6. Simplified equations for an electric motor can be given O"(t) + 20'(t) = u(t) where e(t) is the motor shaft angle, and u(t) is the voltage applied to the armature windings. a. Write down a state equation for the motor assuming a state vector x(t) = [0(t) O'(t)] and input u(t). b. Transform the state equation to that for a new state variable z(t) so that the new "A-matrix" is diagonal. c. Assuming that (0) = 0'(0) = 0 , solve for x(t), t > 0, when u(t) = et, t > 0.
6. Simplified equations for an electric motor can be given O"(t) + 20'(t) = u(t) where e(t) is the motor shaft angle, and u(t) is the voltage applied to the armature windings. a. Write down a state equation for the motor assuming a state vector x(t) = [0(t) O'(t)] and input u(t). b. Transform the state equation to that for a new state variable z(t) so that the new "A-matrix" is diagonal. c. Assuming that (0) = 0'(0) = 0 , solve for x(t), t > 0, when u(t) = et, t > 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![6. Simplified equations for an electric motor can be given
O"(t) + 20'(t) = u(t)
where 0(t) is the motor shaft angle, and u(t) is the voltage applied to the armature
windings.
a. Write down a state equation for the motor assuming a state vector
x(t) = [0(t) O'(t)] and input u(t).
b. Transform the state equation to that for a new state variable z(t) so that the new
"A-matrix" is diagonal.
c. Assuming that (0) = 0'(0) = 0, solve for x(t), t 2 0, when u(t) = e*, t 2 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cc8cd8e-d9b8-43a5-90af-c52233dc69b0%2F873029a1-abea-49f4-a4d6-bed20c054532%2Fincv6vq_processed.png&w=3840&q=75)
Transcribed Image Text:6. Simplified equations for an electric motor can be given
O"(t) + 20'(t) = u(t)
where 0(t) is the motor shaft angle, and u(t) is the voltage applied to the armature
windings.
a. Write down a state equation for the motor assuming a state vector
x(t) = [0(t) O'(t)] and input u(t).
b. Transform the state equation to that for a new state variable z(t) so that the new
"A-matrix" is diagonal.
c. Assuming that (0) = 0'(0) = 0, solve for x(t), t 2 0, when u(t) = e*, t 2 0.
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