10 - This system is not very robust.. 12 - This system is not very robust.. number of poles in the right-hand s-plane.. 20 - According to Routh – Hurwitz criterion, this system is stable
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CONTROL SYSTEM DESIGN
Lecture Notes Robust Control Systems
Page Notes
/
i
r r i
S
: r i is the ith root
-
1
i
T
i i
S S
s r
: if zeros of T(s) are independent of the parameter α
8
-
1
i
T
i i
S S
s r
: relationship of two sensitivities
10 - This system is not very robust
11 - This is a PD controller
12 - This system is not very robust
14 - G m (s): a multiplicative perturbation
- ( ) 1 1 for all
( ) ( )
c
M j
G j G j
: assume that G & G m have the same
number of poles in the right-hand s-plane.
15 - If K = 1, the system is unstable.
16 - G s m( ) G s( )[1 M s( )]: the process G becomes G m
17
- ( ) 1 1 for all
( ) ( )
c
M j
G j G j
s a s a s a : the characteristic equation
-
( )
( )
( )
( )
: 4 possible characteristic equations when coefficients
change
20 - According to Routh – Hurwitz criterion, this system is stable
22 - q s( ) s3 3s2 2s 4.5 0 : the nominal characteristic equation
( )
Y s
T s
R s
: one possible objective in the design of a control system is that the controlled system's output should exactly and instantaneously reproduce its input That is, the system transfer function should be unity
28 - G s p( ): the prefilter
30 - s3 1.75 n s2 2.15 n2s n3: see page #46, Performance of FCS
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Page Notes
32 - Percent overshoot is not very good, then a prefilter is required
36 - This system is very stable
39 - K = 0: no state variable feedback
- s2 3.2 n s n2: see page #47, Performance of FCS
40 - Suppose that settling time is 1 second
41 - This system is very stable
42 - Poles can change by 50%
43 - Table: see page #53, Design of FCS
- Suppose that K a = 10, K b= 2
44 - This system is very stable