Simplified the equations for an electric motor can be given ϴ``(t) + 2ϴ`(t) = u(t) Where ϴ(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) = [ϴ(t) ϴ`(t)]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 orthogonal. c) Assuming that ϴ(0) = ϴ` (0) = 0 , solve for x(t) , t ≥ 0 , when u(t) = e-t , t ≥ 0 .
Simplified the equations for an electric motor can be given ϴ``(t) + 2ϴ`(t) = u(t) Where ϴ(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) = [ϴ(t) ϴ`(t)]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 orthogonal. c) Assuming that ϴ(0) = ϴ` (0) = 0 , solve for x(t) , t ≥ 0 , when u(t) = e-t , t ≥ 0 .
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Simplified the equations for an electric motor can be given
ϴ``(t) + 2ϴ`(t) = u(t)
Where ϴ(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) = [ϴ(t) ϴ`(t)]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 orthogonal.
c) Assuming that ϴ(0) = ϴ` (0) = 0 , solve for x(t) , t ≥ 0 , when u(t) = e-t , t ≥ 0 .
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