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Engineering course on microcontrollers, Exercises of Electrical and Electronics Engineering

Engineering course on microcontrollers

Typology: Exercises

2024/2025

Uploaded on 02/13/2025

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INC 341 Feedback Control Systems Home Work 2
Assign: 27 Aug 2016 Due for 3AE, 3A, 3WIL: 5 Sep 2016
Instruction: Hand in your work with name and code by hand before the class is started.
DO NOT copy homework from your classmates or lend it to others. Anyone who violates
this regulation will be given -10 for the homework.
1. In the system shown in Figure 1, the inertia, J, of radius, r, is constrained to move
only about the stationary axis A. A viscous damping force of the translational value
bexists between the bodies Jand M. If an external force, f(t), is applied to the
mass, find the transfer function, G(s) = Θ(s)/F(s).
M
k
A
J
r
f(t)
b
b
θ(t)
Figure 1: Problem 1.
1
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INC 341 Feedback Control Systems Home Work 2 Assign: 27 Aug 2016 Due for 3AE, 3A, 3WIL : 5 Sep 2016

Instruction: Hand in your work with name and code by hand before the class is started. DO NOT copy homework from your classmates or lend it to others. Anyone who violates this regulation will be given -10 for the homework.

  1. In the system shown in Figure 1, the inertia, J, of radius, r, is constrained to move only about the stationary axis A. A viscous damping force of the translational value b exists between the bodies J and M. If an external force, f (t), is applied to the mass, find the transfer function, G(s) = Θ(s)/F (s).

M

k

A

J

r

f (t)

b

b

θ(t)

Figure 1: Problem 1.

  1. The motor whose torque-speed characteristics are shown in Figure 2 drives the load shown in the diagram. Some of the gears have inertia. Find the transfer function, G(s) = Θ 2 (s)/Ea(s). (10 points)

− e^ + a(t)

Ra

M

ia(t)

θm(t)

J 4

J 4 = 16 kg-m^2

θ 2 (t)^ b^ = 32^ N-m s/rad

N 1 = 10

J 1 = 1 kg-m^2

N 2 = 20

J 2 = 2 kg-m^2

N 3 = 10

J 3 = 2 kg-m^2

N 4 = 20

(a)

τ (N-m)

RPM

π

ea = 5 V

(b)

Figure 2: Problem 2.