Optimum dead-beat controller design for SISO systems using time-weighted performance indices

Abstract

An analytical method for the design of optimum digital controllers for SISO systems that exhibit dead-beat response to polynomial type inputs is proposed. The optimization is performed through the minimization of the sum of the time-weighted squared errors (STWSE) of the step response. This criterion attaches little importance to initial errors and places emphasis on long-duration transients, provided that the weighting function is monotonously increasing with time, thus offering a good tracking performance to complex inputs. The cases where the system exhibits dead-beat response to ramp and to parabolic inputs are considered, and the response to a complex input is also examined.