Root locus design with Complex Proportional-Integral-Lead compensation

The Complex Proportional-Integral-Lead (CPIL) compensator is a relatively new compensator structure that is a variation of the commonly used PI-lead compensator. The complex conjugate zeros provide additional design flexibility compared with the standard structure. Until now, the potential of the CPIL has only been examined for controller design via frequency response. This paper examines the utility of the CPIL for root locus design. We illustrate two design strategies by considering compensator design for a double integrator and for a second order system with a very lightly damped resonance.