Then
Ap = PAP-I
Bp = PB
For the general aviation airplane, substitution gives
Qc =
-0.005 8
-11.2112
36.4568
-11.8674
0.2997
-0.1003
-0.0475
-0.0180
1.7650
58.6517
-30.0574
36.4568
-0.0883
0.0014
0.0006
0.0002
(6.312)
(6.313)
(6.314)
(6.315)
(6.316)
(6.317)
(6.318)
-4.6225
-321.18C
-30.057
-0.0180 0.0002 0.0177
0.0436 -0.0006 -0.0430
-0.0847 0.0011 -0.0007
0.1638 -0.0865 0.0057
100
010
001
-0.3860 -13.1052 -5.0574
(6.320)
(6.321)
(6.322)
(6.323)
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL
The input with full-state feedback in the transformed system is
U -r(t) - KZ
where K is given by
K=[ki k2 k3 k4]
Then
Z = (Ap - Bp K )Z+ Bpr(t)
and
O
0
O
-(0.5918 + ki)
-(0.3860 + k2) -(13.1052 + k3)
603
(6.324)
(6.325)
(6.326)
0
O
1
-(5.0574 + k4)
(6.327)
The characteristic equation of tfus transformed phase variable form is
S4 + (5.0574 + k4)S3 + (13.1052 + k3)S2 + (0.3860 + k2)S
+ (0.5918 + ki) : 0 (6.328)
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