IDENTIFICATION OF NONLINEAR PLANTS VIA DISTRIBUTIONS; APPLICATION FOR WASTEWATER BIODEGRADATION PROCESS

摘要

The paper presents a procedure for continuous time nonlinear systems identification based on distribution theory. It is a functional type method, which transforms a differential system of equations to an algebraic system in unknown parameters. The identification problem is formulated as a condition of vanishing the existence relation of the system. Then, this relation is represented by functionals using techniques from distribution theory based on testing function from a finite dimensional fundamental space. Rational dependences between parameters and some measurable variables of the system are admitted. The main idea of this paper is to use a hierarchical structure of identification, which allows obtaining a linear algebraic system of equations in the unknown parameters. The coefficients of this algebraic system are functionals depending on the input and output variables evaluated through some testing functions from distribution theory. According to the proposed procedure, first, only some state equations are evaluated throughout testing functions to obtain a set of linear equations in some parameters. The results of this first stage of identification are utilized for expressing other parameters by linear equations. This process is repeated until all parameters are identified. An application for parameter identification of a waste water biodegradation process is presented. By some examples, the potential of the method is revealed.