Deadbeat Feedback Design For Time Varying Systems

New results are given for the design of a step-varying digital control system's feedback gains that shape the zero-input response of single-input plants. These gains are calculated forward in time, the only requirement being that the plant be completely controllable. An algebraic matrix proof is given that these gains provide an ongoing solution to the problem of unmodeled disturbances. The classical method used for determining deadbeat feedback gains for both discrete and continuous time-invariant plants is shown to be a subset of this procedure. This method does not require a knowledge of the system's characteristic equation or eigenvalues. A stable and efficient computational method for the calculation of these gains is introduced. A tracking system is presented, deadbeat feedback and input gains calculated, and the system response analyzed. Numerical results are presented which demonstrate the utility of this method.