Difference between revisions of "FAQ: In equation (6.23), shouldn't the B matrix have omega 0^2?"
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{{FAQ page | {{FAQ page | ||
− | | chapter = | + | | chapter = State Feedback |
| contributor = Richard Murray | | contributor = Richard Murray | ||
− | | date = | + | | date = 28 Aug 2016 |
| answer = | | answer = | ||
− | + | In equation (6.22), the input term has a factor <math>k \omega_0^2 u</math>. Shouldn't the <math>B</math> matrix in equation (6.23) be <math>k \omega_0^2</math> to match this? | |
+ | |||
+ | A: Actually, the term as listed is correct. The model uses the state space representation | ||
+ | <center><math> | ||
+ | x = \begin{bmatrix} x_1 \\ x_2 \end{matrix} = \begin{bmatrix} q \\ \dot q/omega_0 \end{matrix}. | ||
+ | </math></center> | ||
+ | It follows by working through the equations that the given equations are correct. | ||
}} | }} |
Revision as of 13:03, 28 August 2016
(Contributed by Richard Murray, 28 Aug 2016)
In equation (6.22), the input term has a factor . Shouldn't the
matrix in equation (6.23) be
to match this?
A: Actually, the term as listed is correct. The model uses the state space representation
It follows by working through the equations that the given equations are correct.