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Paper 2005-493

Frequency Domain System Identification of One, Two, and Three Degree of Freedom Systems in an Introductory Controls Class

Robert D. Throne Rose-Hulman Institute of Technology

Abstract

We have developed a sequence of laboratories for our introductory controls classes to identify and control one, two, and three degree of freedom mass-spring-damper systems. Initial estimates of damping ratios and natural frequencies are made using the log-decrement method with only one cart free to move at a time. By exciting the system at various frequencies the magnitude portion of the Bode plot for the transfer functions between the input and the position of each cart is determined, and the resonant frequencies are estimated. Once the parameters for the transfer functions have been determined and the corresponding state variable model is identified the students control the positions of the carts with state variable control. This sequence of experiments has a number of practical benefits. By exciting these systems with various frequencies, the students understand transient response and sinusoidal steady state in terms of the physical behavior of mechanical systems. The students also develop a better appreciation for the use of Bode plots. Finally, nearly all of the parameters can be estimated in at least two ways and the students must compare these estimates to check for consistency.

Background

Eleven ECP-210a spring/mass/damper rectilinear systems were purchased through an NSF CCLI grant obtained by investigators from both the Electrical and Computer Engineering and Mechanical Engineering departments at Rose-Hulman Institute of Technology. These systems allow for easy implementation of different standard controller types and are easily reconfigurable. Figure 1 shows one of the “carts” of the system, connected with two springs. The position encoder is shown toward the back of the system. The carts are moved via a motor with a rack and pinion mechanism.

Faculty from both the Mechanical Engineering and Electrical and Computer Engineering departments have developed weekly 3 hour labs utilizing these systems in their introductory control systems classes. In the ECE introductory class the students regularly utilize these systems to first identify and then control a one degree of freedom system (only one cart moves) utilizing classical control techniques including root locus methods and various model matching “Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education”

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Throne, R. (2005, June), Frequency Domain System Identification Of One, Two, And Three Degree Of Freedom Systems In An Introductory Controls Class Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--15269