作者COBRAS518 (Never Stop)
看板Electronics
標題[問題] 兩題控制
時間Mon Jan 10 10:54:04 2011
1. Let P(s) = (s-4)/[(s+5)(s-5)]
(a) Find x,y,n,d∈S such that P = n/d, d is a Blaschke product, and
xd + yn = 1.
(b) Find a controller C(s) with a pole at s = 10, which stabilizes P in the
standard feedback system.
(c) W(s) = (1+0.1s)/(1+s)
Find a lower bound L on the achievable ||W H (s)|| (using a
yd ∞
stabilizing controller)
(d) Suppose for robustness considerations, it has been determined that the
stabilizing controller C(s) should satisfy
||C/(1+PC)|| ≦50
∞
Is there such a controller?
2. Suppose a controller is found which stabilizes the plant
P(s) = (s-1)/(s^2+s+5) and in addition achieves at least 30dB of disturbance
rejection for |ω|≦2(rad/s). Find a lower bound on ||H (s)|| . If we
yd ∞
require ||H (s)|| ≦12dB, what is the maximum bandwidth over which we can
yd ∞
achieves at least 30dB of disturbance rejection?
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