DETERMINATION OF THE OPTIMUM RESPONSE OF LINEAR SYSTEMS (ZERO DISPLACEMENT ERROR SYSTEMS)

Abstract

In (1) two response functions L and L₁ were defined by the equations where e is the error at time τ. These relations are applied to a linear system having one degree of freedom. By considering the response to a step-function disturbance it is found that systems making L a minimum have a lightly damped oscillatory response. The smaller L₁ is, the ‘smoother’ is the response. Values are obtained for the coefficients of the characteristic equation of any order making L a minimum. An approximate method is given for correcting these coefficients to enable the response to be improved to give equal damping in the least damped modes of oscillation.