Parameter plane approach to the analysis of optimal linear control systems

Abstract

The paper shows how the parameter plane technique can be applied to the characteristic equation of the optimal linear control system chosen to minimize a quadratic performance criterion. The technique, as applied to a general polynomial equation, is described paying particular attention to the plotting of constant relative damping, constant undamped natural frequency and constant real pole position characteristic curves in the parameter plane which has two variable parameters as co-ordinates. The method is then applied to an optimal linear control system characteristic equation which is written in a convenient form for determining the structure of the characteristic equation coefficients in terms of the variable parameters. Particular attention is given to two parameters contained within a diagonal control weighting matrix and by observing the characteristic curves in the parameter plane the effect of different values of these two parameters on the optimal transient performance can be investigated without...