Linear circuits: A measurement based approach

In this paper, we evaluate a useful general model for linear direct current (DC) networks, containing design parameters, multiple inputs and outputs. The outputs are rational multivariate functions of the parameters and linear functions of the inputs. For an unknown linear system, the unknown coefficients of these functions can be determined by taking a suitable number of measurements and solving a set of linear equations constructed from selected measurement data. The rational functions are useful to support the design such that outputs can be constrained to a desired interval. An interesting result was the particular case where the parameter varied is located at the output terminal. This is an alternative way to estimate the Thévenin equivalent of a circuit. Real data are in general noisy with accuracy dependent on the tolerance of components and on the measurement device used. We present a detailed analysis of the application of the measurement-based approach under real experiments. Initially, a resistive DC circuit case is presented, and the results are verified by simulation and experimental laboratory data. Finally, practical circuits, such as a conditioning signal stage with an operational amplifier, and a boost DC-DC converter are considered. 1921The kind of problems described earlier was addressed in [2][3][4][5]. Along this line of research, results on the determination of power levels in unknown linear DC circuits appeared in [6]. It is shown that design can be carried out in an unknown-model environment by taking a few critical measurements from which the functional behaviour desired is reconstructed. These results were used to develop design theory based on a few strategic measurements to extract the functional behaviour needed to solve the design requirements.In the literature, a functional dependence of multivariate polynomial forms was derived for symbolic network functions in [7][8][9]. The results presented for symbolic network functions considered all the elements of a network and can be used for instance to obtain the voltage trans-admittance of a circuit with the components described by symbols. In [8,10], implicitly, only the unity rank case was considered, as in Bode's bilinear form which is a special case of the results given in [4] and [5].The present paper builds on the results in [3][4][5] and considers the general input-output model inspired in the space-state model introduced in [11]. The main contribution is in the analysis of the illposed problem arising in the measurement-based approach with real experiments and in its proposed practical applications. A CONCEPTUAL MODEL], i = 1, … , m, j = 1, … , r.

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“…We consider now model (2) written in terms of a design parameter vector denoted as p = [ p 1 · · · p ] T :…”

Section: Preliminariesmentioning

confidence: 99%

“…The kind of problems described earlier was addressed in [2][3][4][5]. Along this line of research, results on the determination of power levels in unknown linear DC circuits appeared in [6].…”

mentioning

confidence: 99%

A measurement‐based approach with accuracy evaluation and its applications to circuit analysis and synthesis

Oliveira

Alzate

Bhattacharyya

2017

Circuit Theory & Apps

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“…Specifically, it is shown that, for linear control systems, the functional dependence of the controlled variables on the design parameters can be completely determined with a very small set of experimental measurements even for highly complex systems (as long as they are linear). Exemplifying this in the case of resistive circuits, it has been shown in that the behavior of the current in a specified branch of a linear circuit as a function of an arbitrary resistor in the circuit can be completely determined from at most three measurements. This result can be extended to m variable resistances or even to complex impedances, and to unknown systems containing controllers.…”

Section: Introductionmentioning

confidence: 99%

Towards data‐based adaptive control

Datta

Layek

Nounou

et al. 2012

Adaptive Control & Signal

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This paper presents a possible new direction for the design of adaptive controllers. It begins by outlining a measurement-based approach to the analysis, synthesis, and design of unknown systems. The systems under consideration can typically be electrical, mechanical, hydraulic, continuous, discrete, real, artificial, or biological, or of societal origin. Our approach is novel in the sense that we propose to use the measurement, or measured data, to directly design the control or decision variables whereas the current approach in the mainstream of system theory advocates that measured data be used to first identify the plant, and control design, or synthesis, then be based on the identified model. This latter approach has necessitated the creation of fields such as robust control and (indirect) adaptive control that try to account for errors in the identified model. Our approach, being data based, would potentially be automatically robust and adaptive. We show that such a measurement-based approach is certainly feasible by considering DC circuits, AC circuits, block diagrams, and control systems. These results are then used to formulate the research problems for data-based adaptive control.

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