Extended root-locus technique applied to pole-placement for PI controller design

The root-locus method is often employed when a controller that can find its gains is designed. Usually the method is used to determine only one design parameter. However most controllers for industrial applications have more than one controller gain: for example proportional-integral-derivative (PID) controllers have three controller gains, P, I, and D. As the root-locus technique cannot complete the designs of controllers with more than one gain, designing controller with more than one parameter requires an extension of the conventional root-locus technique. This paper proposes an extended root-locus method for controllers with two parameters. Matlab is used as a computation tool to demonstrate the effectiveness of the proposed method through the solution of numerical examples. We demonstrate the determination of two controller gain parameters based on this extension of the root-locus method, which can be applied to controller design problems with multiple parameters.