Lecture notes Control Systems 1 (EEE3094S)

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 )