Suppose that the motion of the adjustable roller has a damping coefficient b, and that the forceexerted by the rolled material on the adjustable roller is proportional to the material's change inthickness: 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 ofthe input material. T. is one of the inputs. but here for simplicitv assume T is constant. Do notneglect 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 theoutput material ,x.1. Draw free body diagram of adjustable roller2. Prepare a mathematical block diagram showing mathematical relations in terms of the transferfunctions. The block diagram should at least contains a block for DC-motor and a block formechanical 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) asa function of time if the input voltage vs (t) is an unit step. Express the result in terms of theappropriate system parameters: i.e. damping ratio and undamped natural frequency. Consider the continuous rolling mill depicted below.Thickness T00000Rack and pinionÖThickness a1: NGear ratio1en(t)i(t)vs(t)Motion of material out of the roller6Suppose that the motion of the adjustable roller has a damping coefficient b, and that the forceexerted by the rolled material on the adjustable roller is proportional to the material's change inthickness: 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 ofthe input material, T, is one of the inputs, but here for simplicity assume T is constant. Do notneglect 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 theoutput material ,.Part 11. Draw free body diagram of adjustable roller2. Prepare a mathematical block diagram showing mathematical relations in terms of the transferfunctions. The block diagram should at least contains a block for DC-motor and a block formechanical 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) asa function of time if the input voltage v, (t) is an unit step. Express the result in terms of theappropriate system parameters: i.e. damping ratio and undamped natural frequency.

Given: To find: Free body diagram of adjustable roller Block diagram Transfer function

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

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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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.

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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