C H 1 : C C N T R 0 L & F E E D BA C K PRINCIPLES
& BLOCK DIAGRAM 5 .
Purpose of feedback control
-
we dont always feedback
need
,
cat solve these problems
where there is
significant delay .
Industrial
Generally need to buy high integrity instruments and
'
design controllers for particular applications , one at a time
commercial
I
Very cost sensitive and
high volume still require reliable
•
-
, operation
military ,
nuclear and aerospace
-
cost not an
objective
-
ultimate reliability precision
-
Almost unlimited budget for controls
Objectives
follow reference signal
Tracking external r ( t ) w/o
-
-
,
saturating the input ult )
'
Disturbance rejection ( regulation D -
reduce effect of
external dist - braces d( E) on system output
.
Reduce effect of process uncertainty
-
Stabilisation - must operate with feedback
In most control problems ,
we create a feedback loop .
( Negative gain loop )
for LTI systems ( linear time invariant) -
loop transfer faction
is product of all components in feedback loop
( ( s ) = G- ( s ) PCs )H( s )
Feedback loop gain is used to control system benefits but may
,
the of
carry danger making otherwise stable system unstable .
, Feedback System Components
41s ) = Pls ) Uls ) 1- Docs )
loop gain :
Lcs ) =
G- ( s ) Pcs ) His )
for disturbance P* =p
input
-
✗
1
i
for output disturbance P =
output
=
( I 1- GPHJY =
FGPR + P 'D -
G- PMN
input = ( I + GPHJU = FGR
-
C- HINT P' D)
This gives transfer functions ( other external signals = 0
)
( high gain)fc ( 772
Reference → output :
Ty / R =
F¥÷µ =
¥ ¥-
-
s
¥
,
disturbance →
output
:
Ty / ☐ =
ltapm
=%÷ → o
Reference → input : Tu / r =
FI
=
F€ f
I 1- GPH ith →
FH
disturbance →
input :
TUID
¥÷µ -9¥
-
=
-÷
I
, →
-
high gain feedback solves control problems
constraints
require large Lhnrealisticl input signals
-
High gain may not be possible non minimum
-
-
,
phase lag causing stability issues
, 2
loop transfer functions -
special importance in
feedback systems
#
6
in sensitivity S
it Lcs)
.
I + ((s )
is complementary sensitivity T
Tls)
=
I -
Sls)
B. lock Diagram Reduction
only applies to linear
systems
•
output signal
=
transfer function ✗ input signal
'
Ylsj G- issues )
¥§y→ )
=
-11s
can get transfer function
signals
-
-
Block diagram reduction
-
Masais Rule
Rules
Associative
property
•
✗ ( s) =( ✗ (5) 1- PCs ) ) 1- His )
✗( s)
=
( XIs) 1- HCSJ ) 1- Pcs )
splitting crccmbi nation
summing joint
•
, I
commutative property of linear systems
•
Blocks in series
U ( s)
= G- it 5) ✗ Cs ) ,
YCS) =
Gzcs)Us
-
yes ) =
Gics) G- zcs ) ✗ (d)
be
Blocks in Parallel
✗ ics) = G- its) Ucs )
,
Y> (s ) = G- zlsjucs)
Gcs ) =) , is ) )
'
1- Tzcs
r
✗ Is)
= G- CSJXLSJ t PCs )
-
Yes ) =
Gcs)( ✗ ( s ) t s )
Pcs) )
-
internal signal level Changes
Ccs) ( Xis) )
•
yes) =
+ PCs)
'
✗ Is) =
G- ( s) ✗ ( s ) t C- ( s) PCs )
•
pls ) =
7 Cs )
=
G- CSJXCS )
✗ (s ) =
C- (5) Ycs )
pls) = Gcs )XCs )
& BLOCK DIAGRAM 5 .
Purpose of feedback control
-
we dont always feedback
need
,
cat solve these problems
where there is
significant delay .
Industrial
Generally need to buy high integrity instruments and
'
design controllers for particular applications , one at a time
commercial
I
Very cost sensitive and
high volume still require reliable
•
-
, operation
military ,
nuclear and aerospace
-
cost not an
objective
-
ultimate reliability precision
-
Almost unlimited budget for controls
Objectives
follow reference signal
Tracking external r ( t ) w/o
-
-
,
saturating the input ult )
'
Disturbance rejection ( regulation D -
reduce effect of
external dist - braces d( E) on system output
.
Reduce effect of process uncertainty
-
Stabilisation - must operate with feedback
In most control problems ,
we create a feedback loop .
( Negative gain loop )
for LTI systems ( linear time invariant) -
loop transfer faction
is product of all components in feedback loop
( ( s ) = G- ( s ) PCs )H( s )
Feedback loop gain is used to control system benefits but may
,
the of
carry danger making otherwise stable system unstable .
, Feedback System Components
41s ) = Pls ) Uls ) 1- Docs )
loop gain :
Lcs ) =
G- ( s ) Pcs ) His )
for disturbance P* =p
input
-
✗
1
i
for output disturbance P =
output
=
( I 1- GPHJY =
FGPR + P 'D -
G- PMN
input = ( I + GPHJU = FGR
-
C- HINT P' D)
This gives transfer functions ( other external signals = 0
)
( high gain)fc ( 772
Reference → output :
Ty / R =
F¥÷µ =
¥ ¥-
-
s
¥
,
disturbance →
output
:
Ty / ☐ =
ltapm
=%÷ → o
Reference → input : Tu / r =
FI
=
F€ f
I 1- GPH ith →
FH
disturbance →
input :
TUID
¥÷µ -9¥
-
=
-÷
I
, →
-
high gain feedback solves control problems
constraints
require large Lhnrealisticl input signals
-
High gain may not be possible non minimum
-
-
,
phase lag causing stability issues
, 2
loop transfer functions -
special importance in
feedback systems
#
6
in sensitivity S
it Lcs)
.
I + ((s )
is complementary sensitivity T
Tls)
=
I -
Sls)
B. lock Diagram Reduction
only applies to linear
systems
•
output signal
=
transfer function ✗ input signal
'
Ylsj G- issues )
¥§y→ )
=
-11s
can get transfer function
signals
-
-
Block diagram reduction
-
Masais Rule
Rules
Associative
property
•
✗ ( s) =( ✗ (5) 1- PCs ) ) 1- His )
✗( s)
=
( XIs) 1- HCSJ ) 1- Pcs )
splitting crccmbi nation
summing joint
•
, I
commutative property of linear systems
•
Blocks in series
U ( s)
= G- it 5) ✗ Cs ) ,
YCS) =
Gzcs)Us
-
yes ) =
Gics) G- zcs ) ✗ (d)
be
Blocks in Parallel
✗ ics) = G- its) Ucs )
,
Y> (s ) = G- zlsjucs)
Gcs ) =) , is ) )
'
1- Tzcs
r
✗ Is)
= G- CSJXLSJ t PCs )
-
Yes ) =
Gcs)( ✗ ( s ) t s )
Pcs) )
-
internal signal level Changes
Ccs) ( Xis) )
•
yes) =
+ PCs)
'
✗ Is) =
G- ( s) ✗ ( s ) t C- ( s) PCs )
•
pls ) =
7 Cs )
=
G- CSJXCS )
✗ (s ) =
C- (5) Ycs )
pls) = Gcs )XCs )
