Parametric Optimization of a Second Order Time Delay System with a PID-Controller

Abstract

Paper addresses parametric optimization problem for second order system with delay in control. Control is realized by means of PID-Controller in feedback loop. As an index is taken the integral of squared error. The value of that index is computed using the Lyapunov functional, which is defined applying the Lyapunov matrix. The value of that functional at the initial function of the time delay deferential equation equals the index value.