Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Suppose that the motion of the adjustable roller has a damping coefficient b, and that the force
exerted by the rolled material on the adjustable roller is proportional to the material's change in
thickness: f=c(T-x). Suppose further that the DC motor has a torque constant K, and a back-
emf constant Ke, and that the rack-and-pinion has effective radius of r. In reality the thickness of
the input material. T. is one of the inputs. but here for simplicitv assume T is constant. Do not
neglect the weight of the adjustable roller and assume mg = cT.
The input of the system is the voltage of DC-motor and the output is the thickness of the
output material ,x.
1. Draw free body diagram of adjustable roller
2. Prepare a mathematical block diagram showing mathematical relations in terms of the transfer
functions. The block diagram should at least contains a block for DC-motor and a block for
mechanical system (i.e gears and adjustable rollers)
3. Determine transfer function G(s)=X(s)/Vs(s)
4. After finding the transfer function in part 3, assume the armature inductance of the DC.
motor is negligible (L = 0), assume zero initial conditions and determine the output x(t) as
a function of time if the input voltage vs (t) is an unit step. Express the result in terms of the
appropriate system parameters: i.e. damping ratio and undamped natural frequency.
Transcribed Image Text:Consider the continuous rolling mill depicted below.
Thickness T
00000
Rack and pinion
Ö
Thickness a
1: N
Gear ratio
1
en(t)
i(t)
vs(t)
Motion of material out of the roller
6
Suppose that the motion of the adjustable roller has a damping coefficient b, and that the force
exerted by the rolled material on the adjustable roller is proportional to the material's change in
thickness: fs = c(T-a). Suppose further that the DC motor has a torque constant K, and a back-
emf constant Ke, and that the rack-and-pinion has effective radius of r. In reality the thickness of
the input material, T, is one of the inputs, but here for simplicity assume T is constant. Do not
neglect the weight of the adjustable roller and assume mg = cT.
The input of the system is the voltage of DC-motor and the output is the thickness of the
output material ,.
Part 1
1. Draw free body diagram of adjustable roller
2. Prepare a mathematical block diagram showing mathematical relations in terms of the transfer
functions. The block diagram should at least contains a block for DC-motor and a block for
mechanical system (i.e gears and adjustable rollers).
3. Determine transfer function G(s) = X(6)
4. After finding the transfer function in part 3, assume the armature inductance of the DC-
motor is negligible (L= 0), assume zero initial conditions and determine the output z(t) as
a function of time if the input voltage v, (t) is an unit step. Express the result in terms of the
appropriate system parameters: i.e. damping ratio and undamped natural frequency.
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