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Abstract
This report covers the exploration of system identification and parameter estimation for a first-order system. The choice of a system is justified by the use of the first-order differential equations. They are necessary to determining time constant ???? and steady-state gain ????. Throughout the experiment, static, frequency response, and transient tests of a DC motor are analyzed.
Introduction
Understanding how a DC motor works require delving into system identification and parameter estimation for a first-order system. The fundamental question of the experiment is determining which parameters should be considered for an adequate analysis of a DC motor.
Analysis
First, the steady-state gain is calculated by dividing the ratio of the load shaft angular velocity by the motor voltage. Before making the calculations, the constant motor voltage, which is input, and the steady-state load shaft angular velocity are specified and measured. For obtaining the motor voltage parameters, a 0-amplitude sine wave is created, with the amplitude set to 0 and the initial offset set to 2.
Second, estimating the time constant required measuring the gain as a function of frequency. For the measuring to transpire, a sinusoidal motor voltage was specified and the load shaft angular velocity was measured. The ratio of maximum velocity divided by the motor voltage amplitude provided the gain. This procedure was repeated to create a sufficient range of frequencies, which would allow obtaining the time constant and steady-state gain from the resulting frequency response function. Finally, the steady-state gain and time constant are calculated from the transient response.
Conclusion
Overall, the calculations required for analyzing the DC motor hinge are dependent upon the variables. For example, estimating the frequency response with an excessively steep slope of the higher-frequency points would probably make the resulting time constant smaller. Similarly, if the lower-frequency points were not a flat line the resulting parameter would change because of the direction of the lower-frequency points. Also, having too much noise in the time series would distort the time constant, which would not provide a reliable parameter. Altogether, the veracity of the experiment could be sufficiently ensured with the moderate variable parameters.
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