New results in feedback modal-controller design

Abstract

The problem of designing a state feedback controller which drives the eigenvalues of a linear multivariable system to prespecified positions is studied. The approach followed is that of transforming the system under control to a phase-variable canonical form prior to the application of the control design procedure. This transformation is possible only when the system is state-controllable which implies that it is also mode-controllable. The single-input design problem is first considered and solved by an elegant utilization of the concept of state similarity transformation. By this transformation one essentially converts the original problem of designing the state feedback modal controller matrix gain F to that of determining the associated similarity transformation T. The multi-input controller design problem is then treated by an extension of the above results which yield the most general state feedback modal controller possible. The state feedback modal controller derived is utilized, and the most general solution to the output (incomplete state) feedback modal-controller design problem is found. A set of examples is provided to illustrate most aspects of the theory.