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Chapter 8 - Mathematics for Control

By John Billingsley
From Essentials of Mechatronics

8.1   DIFFERENTIAL EQUATIONS

8.1.1   Breaking Down the State Equations

In Section 6.6, we saw how a system could be described by a matrix state
equation of the form

 

in which there are several simultaneous first-order equations.

We have looked at an example where

 

and we could consider applying feedback

 

to get

 

In matrix form these equations are

 

We can eliminate v from the two equations to get the “conventional” form of
a single second-order differential equation

 

or

 

 

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