The development, properties, and application of the complex phase lead compensator

Phase lead compensation is an important and reliable method for classical control design in the frequency domain for both continuous-time systems and discrete-time systems. First order or single phase lead compensators consist of a single stable real-axis zero to the right of a single stable real-axis pole. This paper introduces a new phase lead compensator structure which is a variation of a double lead compensator in that the poles and zeros appear in complex conjugate pairs. This new compensator can arbitrarily reduce the difference between the low and high frequency gains compared to a double lead compensator depending on the damping ratios of the complex conjugate poles and zeros; at the cost of a narrowing of the gain peak and an increase in the rate of change between the low and high frequency gain. This paper examines the implications of these tradeoffs and concludes that they may well be worthwhile for some applications