3. Consider the following system described below (parameters and inputs are in SI units): Im = 0.4 R = 0.18 k=30 b = 0.2 M m = 6 b=20 www Im T(t) = 2 R Mr Bammy Note: b is the damping coefficient between the mass and the ground (it is shown as c in the diagram, but we will use b). Complete the following: a) Find an equation of motion for the simplified equivalent mass system. Assume that the shaft between the inertias is rigid. b) Find the equations of motion in state variable form for this system. You should end up with 2 state variable equations. c) Numerically solve for the state variables and plot each state variable versus time. Assume, that the mass is initially displaced a distance of 0.1 in the positive direction and the mass velocity is initially zero. Also plot the spring force and damping force. d) This system is required to have a maximum displacement overshoot that is less than 15% of the steady state value to avoid the rack impacting another portion of the machine. Determine whether this system meets that requirement. If not, what parameters do you recommend changing to cause this system to meet the overshoot design requirement? Verify that your results are reasonable by comparing the initial and steady state values with your expectations.
3. Consider the following system described below (parameters and inputs are in SI units): Im = 0.4 R = 0.18 k=30 b = 0.2 M m = 6 b=20 www Im T(t) = 2 R Mr Bammy Note: b is the damping coefficient between the mass and the ground (it is shown as c in the diagram, but we will use b). Complete the following: a) Find an equation of motion for the simplified equivalent mass system. Assume that the shaft between the inertias is rigid. b) Find the equations of motion in state variable form for this system. You should end up with 2 state variable equations. c) Numerically solve for the state variables and plot each state variable versus time. Assume, that the mass is initially displaced a distance of 0.1 in the positive direction and the mass velocity is initially zero. Also plot the spring force and damping force. d) This system is required to have a maximum displacement overshoot that is less than 15% of the steady state value to avoid the rack impacting another portion of the machine. Determine whether this system meets that requirement. If not, what parameters do you recommend changing to cause this system to meet the overshoot design requirement? Verify that your results are reasonable by comparing the initial and steady state values with your expectations.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:3. Consider the following system described below (parameters and inputs are in SI units):
Im = 0.4
R = 0.18
k=30
b
= 0.2
M
m = 6
b=20
www
Im
T(t) = 2
R
Mr
Bammy
Note: b is the damping coefficient between the mass and the ground (it is shown as c in the
diagram, but we will use b). Complete the following:
a) Find an equation of motion for the simplified equivalent mass system. Assume that the
shaft between the inertias is rigid.
b) Find the equations of motion in state variable form for this system. You should end up
with 2 state variable equations.
c) Numerically solve for the state variables and plot each state variable versus time. Assume,
that the mass is initially displaced a distance of 0.1 in the positive direction and the mass
velocity is initially zero. Also plot the spring force and damping force.
d) This system is required to have a maximum displacement overshoot that is less than 15%
of the steady state value to avoid the rack impacting another portion of the machine.
Determine whether this system meets that requirement. If not, what parameters do you
recommend changing to cause this system to meet the overshoot design requirement?
Verify that your results are reasonable by comparing the initial and steady state values with your
expectations.
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