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In Figure P10.6, the block is pulled up the incline by the

System Dynamics | 3rd Edition | ISBN: 9780073398068 | Authors: William J Palm III ISBN: 9780073398068 208

Solution for problem 10.6 Chapter 10

System Dynamics | 3rd Edition

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System Dynamics | 3rd Edition | ISBN: 9780073398068 | Authors: William J Palm III

System Dynamics | 3rd Edition

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Problem 10.6

In Figure P10.6, the block is pulled up the incline by the tension force f in the inextensible cable. The motor torque T is controlled to regulate the speed v of the block to obtain some desired speed vr. The precise value of the friction coefficient is unknown, as is the slope angle , so we model them as a disturbance. Neglect all masses and inertias in the system except for the block mass m. Also neglect the field time constant of the field-controlled motor. Feedback of the block speed v is provided by a sensor that measures the pulley rotational speed , which is directly related to v by v = R. a. Obtain the equation of motion of the block speed v, with the voltage vm,friction force F = mg cos , and the weight component Wx = mg sin as the inputs.b. Draw a block diagram representing the control system, with the commandinput vr, the output v, and the disturbance D = F + Wx . Model the speedsensor as directly sensing the speed . Show the necessary transferfunctions for each block in the diagram.c. Obtain the output, error, and torque transfer functions from the blockdiagram.

Step-by-Step Solution:

Problem 10.6

In Figure P10.6, the block is pulled up the incline by the tension force f in the inextensible cable. The motor torque T is controlled to regulate the speed v of the block to obtain some desired speed vr. The precise value of the friction coefficient is unknown, as is the slope angle, so we model them as a disturbance. Neglect all masses and inertias in the system except for the block mass m. Also neglect the field time constant of the field-controlled motor. Feedback of the block speed v is provided by a sensor that measures the pulley rotational speed, which is directly related to v by v = R.

a. Obtain the equation of motion of the block speed v, with the voltage vm, friction force F =, and the weight component Wx =  as the inputs.

b. Draw a block diagram representing the control system, with the command input vr, the output v, and the disturbance D = F + Wx. Model the speed sensor as directly sensing the speed. Show the necessary transfer functions for each block in the diagram.

c. Obtain the output, error, and torque transfer functions from the block diagram.

                                                          Step by Step Solution

Step 1 of 13

(a)

Consider the given diagram.

The expression for the total motion is given as,

Thus, the expression is

Step 2 of 13

Chapter 10, Problem 10.6 is Solved
Step 3 of 13

Textbook: System Dynamics
Edition: 3
Author: William J Palm III
ISBN: 9780073398068

Since the solution to 10.6 from 10 chapter was answered, more than 403 students have viewed the full step-by-step answer. The answer to “In Figure P10.6, the block is pulled up the incline by the tension force f in the inextensible cable. The motor torque T is controlled to regulate the speed v of the block to obtain some desired speed vr. The precise value of the friction coefficient is unknown, as is the slope angle , so we model them as a disturbance. Neglect all masses and inertias in the system except for the block mass m. Also neglect the field time constant of the field-controlled motor. Feedback of the block speed v is provided by a sensor that measures the pulley rotational speed , which is directly related to v by v = R. a. Obtain the equation of motion of the block speed v, with the voltage vm,friction force F = mg cos , and the weight component Wx = mg sin as the inputs.b. Draw a block diagram representing the control system, with the commandinput vr, the output v, and the disturbance D = F + Wx . Model the speedsensor as directly sensing the speed . Show the necessary transferfunctions for each block in the diagram.c. Obtain the output, error, and torque transfer functions from the blockdiagram.” is broken down into a number of easy to follow steps, and 199 words. This textbook survival guide was created for the textbook: System Dynamics, edition: 3. This full solution covers the following key subjects: . This expansive textbook survival guide covers 13 chapters, and 752 solutions. The full step-by-step solution to problem: 10.6 from chapter: 10 was answered by , our top Engineering and Tech solution expert on 01/03/18, 09:39PM. System Dynamics was written by and is associated to the ISBN: 9780073398068.

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