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DEVELOPMENT OF VISUALIZATION TOOLS FOR RESPONSE OF 1ST AND 2ND ORDER DYNAMIC SYSTEMS

Abstract

Students often enter a Dynamic Systems course with no real background or exposure to many of the concepts used to define “non-static” systems. The material is often a significant departure from the previous material covered, and the vernacular/terminology is very new and unfamiliar to the students. Nomenclature and concepts such as poles, zeros, s-plane, and others cause some confusion for the students.

In order to help the students further explore these new concepts and ideas and overcome some of the issues related to this departure in material, several MATLAB and LabVIEW graphical user interfaces (GUIs) have been developed. GUIs related to response of first and second order systems due to a variety of different input conditions have been developed. The GUIs present data in a form so that students can immediately see the effects of changing system parameters as they relate to pole locations in the s-plane, time response and settling time, and complex frequency response characteristics. The GUIs are presented along with student survey assessment on the usefulness of the new software tools.

I. Introduction

Mechanical Engineering students take a wide variety of different courses in the solids and thermofluids fields. In the area of solids, courses such as statics, strength of materials, etc. generally revolve around simple concepts of static strength with some material on fatigue but with no real description as to how those dynamic loads are created. In fact, the majority of a student’s curriculum may center on these basic static concepts with little exposure to real response of dynamic systems. Even courses in dynamics generally focus only on the subject of rigid body dynamics. The fundamental concepts of frequencies, damping, poles/zeros, etc. are not addressed until either a Dynamic Systems course taught at the Junior or Senior level or a sequence of Vibrations and Controls courses. However, depending on the particular curriculum of an individual program, many times only one Dynamic Systems course is available along with elective courses in Vibrations and/or Controls. Suffice it to say that the engineering student enters into a course such as Dynamic Systems with very little exposure (if any at all) in vernacular typically used for this material.

The beginning of a Dynamic Systems course finds the student perplexed and confused concerning basic topics. Of course, the student has already seen portions of this basic material in math related courses such as Ordinary Differential Equations, but it is likely that the student has no recollection of that material nor were there any “practical” examples that might have forced the student to remember any of that material. In teaching a Dynamic Systems course, basic concepts of complex numbers (real and imaginary), relationships of exponentials and sines/cosines, solutions of 1st and 2nd order differential equations, Laplace transforms, Fourier Series, etc. are expected to be firmly planted in the student’s skill sets. Often, however, these

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Avitabile, P., & Hodgkins, J. (2006, June), Development Of Visualization Tools For Response Of 1 St And 2 Nd Order Dynamic Systems Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--401