A rotating load is connected to a field-controlled DC electric motor through a gear system. The motor is assumed to be linear. A test results in the output load reaching a speed of 1 rad/s within 0.5 s when a constant 80 V is applied to the motor terminals. The output steady-state speed is 2.4 rad/s. Determine the transfer function of the motor, in rad/V. The inductance of the field may be assumed to be negligible. Also, note that the application of 80 V to the motor terminals is a step input of 80 V in magnitude. Hint: Look to find values for combinations of variables like km/(b* Rf) and b/J. Use the Final Value Theorem in the S Domain and the other condition in the time domain to create equations for the combinations. Answer: Theta(s)/Vs = 0.0324/(s* (s+1.08))

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A rotating load is connected to a field-controlled DC electric motor through a gear system. The motor is assumed to be
linear. A test results in the output load reaching a speed of 1 rad/s within 0.5 s when a constant 80 V is applied to the
motor terminals. The output steady-state speed is 2.4 rad/s. Determine the transfer function of the motor, in rad/V. The
inductance of the field may be assumed to be negligible. Also, note that the application of 80 V to the motor terminals is a
step input of 80 V in magnitude.
Hint: Look to find values for combinations of variables like km/(b* Rf) and b/J. Use the Final Value Theorem in the S
Domain and the other condition in the time domain to create equations for the combinations.
Answer: Theta(s)/Vs = 0.0324/(s* (s+1.08))
Transcribed Image Text:A rotating load is connected to a field-controlled DC electric motor through a gear system. The motor is assumed to be linear. A test results in the output load reaching a speed of 1 rad/s within 0.5 s when a constant 80 V is applied to the motor terminals. The output steady-state speed is 2.4 rad/s. Determine the transfer function of the motor, in rad/V. The inductance of the field may be assumed to be negligible. Also, note that the application of 80 V to the motor terminals is a step input of 80 V in magnitude. Hint: Look to find values for combinations of variables like km/(b* Rf) and b/J. Use the Final Value Theorem in the S Domain and the other condition in the time domain to create equations for the combinations. Answer: Theta(s)/Vs = 0.0324/(s* (s+1.08))
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