Smith predictor design for robust performance

A method is outlined for designing Smith predictor controllers that provide robust performance despite real parameter uncertainties in the process model. Insight into the design process is gained by viewing the Smith predictor from the perspective of internal model control. Performance requirements are written in terms of a frequency-domain weight restricting the magnitude of the closed-loop sensitivity function. A general method for approximating multiple parameter uncertainties by a single multiplicative uncertainty is developed—an exact bound is derived for the magnitude of multiplicative uncertainty used to approximate simultaneous uncertainties in process gain, time-constant, and time-delay. Three different tuning methods are demonstrated; each is applied to a wide range of parameter uncertainties in a first-order with time-delay model. The first tuning method locates loop transfer-function uncertainty regions to test for robust performance—real parameter uncertainties are considered exactly. The second tuning method approximates real parameter uncertainties by multiplicative uncertainty and uses structured singular value analysis to guarantee robust performance. The third is a ‘quick design’ method that considers the unit magnitude crossing of the multiplicative uncertainty. Finally, the Smith predictor controller is compared with the structured-singular-value-optimal controller.