An Improved Analytical PID Controller Design for Non-Monotonic Phase LTI Systems

An improved technique of analytical design of proportional-integral-derivative (PID) controllers in frequency-domain for non-monotonically decreasing phase systems by means of gain crossover frequency and phase margin specifications is presented in this brief. The proposed method guarantees a minimum phase margin inside the desired bandwidth, assuring better performance to step response for the closed-loop system. In order to achieve this feature, it is necessary to redefine the concept of phase margin when the uncontrolled process presents a non-monotonically decreasing phase inside the bandwidth. Hence, the phase margin can still be used as a good robustness indicator and allows the Bode stability criterion to be used for monotonic minimum-phase or non-monotonic minimum-phase systems.