The Reducing Transformation and Smith Predictor Methods for Stabilizing Plants with Transport Lag

The reducing transformation and Smith Predictor methods facilitate finite dimensional controller design techniques for stabilizing plants with transport lag. This paper begins by deriving nominal stability results confirming the fact that for unstable plants, controllers which use the Smith Predictor compensator cannot stabilize the closed loop system. By contrast, it is verified that the reducing transformation can be applied in these unstable plant cases. After developing the nominal stability results, the structured singular value is used to define conditions for robust stability of an entire parameter family of plants. An example, using the reducing transformation, is given at the end of the paper.