Numerical method for testing robust control quality for linear one-dimensional dynamic control systems

Technological processes with multi-tempo components are quite widespread. A characteristic feature of the models of such processes is the allocation in the model of operators of the so - called" basic dynamics", describing the part of the control object that is subject to regulation, and operators of" structural disturbances " - these include those parts of the control object that already have the properties of stability and a given quality of control. In the synthesis of the regulator structural perturbations, as a rule, do not take into account, as a result of the transfer function of a closed system there is uncertainty. Since the properties of stability and control quality of the system are determined by the location of the poles of its transfer function, the question arises: at what operators of structural disturbances in the control object the closed system will still retain the properties of stability (robust stability) and control quality (robust control quality)? In the modal control scheme, the control quality is given as an area S on the complex plane; area S determines the desired location of the poles of the transfer function. Therefore, the questions of research (verification) of robust stability and robust control quality can be considered from a single point of view: is it necessary to check whether the roots of a given family of polynomials in the domain S? In the literature devoted to robust theory focuses on the problem of robust stability, and the problem of robust quality control fades into the background and is still not solved. The purpose of the study is to develop a robust control quality criterion for the case of structural disturbances in the control object model. Method: a theorem known as the "zero elimination principle" is generalized. The article provides a robust control quality criterion for a control system consisting of a control object with structural disturbances and a modal controller. Based on this criterion, a numerical method has been developed to check the robust quality of control. The proposed method is illustrated by an example.

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