An approach to the linear multivariable servomechanism problem†

This paper presents a state-space approach to the multivariable ‘type one’ servo-mechanism problem. Necessary and sufficient conditions for the controllability of such systems are derived and applied to the observability of the (dual) state reconstructor problem for a system with an unknown constant input. The paper also presents a simple systematic design algorithm which provides type one servomechanism performance to command inputs, together with pre-specified closed-loop pole locations. Examples are given to illustrate the utility of the design procedure.