The problem of multiparameter adaptive systems having specified poles and zeros

This paper presents a method of choosing the coefficients of prefiltering, series, and feedback compensators in such a way as to meet given time response specifications despite plant parameter variations. A closed loop transmission T(s) which will result in satisfying the time response specifications is chosen in advance. A general approach for calculating compensator coefficients for any single-input single-output configuration is considered. This leads to two sets of nonlinear algebraic equations. To avoid solving these nonlinear equations, a particular configuration is assumed and coefficients of the necessary series compensation are first calculated from measured values of the plant parameters and T(s) by solving a set of linear algebraic equations. The coefficients of the three compensators are then calculated by assigning appropriate roles to each compensator. For certain plant parameter values, the resulting compensator coefficients imply right-half-plane compensator poles and zeros. These can be realized; however, considerations of reliability and economy may require that all compensator poles and zeros be in the left half plane. This problem is illustrated by a simple example. A second example treats a system having five closed loop poles and one zero.