Robust control of a nonlinear time-delay system

Experiments dealing with the heating of living tissue have resulted in four completely different temperature response characteristics as a result of the application of four different constant power levels. The four response characteristics can be classified as overdamped, critically damped, underdamped, and undamped oscillations. A particular nonlinear, time-delay dynamic equation has previously been shown to exhibit the same type of temperature response characteristics as those in the experiments. Herein, a control strategy is applied to the nonlinear, time-delay equation to inhibit the oscillatory behavior. A proportional plus integral (PI) controller with antiwindup, that is restricted to be nonnegative, is shown to be an effective controller in eliminating the oscillatory responses. This effectiveness is shown by analyzing and explaining the robustness properties of this controller as applied to this nonlinear, time-delay system.This work was supported by National Cancer Institute Grant CA 36428. An earlier version of this article appears in the proceedings of the31st IEEE Conference on Decision and Control.