Date Available
1-10-2013
Year of Publication
2012
Document Type
Master's Thesis
Degree Name
Master of Science in Mechanical Engineering (MSME)
College
Engineering
Department/School/Program
Mechanical Engineering
Advisor
Dr. Jesse B. Hoagg
Abstract
This thesis presents rules that characterize the root locus for polynomials that are nonlinear in the root-locus parameter k. Classical root locus applies to polynomials that are affine in k. In contrast, this thesis considers polynomials that are quadratic or cubic in k. In particular, we focus on constructing the root locus for linear feedback control systems, where the closed-loop denominator polynomial is quadratic or cubic in k. First, we present quadratic root-locus rules for a controller class that yields a closed-loop denominator polynomial that is quadratic in k. Next, we develop cubic root-locus rules for a controller class that yields a closed-loop denominator polynomial that is cubic in k. Finally, we extend the quadratic root-locus rules to accommodate a larger class of controllers.
We also provide controller design examples to demonstrate the quadratic and cubic root locus. For example, we show that the triple integrator can be high-gain stabilized using a controller that yields a closed-loop denominator polynomial that is quadratic in k. Similarly, we show that the quadruple integrator can be high-gain stabilized using a controller that yields a closed-loop denominator polynomial that is cubic in k.
Recommended Citation
Wellman, Brandon, "Root Locus Techniques With Nonlinear Gain Parameterization" (2012). Theses and Dissertations--Mechanical Engineering. 21.
https://uknowledge.uky.edu/me_etds/21
