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R. (. s. ). Step input. Ramp input. Parabolic input. Final value theorem:. 3. Steady-State Errors. R. (. s. ). Step. Ramp. Parabol. Final value theorem:. Step. Ramp. Parabol. e ss :. Step. Ramp. Parabol. [c n ] ss :. Example 3.1 a). Sistem type: 0. Stability test. R. - PowerPoint PPT Presentation
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3. Steady-State Errors
)s(E)s(R )s(Gc )s(Gp)s(C
)s(N )s(R)GG1(
GG)s(C
pc
pc
)s(R)GG1(
1)s(E
pc
)s(N)GG1(
G)s(C
pc
pn
Final value theorem: )]s(sX[lim)t(xlimx
0stss
c
cc D
NG
p
pp D
NG R
NNDD
DD)s(E
pcpc
pc
N
NNDD
ND)s(C
pcpc
pcn
t
)t(r
Step input
t
)t(r At)t(r
Ramp input
t
)t(r2t
2
A)t(r
Parabolic input
s
A)s(R
2s
A)s(R 3s
A)s(R
13
)s(E)s(R )s(Gc )s(Gp)s(C
)s(N
pc K)s(G
)10s3s(
)10s()s(G
2p
RGG1
1)s(E
pc
Final value theorem: )]s(sX[lim)t(xlimx0st
ss
23
0spcpc
pcss R
NNDD
DDse
)K1(
A
p ess:
Step Ramp Parabol
s
A2s
A3s
AStep Ramp Parabol
Example 3.1 a)
NGG1
G)s(C
pc
pn
0s
pcpc
pc
ssn
NNNDD
NDs
]c[
pK Sistem type: 0
0sp2
2
R)10s)(K()10s3s)(1(
)10s3s)(1(s
0sp2
R)10s)(K()10s3s)(1(
)10s)(1(s
)K1(
A
p [cn]ss:
Step Ramp Parabol
Stability test
)s(E)s(R )s(Gc )s(Gp)s(C
)s(N
s
KsK
s
KK)s(G ipipc
)10s3s(
)10s()s(G
2p
33
0spcpc
pcss R
NNDD
DDse
0sip2
2
R)10s)(KsK()10s3s(s
)10s3s(ss
iK
A0 ess:
Step Ramp Parabol
Example 3.1 b)
System type: 1
Integral control improves error performance
sKK)s(G dpc
)K1(
A
p ess:
Step Rampa Parabol
System type: 0
Derivative control does not change error performance
)s(E)s(R )s(Gc )s(Gp)s(C
)s(N
pc K)s(G
)10s3s(s
)10s()s(G
22p
43
0spcpc
pcss R
NNDD
DDse
0sp234
234
R)10s)(K()s10s3s)(1(
)s10s3s)(1(s
Example 3.1 c)
pK
A0 0ess:
Step Ramp Parabol System type: 2
DcDp de s0 System type: 0
DcDp de s1 System type: 1 DcDp de s2 System type: 2
DcDp de s3 System type: 3
sse Overshoot sst rt
pK
iK 0
dK
