Непараметрическая идентификация элементов системы терморегулирования

Abstract

The thermal control system “Heater-Fan-Room” is represented by three different-type interconnected simpler subsystems. In this paper, a “black-box” whose structure is not specified is used as a mathematical model of the system and subsystems due to complexity of physical processes proceeding in these subsystems. For stationary linear systems, the connection between an input and an output of the “black-box” is defined by the Volterra integral equation of the first kind with an undetermined difference kernel also known as impulse response in the automatic control theory. In such a case, it is necessary to evaluate an unknown impulse response to use the “black-box” model and formulate all subsystems and the system as a whole. This condition complicates significantly the solution search of non-parametric identification problems in the system because an output of one subsystem is an input of another subsystem, so active identification schemes are unappropriated. Formally, an impulse response evaluation is a solution of the integral equation of the first kind for its kernel by registered noise-contaminated discrete input and output values. This problem is ill-posed because of the possible solution instability (impulse response evaluation in this case) relative to measurement noises in initial data. To find a unique stable solution regularizing algorithms are used, but the specificity of the impulse response identification experiment in the “Heater-Fan-Room” system do not allow applying computational methods of these algorithms (a system of linear equations or discrete Fourier transformation). In this paper, the authors propose two specific identification algorithms for complex technical systems. In these algorithms, impulse responses are evaluated using first derivatives of identified system signals that are stably calculated by smoothing cubic splines with an original smoothing parameter algorithm. The results of the complex “Heater-Fan-Room” system modeling and identification prove the efficiency of the algorithms proposed. Acknowledgments: The reported study was funded by RFBR, project number 20-38-90041.