Identification of electric circuits described by ill-conditioned mathematical models

This paper treats the problem of identification of a linear electric circuit described by an ill-conditioned mathematical model. The identification problem is considered as the problem of model parameters determination by means of processing experimental data measured for the objective circuit. Topological singularities (low-admittance cutsets and low-impedance loops) in a circuit are found to be origins of ill-conditionality of a circuit model. For more in-depth investigation the classification of electric circuits is made in respect to singularities position. It is shown that the first set of experimental data obtained for an ill-conditioned model is useless for getting the required solution of the identification problem. In this case a solution error amounts to a huge value that exponentially increases with growth in condition number of a model matrix. It is found that linear relations between model parameters can be determined in an ill-conditioned problem. Accuracy of these relations does not depend on condition number, but is defined only by measurement precision. An approach named as repeat measurements principle (RMP) and based on linear relations is suggested to solve an ill-conditioned identification problem. A new RMP-based algorithm of linear circuit identification is developed. The algorithm shows a high efficiency and allows us to determine model parameters accurate to measurement precision as applied to any type of reciprocal and nonreciprocal linear circuits.