Analytical design of dynamic system regulators taking into account the effect of disturbing factors

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Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University

This article deals with the problem of synthesis of optimal by the minimal value of integral-quadratic criterion dynamic systems, which are described by a model of equations in state variables.

Based on finding the Lyapunov matrix and optimization equations, we propose a method for synthesizing a set of feedback loop coefficients with respect to state variables that provide the minimal value of integral quadratic criteria when exposed to external coordinate  disturbances. Finding the feedback loop coefficients with respect to state variables of the dynamic system using the proposed method extends the optimization methods of such systems by integral-quadratic criteria in a vector-matrix description taking into account the action of external influences. The synthesis of the coefficients carried out on the example of a second-order dynamic system is also given.

This method makes it possible to find the dependences of these coefficients on  the initial  coordinates of the dynamic system, as well as to synthesize a functional converter whose influence in the feedback loops optimizes the given system

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