By S. P. Bhattacharyya
This short provides contemporary effects acquired at the research, synthesis and layout of platforms defined through linear equations. it truly is renowned that linear equations come up in so much branches of technology and engineering in addition to social, organic and fiscal platforms. the newness of this procedure is that no types of the procedure are assumed to be to be had, nor are they required. as a substitute, a couple of measurements made at the process may be processed strategically to without delay extract layout values that meet necessities with no developing a version of the method, implicitly or explicitly. those new recommendations are illustrated by means of utilising them to linear DC and AC circuits, mechanical, civil and hydraulic structures, sign circulation block diagrams and regulate platforms. those functions are initial and recommend many open difficulties. the consequences awarded during this short are the most recent attempt during this path and the authors wish those will bring about beautiful choices to model-based layout of engineering and different systems.
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Additional info for Linear Systems: A Measurement Based Approach
Sample text
1. Case 2: i = j Let us write the power level Pi as Pi = Ri Ii2 . 14). 51) 34 2 Application to DC Circuits where the constants α0 , β0 can be obtained as explained in Sect. 1. 52) where α0 is a constant that can be determined as discussed in Sect. 1. 51), with respect to Ri , can be calculated as α 2 (β0 − Ri ) d Pi = 0 . 53) We have the following statements: 1. 51), in this case, is not monotonic. As Ri → 0, Pi → 0 and when Ri → ∞, Pi → 0. Therefore, as the value of the resistance Ri increases from 0 to ∞, the power Pi increases from 0 to the maximum achievable value of α02 4β0 , and then decreases to 0 at very large values of Ri .
2 Power Level Control Using Two Resistors In this case it is desired to control the power level Pi , by adjusting any two resistors R j and Rk at arbitrary locations of the circuit. Assuming that R j and Rk are not gyrator resistances, and based on the results of Sect. 2, we have the following theorem. 7 In a linear DC circuit, the functional dependency of the power level Pi , in any resistor Ri , on any two resistances R j and Rk can be determined by at most 7 measurements of the currents Ii (passing through Ri ) obtained for 7 different sets of values (R j , Rk ), and 1 measurement of the voltage across the resistor Ri , corresponding to one of the resistance settings.
1, we have the following theorem. 5 In a linear AC circuit, the functional dependency of the complex power Pi on any impedance Z j can be determined by at most three measurements of the current phasor Ii (passing through Z i ) obtained for three different complex values of Z j , and one measurement of the voltage across the impedance Z i , for one such setting of the impedance. 2 Power Control Using Two Impedances Suppose that the power Pi is to be controlled by adjusting two impedances Z j and Z k at arbitrary locations of the circuit.