Internal model control and process uncertainty: mapping uncertainty regions for SISO controller design

Abstract

Abstract A complete SISO controller design technique is presented that allows robust controller design in the face of process uncertainty. Process-uncertainty descriptions with meaningful physical interpretations are compatible with the technique. A test for robust performance can be applied when the process is described by a transfer function with real parameter variations. First a method is presented for locating all possible complex variations of a transfer function resulting from real parameter uncertainties. The possible variations are pictured as model uncertainty regions on the complex plane. Next a controller design technique based on the internal model control structure is outlined. The controller is used to map the process uncertainty regions to the Nyquist plane for stability and performance analysis. The region-mapping technique offers a unique opportunity to compare robust performance of PID and Smith Predictor controllers. Finally, applications of the proposed technique to structured singular-value analysis are discussed.