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Session 2793

An Analytical Method for Optimum Frequency Domain Design in Control Applications

Gary L. Dempsey, Eugene S. McVey Bradley University/University of Virginia

Abstract

Our paper will revisit a method that was first introduced at Yale University in the late 1950s by Bower and Schultheiss in their linear control textbook, Introduction to the Design of Servomechanisms. Control system design normally requires several design iterations in a simulation environment to meet a set of system specifications. The analytical method discussed here comprises the first design iteration but normally results in a design that is close to optimum, i.e., the resulting system will have maximum stability margin and bandwidth. The method eliminates trial and error procedures, can accommodate time and frequency domain specifications, and can be applied to continuous-time or sampled-data systems.

I. Introduction

Undergraduate control theory textbooks and courses have typically been heavily weighted to control system analysis while design approaches have received less attention. Design approaches are many times reduced to cookbook methods that are not optimum for a given application. The cookbook methods and lack of design examples do not provide insight into how to modify the controller if a set of system specifications is not met. Therefore, students are unable to solve problems they have not seen in the course or textbook or rely on trial and error procedures to meet specifications. Obviously, analytical design methods for the controllers would be beneficial to undergraduate engineering students and to the control theory community.

Our paper will revisit a method that was first introduced at Yale University in the late 1950s by Bower and Schultheiss1 . The method was illustrated for several minimum-phase continuous-time systems and a system modeled as first-order with time delay. During this period Dr. J. E. Gibson taught the method in control theory courses at Purdue University. The method was observed later in other textbooks although not in its entirety2-4. The authors have presented the method in their control theory courses at Bradley University, Purdue University and the University of Virginia.

The paper is divided into the following five sections. Section II will provide motivation for the analytical method proposed by Bower and Schultheiss. Section III will introduce the frequency domain design method for minimum-phase continuous-time systems. Section IV will show how the method can

Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright ©2001, American Society for Engineering Education

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McVey, E., & Dempsey, G. (2001, June), An Analytical Method For Optimum Frequency Domain Design In Control Applications Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--8904