Page 199 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

An Underdamped Precess 173

or

These three gains will be chosen to make the modified process
behave as a desired process defined by

:,(~)=(~ -~:mJ~)+(g~)u

s(~)=(~ -~:wJ::)+(g~)a

dx
Tt=A 0 x+B 0 U

si = A i + B U
0
0
Ao =( 0 2 1 )
-wo -2,oWo

(6-17)

To make Eqs. (6-16) and (6-17) match, the following must be
true:

o 1 ) + ( o )Lk k J _ ( o 1 )
( -~ -2'(1)" g~ xt x2 - -w5 -2,oWo

or

(6-18)
This single matrix equation yield two scalar equations: