Linear Systems by S. P. Bhattacharyya L. H. Keel & D. N. Mohsenizadeh

Author:S. P. Bhattacharyya, L. H. Keel & D. N. Mohsenizadeh
Language: eng
Format: epub
Publisher: Springer India, New Delhi

3

21

19

2.47

4

35

26

2.57

5

40

32

2.52

6

52

45

2.47

7

59

56

2.44

Exp. no.

1

7

1

33.3

Example 2.3.

Consider the unknown linear DC circuit shown in Fig. 2.12.

In this example, are resistors, is a gyrator resistance, are independent sources and are dependent sources. Our goal is to control the power levels in , and , denoted by , and , respectively, to be within the following ranges:

(2.68)

(2.69)

(2.70)

Assume that the design elements are the resistances and . Therefore, we need to find the region in the – plane where the constraints (2.68), (2.69) and (2.70) are satisfied. Based on the approach presented in Sect. 2.3.2, in order to find the functional dependency of any power level in terms of any two resistances, one needs to do at most 7 measurements of current and one measurement of voltage. Let us treat each power level problem separately as follows:

(a) versus and

Based on the results obtained in Sect. 2.3.2, in order to find the functional dependency of on and , one needs to conduct 7 experiments by setting 7 different sets of values for the resistances , and measuring the corresponding values for current . In addition to the current measurements, one measurement of the voltage, across the resistor , is needed to determine the functional dependency of interest. Suppose that this measurement is taken from the first experiment and denoted as . Suppose that experiments are done and let Table 2.3 summarize the numerical values assigned to the resistances and along with the corresponding measurements of and . Substituting the numerical values of Table 2.3 into the matrix , in (2.26), it can be verified that . Thus, the functional dependency of interest will be of the form

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