Mechanical Engineering ETDs

Publication Date



The following generalized problem was investigated in this study:

"Given a system that can be described by a vector differential equation of the type,

x = f (x, u, a, t) ,

and given both input data, u~ and output data, x~, determine both the general form of the differential equation, f~ (.,.,.,.), and the unknown parameters, a~."

This study describes a method of identifying the parameters, a~, and the form, f~, of the above equation. Initially, the form of the equation must be hypothesized to determine the unknown parameters; however, after the parameters are identified, then both the form and the parameters are evaluated using a residual evaluation technique. The method was applicable to both linear and nonlinear differential equations.

The method utilized test data obtained by exciting the system with a sinusoidal input over a wide frequency range. Experimental data from tests on two distinct systems were used in the study; these were a rubber isolator and a servocontrolled accelerometer. Differ­ential equations were developed to describe both test items.

The method was shown to be applicable for use with transient data and demonstrated with a real test of a servocontrolled gyroscope. Extensions to random excitation were considered, but no physical tests were performed.

Degree Name

Mechanical Engineering

Level of Degree


Department Name

Mechanical Engineering

First Committee Member (Chair)

William Ernest Baker

Second Committee Member

Larry W. Bickel

Third Committee Member

Daniel Paul Petersen

Document Type





See original for correct equations in abstract.