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483
li£l = 2
W(s) r+-2O
(2)
In this case, the state equation of the disturbance is written by
(3)
where
o i o
o o i
0 -co. 1 -If
> A* =
(4)
Utilizing Eqs.( 1) and (3), we have the following augmented state equation
B = #, (5)
Switching Hyperplane Designed by Disturbance-Accommodating Bilinear Control
In this chapter, by appling the bilinear optimal control theory to the agumented system, we derive the
switching hyperplane. Generally, such semi-active control as parameter control is classified into a bilinear
system which belongs to non-linear systems. It is considered that that design restriction in semi-active damper
is a damping power rather than a damping coefficient. From this viewpoint, the maximum damping power of
damper design is the designed parameter. In this study, term of the damping power is introduced to the
criterion function.
We consider the following control strategy to minimize the criterion
+« T (0^TW^(0^(0«(0]*'
(6)
where Q and R are weighting functions. And the optimal control input U Q which satisfies the following equation
is synthesized
J r (w°) = minJ r (n) (7)
Then the dynamic programming method is applied to obtain the optimal control input u°. This problem is