Ripple performance and choice of sampling frequency for a direct digital control system

A method of computing the steady-state output ripple power for single-rate and multirate direct digital control systems with a stochastic input is presented in the paper. The formulas derived appear to be more easily evaluated than those proposed in earlier work. Experimental evidence obtained for sinusoidal inputs to two practical systems confirms the theoretical results. Considerable attention is given to the choice of a sampling frequency which produces a ripple power consistent with the specified design accuracy and component wear and tear. The results show that the sampling frequency cannot be chosen directly, and that an iterative design procedure is generally necessary. A simplification of the expression for the steady-state output ripple power of a single-rate system subjected to a particular sinusoidal input is suggested as providing a realistic starting point for the iteration procedure. The sufficiency of this initial estimate as a worst-case design is established for a practical system.