Controle em Malha Fechada

Prévia do material em texto

Problem 10.14PP
Three alternative designs are sketched in Fig. for the closed-loop control of a system with the 
plant transfer function Gfsj = l/sfs + 1). The signal w is the plant noise and may be analyzed as if 
it were a step; the signal v is the sensor noise and may be analyzed as if it contained power to 
very high frequencies.
(a) Compute values for the parameters K \, a, K2, KT. K3, d. and KD so that in each case 
(assuming w = 0 and v = 0),
* j2+4 i + I6 ‘
Note that in system III, a pole is to be placed at s = -4.
(b) Complete the following table, expressing the last entries as A/sk to show how fast noise from 
V is attenuated at high frequencies:__________________________________________________
(b) Complete the following table, expressing the last entries as A/sk to show how fast noise from 
V is attenuated at high frequencies;
System Kv -1i r l t ^ -1
1
II
III
(c)Rank the three designs according to the following characteristics (the best as “1 the poorest 
as “3”):
Performance
Tracking
Plant-noise rejection
Sensor-noise rejection 
Figure Alternative feedback structures
Step-by-step solution
step 1 of 2
R ^ + aS + k̂
:>Ai=16. a = 4
^ A_
R S ^+{U k^)S + k2 
=^^1^=16. k j.^ 3
m . 
R̂ S’ + ( l+ r f )S ‘ + ( * „+ f l(+ * i)S + 4 1 ^
r ^ Â = 16. d = l . k j , = 9
Step 2 of 2
£ f s ) = R - y = R - ,
 ̂ ^ + 4 s + U
S^+As
S" +4S+16
•R.
e , = U e (t) = U SB(s) = 1
k , = — ^ k , s 4 for all the design
, 1 1 - 2 . . 1
w I j, *, 4
= 1 = 1
W^L , 16
m - . L \ = 1
4* i 64