By S. P. Bhattacharyya, L. H. Keel, D. N. Mohsenizadeh
This short provides fresh effects received at the research, synthesis and layout of structures defined by means of linear equations. it's renowned that linear equations come up in such a lot branches of technological know-how and engineering in addition to social, organic and monetary platforms. the newness of this procedure is that no types of the procedure are assumed to be on hand, nor are they required. in its place, a number of measurements made at the procedure should be processed strategically to without delay extract layout values that meet requirements with out developing a version of the approach, implicitly or explicitly. those new options are illustrated by means of using them to linear DC and AC circuits, mechanical, civil and hydraulic platforms, sign stream block diagrams and keep an eye on platforms. those functions are initial and recommend many open difficulties. the consequences offered 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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Extra resources for Linear Systems: A Measurement Based Approach (SpringerBriefs in Applied Sciences and Technology)
Rm ). Proof. Let us consider two cases: (1) i = j for j = 1, 2, . . , m, and (2) i = j for some j = 1, 2, . . , m. Case 1: i = j, j = 1, 2, . . 5), are both of rank 1 with respect to R j , j = 1, 2, . . , m. 2, the functional dependency of Ii on R1 , R2 , . . , Rm can be written as Ii (R1 , R2 , . . 30) Fig. 6 An unknown linear DC circuit Unknown Linear Ri DC Circuit ······ R1 Rm Ii 28 2 Application to DC Circuits where α˜ i1 i2 ···im ’s and β˜i1 i2 ···im ’s are constants. 30) by β˜11···1 , results in Ii (R1 , R2 , .
30) Fig. 6 An unknown linear DC circuit Unknown Linear Ri DC Circuit ······ R1 Rm Ii 28 2 Application to DC Circuits where α˜ i1 i2 ···im ’s and β˜i1 i2 ···im ’s are constants. 30) by β˜11···1 , results in Ii (R1 , R2 , . . 31) where β11···1 = 1, and αi1 i2 ···im ’s and βi1 i2 ···im ’s are 2m+1 − 1 constants. In order to determine these constants, one conducts 2m+1 − 1 experiments, by setting 2m+1 − 1 different sets of values to the resistances (R1 , R2 , . . , Rm ), and measuring the corresponding currents Ii .
We consider several cases of design elements and provide the results for each case. 1) where A(p( jω)) is the circuit characteristic matrix containing the circuit impedances, x( jω) is the vector of unknown current phasors and q( jω) represents the vector of independent voltage and current sources. Suppose that we want to control the current phasor in the i-th branch of the circuit, denoted by Ii ( jω). 2) where Bi (p( jω), q( jω)) is the matrix obtained by replacing the i-th column of the characteristic matrix A(p( jω)) by the vector b(q( jω)).