RST Digital Controls - indico.cern.ch · Kd Kp Td Ti Kp Ki s Td s Ti PID Kp Pole Placement for...
Transcript of RST Digital Controls - indico.cern.ch · Kd Kp Td Ti Kp Ki s Td s Ti PID Kp Pole Placement for...
![Page 1: RST Digital Controls - indico.cern.ch · Kd Kp Td Ti Kp Ki s Td s Ti PID Kp Pole Placement for continuous PID . POPCA3 Desy Hamburg 20 to 23rd may 2012 ... Ipk=6kA Vpk=10kV . POPCA3](https://reader030.fdocuments.us/reader030/viewer/2022040416/5d209aaf88c993e9188c7f88/html5/thumbnails/1.jpg)
RST Digital Controls
POPCA3 Desy Hamburg 20 to 23rd may 2012
Fulvio Boattini CERN TE\EPC
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Bibliography
• “Digital Control Systems”: Ioan D. Landau; Gianluca Zito
• “Computer Controlled Systems. Theory and Design”: Karl J. Astrom; Bjorn
Wittenmark
• “Advanced PID Control”: Karl J. Astrom; Tore Hagglund;
• “Elementi di automatica”: Paolo Bolzern
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POPCA3 Desy Hamburg 20 to 23rd may 2012
SUMMARY
•RST Digital control: structure and calculation
•RST equivalent for PID controllers
•RS for regulation, T for tracking
•Systems with delays
•RST at work with POPS
•Vout Controller
•Imag Controller
•Bfield Controller
•Conclusions
SUMMARY
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST Digital control: structure and calculation
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: control structure
n
n
n
n
n
n
ztztzttT
zszszssS
zrzrzrrR
...
...
...
2
2
1
10
2
2
1
10
2
2
1
10
S
RHfb
S
THff
yRrTuS
A combination of FFW and FBK actions
that can be tuned separately
)()()()()( 11111 zPzRzBzSzA des
REGULATION
RBSA
SA
d
y
RBSA
TB
r
y
TRACKING
)1(
)1(
)1(
)( 1
B
P
B
zP
Tdes
des
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: Diophantine Equation
3.0
1002
2 22
2
ss
Sample Ts=100us 2-1-
-2-1
z0.963 + z 1.959 - 1
z0.001924 + z 0.001949
-2-1 z0.963 + z 1.959 - 1 desP
Getting the desired polynomial
pxMzPzRzBzSzA des )()()()()( 11111
Calculating R and S: Diophantine Equation
nBnA
nBnA
ba
bbaa
ba
ba
ba
M
0000...0
00
01
00
0......00...01
22
11
22
11
nB+d nA
nA
+nB
+d
Matrix form:
0,...,0,,...,,1
,...,,,,...,,1
1
101
nP
T
nRnS
T
ppp
rrrssx
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: fixed polynomials
Controller TF is:
)(
)(1
1
zS
zRHfb
)(1
)(1*1
1
zSz
zR
RBSA
SA
d
y
Add integrator
Add 2 zeros more on S RBSA
SzzzA
*2
2
1
1
1 11
R ofpart fixed)(
S ofpart fixed)(
)()()()()()()(
1
1
1111111
zHr
zHs
zPzRzHrzBzSzHszA des
Calculating R and S: Diophantine Equation
Integrator active on step reference and step disturbance.
Attenuation of a 300Hz disturbance
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent for PID controllers
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID controller: continuous PID design
3.0
1002
2 22
2
ssA
B
Consider a II order system:
2
000
2
00
222223 22
1.1
11
sssKisKpsKds
HsyPIDDenHclPIDcHsyPID
HsyPIDHclPIDc
TdKpKdTi
KpKi
TdsTis
KpPID
Pole Placement for
continuous PID
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID controller: continuous PID design
3.0
1002
2 22
2
ssA
B
Consider a II order system:
TdKpKdTi
KpKi
NTds
Tds
TisKpPIDf
1
11
2
000
2
3
00
2
2
000
22
121
Kd
Ki
Kp
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID: s to z substitution
Choose R and S coeffs such that the 2 TF
are equal )(
)(
)( 1
2
2
1
10
2
2
1
10
1
1
zPIDd
zszss
zrzrr
zS
zR
21
21
1
1
1
1
210
210
1
1
1
11
zszss
zrzrr
S
R
zTdTsNTsNTd
zTdN
z
z
Ti
TsKpPIDd
= 0 forward Euler = 1 backward Euler = 0.5 Tustin
)()( 11 zRzT
)1()( 1 RzT
All control actions on error
Proportional on error;
Int+deriv on output
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID: pole placement in z
Choose desired poles
8.0
1502
2 22
2
ss
Sample Ts=100us 2-1-
-2-1
z0.963 + z 1.959 - 1
z0.001924 + z 0.001949
-2-1 z0.963 + z 1.959 - 1 desP
1 1 1 HrzHs
Choose fixed parts for R and S
)()()()()()()( 11*111*11 zPzRzHrzBzSzHszA des
Calculating R and S: Diophantine Equation
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID: pole placement in z
The 3 regulators behave very
similarly
Increasing Kd
Manual Tuning with Ki, Kd and
Kp is still possible
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RS for regulation, T for Tracking
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RS for regulation, T for tracking
9.0/9405.12 000
2
000
2
00 srsssPdes
PauxPdesRBSHsA
Hs
* :Equation eDiophantin
integrator ]11[
0.963z -2) + 1.959z -1 - (1 )0.6494z -1-(1 z -1)-(1
)0.9322z -2 + 1.929z -1 - (1 )0.9875z -1+(1 z -1 0.022626
SA
RBHol
After the D. Eq solved we get the following open loop TF:
=942r/s
=0.9
=1410r/s
=1 =1260r/s
=1
Pure delay
=31400r/s
=0.004
Closed Loop TF without T
0.844z -2) + 1.836z -1 - (1 )0.8682z -1-(1 )0.8819z -1-(1
)0.9875z -1+(1 z -1 0.0019487
RBSA
BHcl
)1(B
PauxPdesT
REGULATION
TRACKING
1
)0.9875z^-1+(1 z^-1 0.50314
RBSA
BTHcl
T polynomial compensate most of
the system dynamic
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Systems with delays
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Systems with delays
II order system with pure delay
ms
sr
ss
e
A
B s
3
3.0/1002
2 22
2
Sample Ts=1ms 2-1-
-5-4
z 0.6859 + z 1.368 - 1
z 0.149 + z 0.1692
Continuous time
PID is much
slower than before
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Systems with delays
Predictive controls
Diophantine Equation
)()()()()()( 1111
0
11 zPzAzRzBzzSzA aux
d
1 1 1 HrzHs
Choose fixed parts for R and S
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS
DC3
DC
DC +
-
DC1
DC
DC
DC5
DC
DC +
-
DC4
DC
DC-
+
DC2
DC
DC-
+
DC6
DC
DC
MAGNETS
+
-
+
-
CF11
CF12
CF1
CF21
CF22
CF2
AC
CC1
DC
MV7308
AC AC
CC2
DC
MV7308
AC
18KV AC
Scc=600MVA
OF1 OF2
RF1 RF2
TW2
Crwb2
TW1
Lw1
Crwb1
Lw2
MAGNETS
AC/DC converter - AFE
DC/DC converter - charger module
DC/DC converter - flying module
Vout Controller Imag or Bfield control
Ppk=60MW
Ipk=6kA
Vpk=10kV
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Vout Control
Lfilt
C fCdm p
Rdm p
Vin
Vout
Iind Im ag
Icf
Icdm
p
III order output filter
HF zero
responsible for
oscillations
2-1-
2-1-
-2-11msTs 2
22
2
z0.3897 + z 1.142 - 1
z0.3897 + z 1.142 - 1
z0.1043 + z0.1431
85.0
1502
2
des
dc
P
ss
Decide desired dynamics
)()()()()()( 111111 zPzPzRzBzSzA zerosdes
Solve Diophantine Equation
Calculate T to eliminate all dynamics
)1(
)()(
11
B
zPzT des
RBSA
TB
r
y
Eliminate process well dumped zeros
0.8053-zzerosP
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Vout Control
Identification of output filter with a step
Well… not very nice performance….
There must be something odd !!!
Put this back in the RST
calculation sheet
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Ref following ------
Dist rejection ------
Performance to date (identified with initial step
response):
Ref following: 130Hz
Disturbance rejection: 110Hz
RST at work with POPS: Vout Control
In reality the response is a bit less nice… but still very good.
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Imag Control
Magnet transfer function for Imag:
32.0
96.01
mag
mag
magmagmag
mag
R
HL
RLsV
I
PS magnets deeply saturate:
26Gev without Sat compensation
The RST controller was badly oscillating at the flat
top because the gain of the system was changed
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POPCA3 Desy Hamburg 20 to 23rd may 2012
26Gev with Sat compensation
RST at work with POPS: Imag Control
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Bfield Control
Magnet transfer function for Bfield:
5.2
32.0
96.01
mag
mag
mag
mag
mag
mag
magmag
mag
K
R
HL
KL
RKs
V
B
Tsampl=3ms.
Ref following: 48Hz
Disturbance rejection: 27Hz
Error<0.4Gauss
Error<1Gauss
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POPCA3 Desy Hamburg 20 to 23rd may 2012
RST control: Conclusions
•RST structure can be used for “basic” PID controllers and
conserve the possibility to manual tune the performances
•It has a 2 DOF structure so that Tracking and Regulation
can be tuned independently
•It include “naturally” the possibility to control systems with
pure delays acting as a sort of predictor.
•When system to be controlled is complex, identification is
necessary to refine the performances (no manual tuning is
available).
•A lot more…. But time is over !
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Thanks for the attention
Questions?
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Towards more complex systems
(test it before !!!)
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Unstable filter+magnet+delay
1.2487 (z+3.125) (z+0.2484)
--------------------------------------
z^3 (z-0.7261) (z^2 - 1.077z + 0.8282)
150Hz
Ts=1ms
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POPCA3 Desy Hamburg 20 to 23rd may 2012
Unstable filter+magnet+delay
Aux Poles for Robusteness lowered
the freq to about 50Hz @-3dB
(not Optimized)
Choose Pdes as 2nd order system 100Hz well dumped