Design of proportional-plus-integral controllers for multivariable systems

The paper presents a simple method for the design of proportional-plus-integral controllers for multivariable systems where the controllers act directly on the available system outputs. For an m-input l-output system of order n, the PI controller can place 2m+l-1 poles of the (n+l)th order closed-loop system at any desired locations. In the closed-loop system, the outputs follow step commands in the steady-state and reject unmeasurable arbitrary disturbances with constant final values. The steady-state properties are preserved for variations or uncertainities in the system parameters provided the closed-loop stability is maintained. The transient responses of the closed-loop system may be improved by tuning the controller as described in the paper. The controller design method is illustrated by a numerical example.