ON THE MODEL-PROCESS MISMATCH TOLERANCE OF VARIOUS PARAMETER ADAPTATION ALGORITHMS IN DIRECT CONTROL SCHEMES: A SECTORICITY APPROACH

Designing adaptive controllers under model-process mismatched situations is considered. A suitable representation for the uncertainty is explicitly incorporated, what renders the stability analysis problem suitable for a sector condition formulation ( Safonov, 1980 ). The performance from the robustness point of view, of various currently used parameter adaptation algorithms is compared. This is done by determining regions on the complex plane where an uncertainty dependent Nyquist locus must be contained to insure boundedness of the tracking error. It is shown that uniform boundedness of all signals may only be proven for a weighted least squares scheme under suitable weighting coefficients selection knowkdge of the process steady-state gain is required to insure convergence to zero of the tracking error. The proposed framework is shown to be amenable for the study of non-stably invertible or mismatched delay systems.