Question 01. From the second-order differential equations that model the direct current motor (electrical and mechanical equations), describe how the model is found in the LAPLACIAN DOMAIN in which the state variables ia and wom are a function of va and cm. Equations Electric: va = ra*ia+la*dia/dt+ea where: ea = ke*e*wm Mechanics: ce-cm-Fm*wm = Jm*dwm/dt where: ce = ke*e*ia Tip: write in state model: dx/dt = A*X + B*U where X = [ia; wm] and U = [va; cm] For steady state: dx/dt => s Thus, the model to be found will be: X = G*U Another question = From the model found in steady state, determine the transfer function Qm/Va. To do this, consider: Ra=0.8 Fm= 0.01 LA=0.001 Jm=1 Ke= 0.8 λε= 1 Another question = Considering the insertion of a controller proportional to the system, present the block diagram for the closed loop and determine the transfer function Qm/Qm*. Determine the roots of the system, considering Kp = 1, Kp = 10 and Kp = 1000. Another question = Considering, now, that the controller in the previous question has been replaced by a proportional-integral controller, present what changes in the block diagram for the closed loop, determine the transfer function Qm/Qm* and determine the roots of the system, considering Kp = 1, Kp = 10 and Kp = 1000. Note that it is necessary to compensate for the slower pole of the Qm/Va system.
Question 01. From the second-order differential equations that model the direct current motor (electrical and mechanical equations), describe how the model is found in the LAPLACIAN DOMAIN in which the state variables ia and wom are a function of va and cm. Equations Electric: va = ra*ia+la*dia/dt+ea where: ea = ke*e*wm Mechanics: ce-cm-Fm*wm = Jm*dwm/dt where: ce = ke*e*ia Tip: write in state model: dx/dt = A*X + B*U where X = [ia; wm] and U = [va; cm] For steady state: dx/dt => s Thus, the model to be found will be: X = G*U Another question = From the model found in steady state, determine the transfer function Qm/Va. To do this, consider: Ra=0.8 Fm= 0.01 LA=0.001 Jm=1 Ke= 0.8 λε= 1 Another question = Considering the insertion of a controller proportional to the system, present the block diagram for the closed loop and determine the transfer function Qm/Qm*. Determine the roots of the system, considering Kp = 1, Kp = 10 and Kp = 1000. Another question = Considering, now, that the controller in the previous question has been replaced by a proportional-integral controller, present what changes in the block diagram for the closed loop, determine the transfer function Qm/Qm* and determine the roots of the system, considering Kp = 1, Kp = 10 and Kp = 1000. Note that it is necessary to compensate for the slower pole of the Qm/Va system.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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![Question 01. From the second-order differential equations that model the direct current motor
(electrical and mechanical equations), describe how the model is found in the LAPLACIAN
DOMAIN in which the state variables ia and wom are a function of va and cm.
Equations
Electric: va = ra*ia+la*dia/dt+ea where: ea = ke*e*wm
Mechanics: ce-cm-Fm*wm = Jm*dwm/dt where: ce = ke*e*ia
Tip: write in state model: dx/dt = A*X + B*U where X = [ia; wm] and U = [va; cm]
For steady state: dx/dt => s
Thus, the model to be found will be: X = G*U
Another question = From the model found in steady state, determine the transfer function
Qm/Va. To do this, consider:
Ra=0.8
Fm= 0.01
LA=0.001
Jm=1
Ke= 0.8
λε= 1
Another question = Considering the insertion of a controller proportional to the system, present
the block diagram for the closed loop and determine the transfer function
Qm/Qm*. Determine the roots of the system, considering Kp = 1, Kp = 10 and Kp = 1000.
Another question = Considering, now, that the controller in the previous question has been
replaced by a proportional-integral controller, present what changes in the block diagram for
the closed loop, determine the transfer function Qm/Qm* and determine the roots of the
system, considering Kp = 1, Kp = 10 and Kp = 1000. Note that it is necessary to compensate
for the slower pole of the Qm/Va system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf913378-ade0-4628-ac57-fdb243e5fba4%2Fdc81ad8b-6a15-4611-a96a-b069a4647ffd%2Fe5ykjd9_processed.png&w=3840&q=75)
Transcribed Image Text:Question 01. From the second-order differential equations that model the direct current motor
(electrical and mechanical equations), describe how the model is found in the LAPLACIAN
DOMAIN in which the state variables ia and wom are a function of va and cm.
Equations
Electric: va = ra*ia+la*dia/dt+ea where: ea = ke*e*wm
Mechanics: ce-cm-Fm*wm = Jm*dwm/dt where: ce = ke*e*ia
Tip: write in state model: dx/dt = A*X + B*U where X = [ia; wm] and U = [va; cm]
For steady state: dx/dt => s
Thus, the model to be found will be: X = G*U
Another question = From the model found in steady state, determine the transfer function
Qm/Va. To do this, consider:
Ra=0.8
Fm= 0.01
LA=0.001
Jm=1
Ke= 0.8
λε= 1
Another question = Considering the insertion of a controller proportional to the system, present
the block diagram for the closed loop and determine the transfer function
Qm/Qm*. Determine the roots of the system, considering Kp = 1, Kp = 10 and Kp = 1000.
Another question = Considering, now, that the controller in the previous question has been
replaced by a proportional-integral controller, present what changes in the block diagram for
the closed loop, determine the transfer function Qm/Qm* and determine the roots of the
system, considering Kp = 1, Kp = 10 and Kp = 1000. Note that it is necessary to compensate
for the slower pole of the Qm/Va system.
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