Question

Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known to be J-4 kg-m2, and we wish to determine the system damping (B,) and the motor gain (Kamp One common method for doing this is to look at the frequency response plots Using the results from lecture about Bode plots, determine the values for these two (i.e. Bode plots) of the system, which are provided in this handout. stem parameters. sy - Be sure to show vour work CLEARLY Bode plots for the rotational systern a 30 20 E 10 -10 100 10 10 Frequency (radlsec) 70- -20 40 100 100 103 To-1 Frequency (rad/sec)

Answer 1

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We have GCS)- _Kam JS+ Br We have a constant of (kamp/8t) ghichis 40 db from 'magnitude plot. 40: 2019( same) .'. KomP -100 Kamp Br Also, te have a pole at S- -J/Br he slanb and horizontal lines intersect each other at 0 rad /s Taking magnitude any GS) 40 4S+0.4