Design of PID controllers for multivariable systems

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Abstract
The paper develops a simple method for the design of PID controllers for linear multivariable systems where the controllers use only the available system outputs. The resulting closed-loop system has a specified set of poles and in the steady state the outputs follow step commands and reject disturbances of any form with constant final values. For an m-input, l-output system of order n, the PID controller can place 3m poles of the (n + J)th-order closed-loop system at any desired locations. The controller matrices are assumed to have unity-rank and are obtained from linear equations. The method is illustrated by an example.