The approximation of discrete control by a transport delay

The analytical derivation of z-transform models for discretely-controlled, continuous processes of high order, is too tedious an exercise in practice, particularly where adjustable sampling rates are to be explored. In order to retain an analytical approach, the possibility is examined of using a continuous transport delay to replace the sample-hold operation, thereby permitting design on a conventional, continuous-system basis. Comprehensive analysis of first-and second-order systems reveals that the continuous delay approximation yields stability predictions that are generally pessimistic, but not excessively so. Where the approximation is optimistic, the discrepancy between predicted and true gains for critical stability is insignificant practically. Simulation is used across a wide dynamic range of process and computer-dominated systems to verify the critical gain formulae derived for the delay and discrete systems. Simulation results moreover demonstrate the adequacy of the proposed delay approximation for performance prediction closer to desired damping levels.