Saturated Root Locus: Theory and Application

This paper extends the standard root locus technique to systems with saturating actuators. This is accomplished by introducing the notion of S-poles, which are the poles of the quasilinear system obtained by applying the method of stochastic linearization to the system with saturation. The path traced by the S-poles on the complex plane when the gain of the controller changes from 0 to ∞ is the S-root locus. We show that the S-root locus is a subset of the standard root locus, which may terminate prematurely at the so-called termination points. A method for calculating these points is presented. In addition, the issue of amplitude truncation in terms of the S-root locus is investigated. Finally, an application of the S-root locus to hard disk drive controller design is presented, and it is shown that this simple technique results in a controller that compares favorably with those designed using more sophisticated approaches.