User`s guide

7 Control Design Tools
7-6
The estimator poles are the eigenvalues of , which can be arbitrarily
assigned by proper selection of the estimator gain matrix . As a rule of
thumb, the estimator dynamics should be faster than the controller dynamics
(eigenvalues of ).
Replacin g by its estimate in yields the dyna micoutput-feed back
compensator
Note that the resulting closed-loop dynamics are
Hence, you actually assign all closed-loop p oles by independently placing the
eigenv alues of and .
Pole Placement Tools
The Control System Toolbox contains functions to:
• Compute gain matrices and that achieve the desired closed-loop pole
locations
• Form the state estimator and dynamic compensator using these gains
ξ
·
Aξ Bu L y Cξ– Du–()++=
ALC
–
L
ABK
–
x
ξ
uKx
–=
ξ
·
ALC– BLD–()K–
ξLy+=
uKξ–=
x
·
e
·
ABK– BK
0 ALC–
x
e
,= exξ–=
ABK
–
ALC
–
K
L