Robust control of a nonlinear time-delay system [heating of living tissue]

The authors investigate the use of control theory techniques as applied to the heating of living tissue. 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 are overdamped, critically damped, underdamped, and undamped oscillations. A nonlinear, time-delay dynamic equation is presented and shown to exhibit the same type of temperature response characteristics as those in the experiments. A control strategy is then applied to the dynamic equation to inhibit the oscillatory behavior. It turns out that a proportional plus integral controller that is restricted to be nonnegative and bounded from above with antireset windup is sufficient to eliminate the oscillatory responses