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.

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