rst digital controls popca3 desy hamburg 20 to 23 rd may 2012 fulvio boattini cern te\epc
TRANSCRIPT
![Page 1: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/1.jpg)
RST Digital Controls
POPCA3 Desy Hamburg 20 to 23rd may 2012
Fulvio Boattini CERN TE\EPC
![Page 2: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/2.jpg)
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
![Page 3: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/3.jpg)
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
![Page 4: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/4.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST Digital control: structure and calculation
![Page 5: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/5.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: control structure
nn
nn
nn
ztztzttT
zszszssS
zrzrzrrR
...
...
...
22
110
22
110
22
110
S
RHfb
S
THff
yRrTuS
A combination of FFW and FBK actions that can be tuned separately
)()()()()( 11111 zPzRzBzSzA des
REGULATIONRBSA
SA
d
y
RBSA
TB
r
y
TRACKING
)1(
)1()1(
)( 1
B
PB
zP
Tdes
des
![Page 6: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/6.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: Diophantine Equation
3.0
1002
2 22
2
ss
Sample Ts=100us2-1-
-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
nPT
nRnST
ppp
rrrssx
![Page 7: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/7.jpg)
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
21
11 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
![Page 8: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/8.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent for PID controllers
![Page 9: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/9.jpg)
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:
2000
200
222223 22
1.1
11
sssKisKpsKds
HsyPIDDenHclPIDcHsyPID
HsyPIDHclPIDc
TdKpKdTi
KpKiTds
TisKpPID
Pole Placement for continuous PID
![Page 10: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/10.jpg)
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
30
0
2
20
00
22
121
Kd
Ki
Kp
![Page 11: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/11.jpg)
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
)()(
)( 12
21
10
22
110
1
1
zPIDdzszss
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
![Page 12: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/12.jpg)
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=100us2-1-
-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 HrzHsChoose fixed parts for R and S
)()()()()()()( 11*111*11 zPzRzHrzBzSzHszA des
Calculating R and S: Diophantine Equation
![Page 13: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/13.jpg)
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
![Page 14: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/14.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RS for regulation, T for Tracking
![Page 15: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/15.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RS for regulation, T for tracking
9.0/9405.12 0002
0002
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
![Page 16: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/16.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
Systems with delays
![Page 17: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/17.jpg)
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
![Page 18: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/18.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
Systems with delaysPredictive controls
Diophantine Equation
)()()()()()( 11110
11 zPzAzRzBzzSzA auxd
1 1 1 HrzHsChoose fixed parts for R and S
![Page 19: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/19.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS
![Page 20: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/20.jpg)
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 ACScc=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=60MWIpk=6kAVpk=10kV
![Page 21: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/21.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Vout ControlLfilt
C fCdm p
Rdm p
Vin
Vout
Iind Im ag
Icf
Icdmp
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
![Page 22: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/22.jpg)
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
![Page 23: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/23.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
Ref following ------Dist rejection ------
Performance to date (identified with initial step response):Ref following: 130HzDisturbance rejection: 110Hz
RST at work with POPS: Vout Control
In reality the response is a bit less nice… but still very good.
![Page 24: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/24.jpg)
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
![Page 25: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/25.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
26Gev with Sat compensation
RST at work with POPS: Imag Control
![Page 26: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/26.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Bfield Control
Magnet transfer function for Bfield:
5.2
32.096.0
1
mag
mag
mag
magmag
magmag
mag
mag
K
RHL
KL
RKs
V
B
Tsampl=3ms.Ref following: 48HzDisturbance rejection: 27Hz
Error<0.4Gauss
Error<1Gauss
![Page 27: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/27.jpg)
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 !
![Page 28: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/28.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
Thanks for the attention
Questions?
![Page 29: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/29.jpg)
POPCA3 Desy Hamburg 20 to 23rd may 2012
Towards more complex systems
(test it before !!!)
![Page 30: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/30.jpg)
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
![Page 31: RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012 Fulvio Boattini CERN TE\EPC](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d9f5503460f94a89a1c/html5/thumbnails/31.jpg)
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