Direct design procedure for multivariable feedback systems

Abstract

A direct design procedure is established for linear time-invariant controllable multivariable systems which permits a straightforward calculation of the feedback matrix to attain prescribed closed-loop poles. It permits the choice of the relative tightness of the feedback to each input, and hence allows design with feedback to only some inputs (i.e. incomplete input feedback). Furthermore, it permits the design of the important practical case where some states are not accessible. For these, the procedure produces the necessary and sufficient condition for pole positioning to be possible, and permits the required feedback to be calculated. The procedure is applicable to systems with any number of inputs and states. Computationally, the method is extremely fast, with computation times of the order of seconds, making it well suited to computer-aided control-system design.