Theory of system type for linear multivariable servomechanisms

A theory of system type for linear multivariable servomechanisms is developed. New characterizations of system type are formulated and two systematic methods for determining system type are derived. Both methods are algorithmic and easier to apply than the techniques given in earlier studies. The first applies to the case where the open-loop system is described by its transfer function matrix and the second where its time domain state-space representation is given. New results are also presented for characterizing and identifying the system type for certain composite systems from a knowledge of the individual subsystem types. Methods for specifying pre- and post-compensation to achieve a desired system type in linear multivariable servomechanisms are developed. Sufficient conditions are derived for both forms of compensation when the compensator is restricted to a diagonal input-output representation and a method for realizing reduced-order precompensators is presented for the case where the restriction is removed. Results for closed-loop stability are included.