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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 wm 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 Question 02. From the model found in steady state, determine the transfer function Qm/Va. To do this, consider: Ra=0.8 LA=0.001 Fm= 0.01 Jm=1 Ke= 0.8 λε= 1 Question 03. 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. Question 04. Considering, now, that the controller in the previous question has been replaced by a proportional-integral controller, present what changes in the block diagram for the closed loop, determine the transfer function Qm/Qm* and determine the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 wm 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 Question 02. From the model found in steady state, determine the transfer function Qm/Va. To do this, consider: Ra=0.8 LA=0.001 Fm= 0.01 Jm=1 Ke= 0.8 λε= 1 Question 03. 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. Question 04. Considering, now, that the controller in the previous question has been replaced by a proportional-integral controller, present what changes in the block diagram for the closed loop, determine the transfer function Qm/Qm* and determine the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)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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 wm 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 Question 02. From the model found in steady state, determine the transfer function Qm/Va. To do this, consider: Ra=0.8 LA=0.001 Fm= 0.01 Jm=1 Ke= 0.8 λε= 1 Question 03. 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. Question 04. 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.
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 wm 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 Question 02. From the model found in steady state, determine the transfer function Qm/Va. To do this, consider: Ra=0.8 LA=0.001 Fm= 0.01 Jm=1 Ke= 0.8 λε= 1 Question 03. 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. Question 04. 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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