental Design , 1993 .

[7]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[8]  J. DiStefano,et al.  Identifiability of Model Parameter , 1985 .

[9]  Stefano Marsili-Libelli,et al.  Modelling, Identification and Control of the Activated Sludge Process , 1989, Lignocellulosic Materials.

[10]  A. Holmberg.  On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities , 1982 .

[11]  E. Ayesa,et al.  State and Coefficients Estimation for the Activated Sludge Process Using a Modified Kalman Filter Algorithm , 1991 .

[12]  G. Olsson,et al.  Reduced Order Models for On-Line Parameter Identification of the Activated Sludge Process , 1993 .

[13]  E. Ayesa,et al.  Designing Experiments to Determine the Coefficients of Activated Sludge Models by Identification Algorithms , 1992 .