电路系统的参数识别问题及其数值处理

THE IDENTIFICATION PROBLEM OF PARAMETERS IN A CIRCUIT SYSTEM AND ITS NUMCRICAL TREATMENT

设一个电路在阶跃电压激励下，测出其输出电流或输出电压响应波形，能否确定该电路的等效参数Ｌ、Ｒ和Ｃ的值？这是一个电路系统的逆问题，也是一个识别问题。准确地识别出这些参数的数值，对于电路系统评价和分析设计以及对于实际应用都有着十分重要的意义。本文给出了处理这类问题的有效方法，即采用数值逼近和最小二乘原理。

The potential distribution outside the closed curved surface can be measured while there are charges inside the surface. Inversely, the location and quantity of the charges can be determined from the potential distribution. For example, it is casy to determine the epicardium from body surface potential distribution, etc. We call this kind of topic inverse problem. A circuit consists of resistances (R), inductances (L), capacitances (C) and nonlinear control elements. No matter how complicated the constitution is, the circuit can be equivalent to a series or parallel one composed of a resistance, an inductance, a capacitance and signal sourcer. When an analog or digital circuit is excited, a response, which is the main character in appreciating circuits, will be always generated. Assuming that the output current or voltage under the separate excitation with a step voltage signal is detected, the equivalent serics or parallel parameters (R,L and C) of the circuit system can then be obtained. This is just an inverse problem of circuit systems and also an identification problem of circuit parameters. On the contrary, to calculate the output response according to the equivalent parameters of black box circuit is called forward problem. A circuit consisting of a resistance, an inductance, a capacitance and a signal sourcer in series is described by the following equation u(t)=L d i d t+Ri+1C∫i d t and the equation for a parallel circuit is written out below i(t)=C d u d t+1Ru+1L∫u d t where u(t) is the voltage of a step voltage signal which is used to excite the equivalent paramenter circuits. Based on the current i(t) and voltage u(t), we identify the equivalent parameters R, L and C accurately by using an effective method in which the method of numerical approach and the principle of least square are adopted. The results obtained in this paper are of important significance in appreciating and designing circuit systems, also in practical applications. As to the identification of individual elements in the circuit systems, we introduce a method by levels in this paper.