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
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| chapter = Chapter Name
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| chapter = State Feedback
 
| contributor = Richard Murray
 
| contributor = Richard Murray
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| date = 17 May 2008
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| date = 28 Aug 2016
 
| answer =  
 
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This is a template page for creating a FAQ.  You should replace the information above with the appropriate information for your FAQ and replace this text with the answer to your FAQ.  If your FAQ page is complicated, you may want to substitute this page (use <nowiki>{{subst:FAQ page ...}}</nowiki> and then customize it.
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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?
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A: Actually, the term as listed is correct.  The model uses the state space representation
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<center><math>
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x = \begin{bmatrix} x_1 \\ x_2 \end{matrix} = \begin{bmatrix} q \\ \dot q/omega_0 \end{matrix}.
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</math></center>
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It follows by working through the equations that the given equations are correct.
 
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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

Failed to parse (unknown error):

It follows by working through the equations that the given equations are correct.

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