Analytical phase‐lead controller design using pole placement: a pole‐zero ratio minimisation approach

Abstract

Owing to their simple structure and considerable improvement to the transient response, phase-lead controllers are broadly used in industrial applications. They are designed using root locus or Bode diagrams to introduce extra phase shift at the crossover frequency. Traditional phase-lead design techniques are either graphical or based on trial-and-error. In design techniques using root locus diagrams, there is no direct control on the values of a given time-domain performance index. To make this criterion satisfactory, the designer has to try different locations of the controller's zero and pole. Based on minimisation of the controller's pole-zero ratio subject to pole placement requirements, a simple analytical design technique is developed in this Letter. The necessary and sufficient conditions to determine optimal controller parameters are provided. To evaluate the performance of the proposed method, it is applied to a single integrating plant with time delay.