Algebraic Solution of the Servomechanism Problem With External Disturbances

Abstract

Previous studies of multi-variable servomechanism problems, using modern control theory, have relied almost exclusively on optimal control techniques to formulate and solve the problem. In that way, servo tracking has been obtained as a by-product of minimizing some contrived optimization functional. In this paper, a new servo theory is proposed which makes use of simple linear algebraic methods, rather than optimal control methods, to formulate, study, and solve the multi-variable linear servomechanism problem. The result is a new, algebraic procedure for designing high-performance output-feedback servo controllers for multi-input, multi-output, possibly time-varying linear plants. Moreover, when the plant is also subjected to external disturbances, the servo controllers designed by this new procedure will continue to provide consistently accurate tracking of complex servo command inputs—even though the disturbances are persistent acting, unknown and unmeasurable.