Linear Systems: A Measurement Based Approach by S. P. Bhattacharyya

By S. P. Bhattacharyya

This short offers contemporary effects acquired at the research, synthesis and layout of platforms defined by way of linear equations. it's popular that linear equations come up in such a lot branches of technology and engineering in addition to social, organic and monetary platforms. the newness of this technique is that no types of the approach are assumed to be on hand, nor are they required. as a substitute, a number of measurements made at the method may be processed strategically to without delay extract layout values that meet standards with no developing a version of the procedure, implicitly or explicitly. those new innovations are illustrated by means of utilising them to linear DC and AC circuits, mechanical, civil and hydraulic platforms, sign movement block diagrams and keep watch over platforms. those purposes are initial and recommend many open difficulties. the consequences awarded during this short are the newest attempt during this path and the authors wish those will result in beautiful possible choices to model-based layout of engineering and different systems.

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3) where α0 , α1 , β0 are complex quantities that can be uniquely determined by solving the measurement equations, Fig. 4) m provided |M| = 0. These complex quantities can be written as α0 ( jω) = α0r (ω) + jα0i (ω), α1 ( jω) = α1r (ω) + jα1i (ω), β0 ( jω) = β0r (ω) + jβ0i (ω). 5) where the complex quantities α0 , α1 can be determined from any two of the experiments conducted earlier. 6) where α0 , β0 are complex quantities that can be calculated by solving the measurement equations, α0 I Z 1 −Ii1 = i1 i1 .

5 Notes and References We have shown in this chapter that the design of linear DC circuits can be carried out without knowledge of the circuit model, provided a few measurements can be made. These measurements, strategically processed, yield complete information regarding the functional dependency of the current, voltage or power to be controlled, on the design variables. These relations can then be inverted to extract the design parameters. In the subsequent chapters we show the application of these ideas to AC circuits, mechanical systems, block diagrams and control systems.

12). From this relationship, it is clear that the short circuit current Isc is given by Isc = αβ00 , which is obtained by setting Ri = 0. 12) by Ri and taking the limit as Ri → ∞. This yields Voc = VT h = α0 . 18) Ii (Ri ) = R T h + Ri which is exactly Thevenin’s Theorem. We point out that in our approach, it is not necessary to measure short circuit current or open circuit voltage; indeed two arbitrary measurements suffice. This has practical and useful implications in circuits where short circuiting and open circuiting may sometimes be impossible.

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