SYNTHESIS OF PID CONTROLLERS FOR INTEGRAL PROCESSES WITH TIME DELAY

This article deals with the problem of determination of the stabilizing parameter sets of Proportional-Integral-Derivative (PID) controllers for first-order and second-order integral processes with time-delay. First, the admissible stabilizing range of proportional-gain is determined analytically in terms of a version of the Hermite-Biehler Theorem applicable to quasi-polynomials. Then, based on a graphical stability condition developed in parameter space, the complete stabilizing regions in an integral-derivative plane are drawn and identified graphically, not calculated mathematically, by sweeping over the admissible range of proportional-gain. An actual algorithm for finding the stabilizing parameter sets of PID controllers is also proposed. Simulations show that the stabilizing re-ions in integral-derivative space are either triangles or quadrilaterals.