State Space Analyis - the 'B' matrix

[phiby]

Below is a screen shot from state space analysis in "Control Engineering" by Ogata.

http://www.flickr.com/photos/66943862@N06/6230432028/

I am trying to get at 3-20 from 3-18.

Can't the u part of the matrix also be written as
[1/m 0]T instead of [0 1/m]T?

What's the rationale in choosing one over the other?

[gsal]

There is nothing to do to get to 3-20...if you got to 3-18, you are already at 3-20...well, if you got to 3-17 AND 3-18, you are already at 3-20.

3-20 is exactly the same as 3-17 and 3-18 together, it is simply the expresion of the same set of simultaneous equations, but in matrix form:



x1dot = ( 0 )x1 + ( 1 )x2 + ( 0 )u
x2dot = (-k/m)x1 + (-b/m)x2 + (1/m)u


When 3-17 and 3-18 are written as above, it should be clear to you why 3-20 looks the way it does, right?

Keep in mind the orderly manner in which matrix multiplication works, too, in order to answer your question.

[phiby]

There is nothing to do to get to 3-20...if you got to 3-18, you are already at 3-20...well, if you got to 3-17 AND 3-18, you are already at 3-20.

3-20 is exactly the same as 3-17 and 3-18 together, it is simply the expresion of the same set of simultaneous equations, but in matrix form:



x1dot = ( 0 )x1 + ( 1 )x2 + ( 0 )u
x2dot = (-k/m)x1 + (-b/m)x2 + (1/m)u


When 3-17 and 3-18 are written as above, it should be clear to you why 3-20 looks the way it does, right?

Keep in mind the orderly manner in which matrix multiplication works, too, in order to answer your question.

Yes, I got that. My original question was silly!