Robust Feedback Controller Design based on Bode’s Integrals for General Minimum-phase Systems

Abstract

The gain crossover frequency and the phase margin are the most common design specifications in robust controller design. An additional flat phase constraint is proposed to guarantee the system robustness under gain variations, where the phase of the desired loop transfer function is flat around the gain crossover frequency. This controller design methodology is successfully implemented on integer-order proportional-integral-derivative (IOPID) controllers and fractional-order proportional-integral (FOPI) controllers in a class of first-order plus time-delay (FOPTD) systems. However, it is not easy to apply the flat phase constraint on general minimum-phase systems since the derivative of the loop transfer function with respect to frequency may be difficult to deduce. A flat phase design approach based on the Bode’s integral is proposed for general minimum phase systems which does not need the system model information. An FOPI controller and an IOPID controller are designed in numerical examples to validate the effectiveness of the proposed robust controller design method.