Robust Design and Analysis of Third and Fourth Order Time Delay Systems with Application to Automotive Idle Speed Control

This paper contains the development of an analytical approach for the synthesis of a proportional- integral-derivative (PID) throttle regulated idle speed control (ISC) system that possesses robust stability properties in the presence of parameter variations due primarily to changing system operating point. A fourth order time delay mathematical model suitable for ISC analysis is presented, the robustness problem is formulated, and necessary and sufficient conditions for robustness are determined in terms of experimentally derivable physical parameters. The result is a fairly simple set of robustness inequality conditions that can be employed in throttle control related ISC design and analysis with possible extension to higher order robust system synthesis.