Analytical construction of regulators for oscillatory systems with liquid dampers

TL;DR

This paper develops a mathematical model and control law for oscillatory systems with liquid dampers, ensuring stability and optimality through fractional derivative-based controllers, demonstrated via numerical example.

Contribution

It introduces a novel control law for oscillatory systems with liquid dampers using fractional derivatives, ensuring stability and optimal control.

Findings

Control law guarantees asymptotic stability

Quadratic functional minimized effectively

Numerical example confirms theoretical results

Abstract

A mathematical model of oscillatory systems control with liquid dampers is considered which differs from the classical ones by replacing the first derivative of such a fractional derivative that is between numbers 0 and 2 other than unity. Using the methods of constructing Letov controllers, a control law is constructed that ensures the asymptotic stability of the closed system and minimizes the quadratic functional. The results are illustrated by a specific numerical example.