rst digital controls popca3 desy hamburg 20 to 23 rd may 2012
DESCRIPTION
RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012. Fulvio Boattini CERN TE\EPC. Bibliography. “Digital Control Systems”: Ioan D. Landau; Gianluca Zito “Computer Controlled Systems. Theory and Design”: Karl J. Astrom ; Bjorn Wittenmark - PowerPoint PPT PresentationTRANSCRIPT
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
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
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: control structure
nn
nn
nn
ztztzttT
zszszssS
zrzrzrrR
...
...
...
22
110
22
110
22
110
SRHfb
STHff
yRrTuS
A combination of FFW and FBK actions that can be tuned separately
)()()()()( 11111 zPzRzBzSzA des
REGULATIONRBSA
SAdy
RBSATB
ry
TRACKING
)1()1(
)1()( 1
BPBzP
Tdes
des
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: Diophantine Equation
3.01002
2 22
2
ssSample Ts=100us
2-1-
-2-1
z0.963 + z 1.959 - 1z0.001924 + 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
bbaaba
baba
M
0000...000
01000......00...01
22
11
22
11
nB+d nA
nA+nB
+d
Matrix form:
0,...,0,,...,,1
,...,,,,...,,1
1
101
nPT
nRnST
ppp
rrrssx
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST calculation: fixed polynomials
Controller TF is:
)()(
1
1
zSzRHfb )(1
)(1*1
1
zSzzR
RBSASA
dy
Add integrator
Add 2 zeros more on S RBSA
SzzzA
*22
11
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
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID controller: continuous PID design
3.01002
2 22
2
ssAB
Consider a II order system:
2000
200
222223 22
1.1
11
sssKisKpsKds
HsyPIDDenHclPIDcHsyPID
HsyPIDHclPIDc
TdKpKdTiKpKiTds
TisKpPID
Pole Placement for continuous PID
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID controller: continuous PID design
3.01002
2 22
2
ssAB
Consider a II order system:
TdKpKdTiKpKi
NTdsTds
TisKpPIDf
1
11
2
000
2
30
0
2
20
00
22
121
Kd
Ki
Kp
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
22
110
22
110
1
1
zPIDdzszsszrzrr
zSzR
21
21
1
1
1
1
210210
11
111
zszsszrzrr
SR
zTdTsNTsNTdzTdN
zz
TiTsKpPIDd
= 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
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST equivalent of PID: pole placement in z
Choose desired poles
8.01502
2 22
2
ssSample Ts=100us
2-1-
-2-1
z0.963 + z 1.959 - 1z0.001924 + 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
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
POPCA3 Desy Hamburg 20 to 23rd may 2012
RS for regulation, T for tracking 9.0/9405.12 000
2000
200 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
SARBHol
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(BPauxPdesT
REGULATION
TRACKING
1)0.9875z^-1+(1 z^-1 0.50314
RBSABTHcl
T polynomial compensate most of the system dynamic
POPCA3 Desy Hamburg 20 to 23rd may 2012
Systems with delays
II order system with pure delay
ms
sr
sse
AB s
33.0
/1002
2 22
2
Sample Ts=1ms
2-1-
-5-4
z 0.6859 + z 1.368 - 1z 0.149 + z 0.1692
Continuous time PID is much slower than before
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
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
TW2Crwb2
TW1
Lw1
Crwb1
Lw2
MAGNETS
AC/DC converter - AFEDC/DC converter - charger moduleDC/DC converter - flying module
Vout Controller Imag or Bfield control
Ppk=60MWIpk=6kAVpk=10kV
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Vout ControlLfilt
C fCdm p
Rdm p
Vin
Vou
t
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 - 1z0.1043 + z0.1431
85.01502
2
des
dc
P
ss
Decide desired dynamics
)()()()()()( 111111 zPzPzRzBzSzA zerosdes
Solve Diophantine Equation
Calculate T to eliminate all dynamics
)1()()(
11
BzPzT des
RBSATB
ry
Eliminate process well dumped zeros 0.8053-zzerosP
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
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.
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Imag Control
Magnet transfer function for Imag:
32.096.01
mag
mag
magmagmag
mag
RHL
RLsVI
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
POPCA3 Desy Hamburg 20 to 23rd may 2012
26Gev with Sat compensation
RST at work with POPS: Imag Control
POPCA3 Desy Hamburg 20 to 23rd may 2012
RST at work with POPS: Bfield ControlMagnet transfer function for Bfield:
5.2
32.096.0
1
mag
mag
mag
magmag
magmag
mag
mag
K
RHL
KLR
KsVB
Tsampl=3ms.Ref following: 48HzDisturbance rejection: 27Hz
Error<0.4Gauss
Error<1Gauss
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 !
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