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![Page 1: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/1.jpg)
ControlSystemsDesign Part: Optimisation
Slovak University of TechnologyFaculty of Material Science and Technology in Trnava
2007
![Page 2: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/2.jpg)
Control Process Optimisation Optimisation Process
control loop structure design
optimum criteria selection
optimum control parameters computation
control process simulation
control parameters refinement
control process quality evaluation
documentation production
...SAT
![Page 3: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/3.jpg)
Control Process Optimisation
control process qualitycontrol process stability
steady state - process variable deviation
dynamic control process overshooting
time of control process treg
integral criteria f(dev)
non oscillation control processes
![Page 4: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/4.jpg)
Control Process Optimisation control process stability
characteristic polynomial
characteristic polynomial roots negative part of complex roots!
degree of the stability
critical parameters single control loop with P controller
critical GAIN
critical period Tkr
![Page 5: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/5.jpg)
Control Process Optimisation
steady state - process variable deviation should be = 0; Deviation = Set Point - Process
the P controller problem: GAIN has to be as large as possible; (!) stability violation for higher order systems
else process deviation = 0 --- I part of controller; destabilisation of control loop
stability versus quality - solution is compromise
![Page 6: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/6.jpg)
Control Process Optimisation
Dynamic control process optimisation standard forms of a characteristic polynomial
Ziegler Nichols method
method of optimum module
methods of integral criterions
![Page 7: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/7.jpg)
Dynamic control process optimisationstandard forms of a characteristic polynomial
Naslin form of characteristic polynomial
0*0
n
i
ii sa
1 12
. . i i ia a a
is according the
i = 1,2, .... n-1
![Page 8: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/8.jpg)
Dynamic control process optimisationstandard forms of a characteristic polynomial
Naslin form of characteristic polynomial
The parameter depends on the chosen overshooting
xmax according the table:
1.7 1.75 1.8 1.9 2.0
xmax 20 16 12 8 5
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Dynamic control process optimisationstandard forms of a characteristic polynomial
Graham - Lathrop form
n Characteristic polynomial q
1 1q
2 1q.4,1q2
3 1q.15,2q.75,1q 23
4 1q.7,2q.4,3q.1,2q 234
5 1q.4,3q.5,5q.0,5q.8,2q 2345
0ω
s
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Dynamic control process optimisationZiegler Nichols method
input data:
GAINcr - critical gain
Tcr - critical period
measured or computed at the stability boundary of the single control loop with P - controller
![Page 11: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/11.jpg)
Dynamic control process optimisationZiegler Nichols method
Cont
roller
Para
metersValues
P Kr 0,5 . Kkr
Kr 0,45 . KkrPI
Ti 0,85 . Tkr
Kr 0,6 . Kkr
Ti 0,5 . TkrPID
Td 0,12 . Tkr
![Page 12: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/12.jpg)
Dynamic control process optimisationmethod of optimum module
The transfer function of a controlled system is supposed in the form
The control parameters are for the ideal parallel PID algorithm r0, r-1 and r1:
i
n
ii
s
sa
KsF
.0
0r
KK sr
0
1
r
rTd
1
0
r
rTi
![Page 13: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/13.jpg)
Dynamic control process optimisationmethod of optimum module
PI controller
2021
20
0
1
23
01
..2.5,0.
aaa
a
r
r
aa
aa
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Dynamic control process optimisationmethod of optimum module
PID controller
401122
2021
20
1
0
1
345
123
01
..2..2
..2.5,0.
0
aaaaa
aaa
a
r
r
r
aaa
aaa
aa
![Page 15: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/15.jpg)
Dynamic control process optimisationmethods of integral criterions
IAE Integral of Absolute Error
ITAE Integral of Absolute Error multiplied by Time
Dynamic system approximation
by K, T and D:
DsesT
K
.
1.
![Page 16: Control Systems Design Part: Optimisation Slovak University of Technology Faculty of Material Science and Technology in Trnava 2007.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649f115503460f94c23907/html5/thumbnails/16.jpg)
Dynamic control process optimisationmethods of integral criterions IAE:
A B
P 0,758 -0,861PI
I 1,020 -0,323
P 1,086 -0,869
I 0,740 -1,130
IAE
PID
D 0,348 0,914
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Dynamic control process optimisationmethods of integral criterions ITAE:
A B
P 0,586 -0,916PI
I 1,030 -0,165
P 0,965 -0,865
I 0,796 -0,147
ITAE
PID
D 0,308 0,929
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Dynamic control process optimisationmethods of integral criterions
B
T
DAY
.
rs KKY .
T
DBA
T
T
i
.
B
d
T
DA
T
T
.
For GAIN
For time constants
For Ti
For Td
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Dynamic control process optimisationhalf dumping criterion
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Dynamic control process optimisation half dumping criterion
Dynamic system approximation
by K, T and D:
DsesT
K
.
1.
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Control Process Optimisation half dumping criterion
PI controller:
946,0
.928,0
T
DY
rs KKY .
583,0
.928,0
T
D
T
Ti
Auxiliary parameter
For GAIN
For integral time constant Ti
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Control Process Optimisation half dumping criterion
PID controller:
Auxiliary parameter
95,0
.37,1
T
DY
rs KKY .738,0
.74,0
T
D
T
Ti
95,0
.365,0
T
D
T
Td
For GAIN
For integral time constant Ti
For derivative time constant Td
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