Using Error Dynamics in a New Approach to System Identification
The behavior of a dynamic system is subject to change. This change can come from within the system or from the surrounding environment in a form that we call noise. It is well known that in the absence of noise that the state vector of a deterministic, full state estimator, can be made to systematically converge to the state vector of the system under observation. The above statement is true when the modeling, as reflected in the observer, is “perfect”. When the modeling of the system under observation is less than perfect, the convergence characteristics of the observer are, in some manner, modified. A study of the behavior of the state estimator in the presence of errors in the plant model is usually undertaken. In contrast, a study of the estimation of the modified plant by the means provided in the information which may be gleaned from the modification in the convergence characteristics is undertaken in this paper. The modified plant is determined by using the “system-observer pair” error dynamics. The observer system is initially fixed while the plant of the system is damaged by changing its parameters. This will produce the error vector mentioned above. The information contained in this error vector is used in the identification process of the system plant. Each iteration of the technique improves upon the estimates for the parameters of the damaged plant. This information is subsequently used to modify the observer system to improve upon the overall rate of convergence. This paper presents a new technique that can be used to identify the parameters of a plant after these parameters have been “disturbed” from their nominal values. The proposed identification technique is applicable to any nth order system with multiple inputs and outputs. What is unique about this approach is the ability to update the observer at each iteration until the plant is identified.
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