Towards data‐based adaptive control

Abstract

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.

Revisiting the maximum power transfer for linear n‐ports with uncoupled loads and applications to power systems

“…Finally, it should be pointed out that there has been recent progress in calculating the output load impedance in linear networks without using the traditional Thévenin or Norton-based ideas of load disconnection or source nulling [13].The main conceptual contribution of this paper is to show that the correct approach to the maximum power transfer theorem for n-ports subjected to uncoupled loads is to use the multilinear form theorem for the port currents (or voltages), in order to derive expressions, for power dissipated in the load impedances, that are computationally tractable in the sense that (i) they have a standard form that is computable by solving a linear system, and (ii) are easily maximized, using standard optimization software. Item (i) implies that a small number of measurements allow the calculation of port variables, as already noticed by Bode and, more recently and emphatically, by Datta et al [12]. Furthermore, once port variables have been calculated, it is possible to obtain an expression for the load power that is valid for all loads, not merely for the maximizing ones.…”

“…A recent paper by Datta et al . rediscovers Lin's multilinear generalization of Bode's bilinear theorem, as well as the measurement‐based idea of DeCarlo and Lin , giving several examples from circuit and control systems. Finally, it should be pointed out that there has been recent progress in calculating the output load impedance in linear networks without using the traditional Thévenin or Norton‐based ideas of load disconnection or source nulling .…”

“…Item (i) implies that a small number of measurements allow the calculation of port variables, as already noticed by Bode and, more recently and emphatically, by Datta et al . . Furthermore, once port variables have been calculated, it is possible to obtain an expression for the load power that is valid for all loads , not merely for the maximizing ones.…”

A Measurement‐Based Approach for Designing Fixed‐Order Controllers for Unknown Closed‐Loop Architecture

“…The PID controller parameters K p , K i , and K d are gains of the proportional, integral, and derivative actions, respectively. Using the frequency response data of the three terms A( j k ), B( j k ), and D( j k ) and that of the imposed PID controller (17), the closed-loop frequency response H( j k , ) can be derived at each frequency k ∈ [0, 2000 ]rad∕s using Equation (14). In the latter, C( j k , ) is substituted by the PID controller frequency response, R C ( k , ) + jI C ( k , ), where R C ( k , ) and I C ( k , ) are the real and the imaginary parts defined for each frequency, k , as follows:…”

A measurement-based technique for designing fixed-order RST controllers and application to a coupled water tank system

“…Horowitz (1993) presented the quantitative feedback theory approach which is based on loop-shaping in the Nichols chart. A new measurement-based modeling technique, which is used for controller design, has been developed in Datta et al (2013). Longchamp (2006, 2003) utilized frequency-domain data to design controllers so that some desired closed-loop performance measures are satisfied.…”