Some Connections Between Modern and Classical Control Concepts

Abstract

This is a tutorial paper that discusses the synthesis of optimum constant-gain feedback controllers for stationary linear systems. These controllers minimize the mean value of a weighted sum of squared output error and squared input in the presence of stationary random gaussian disturbances. Symmetric root locus is shown to be a useful graphical technique for visualizing closed loop pole locations as functions of the performance index weighting parameters and the disturbance spectral densities. The main component of the optimal controller is a minimum variance observer that estimates the system state variables using a measurement of the output and a set of observer gains. These estimated states are fed back to the input with a set of optimal regulator gains. This optimal controller is interpreted here as a classical compensator. A fourth order example is used throughout the paper to help clarify the concepts.