RST Digital Controls RST Digital ControlsPOPCA3 POPCA3 Desy Desy
Hamburg 20 Hamburg 20 to 23 to 23rd rdmay 2012 may 2012RST Digital
Controls RST Digital ControlsPOPCA3 POPCA3 Desy Desy Hamburg 20
Hamburg 20 to 23 to 23rd rdmay 2012 may 2012Fulvio BoattiniCERN
TE\EPCBibliography Digital Control Systems: Ioan D. Landau;
Gianluca Zito Computer Controlled Systems. Theory and Design: Karl
J . Astrom; BjornWittenmark Advanced PID Control: Karl J . Astrom;
Tore Hagglund; Elementi di automatica:Paolo BolzernPOPCA3 POPCA3
Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may 2012
Digital Control Systems: Ioan D. Landau; Gianluca Zito Computer
Controlled Systems. Theory and Design: Karl J . Astrom;
BjornWittenmark Advanced PID Control: Karl J . Astrom; Tore
Hagglund; Elementi di automatica:Paolo BolzernSUMMARYRST Digital
control: structure and calculationRST equivalent for PID
controllersRS for regulation, T for trackingSystems with delaysRST
at work with POPSVout ControllerImag ControllerBfield
ControllerConclusionsSUMMARYPOPCA3 POPCA3 Desy Desy Hamburg 20 to
23 Hamburg 20 to 23rd rdmay 2012 may 2012SUMMARYRST Digital
control: structure and calculationRST equivalent for PID
controllersRS for regulation, T for trackingSystems with delaysRST
at work with POPSVout ControllerImag ControllerBfield
ControllerConclusionsRST Digital control: structure and
calculationPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to
23rd rdmay 2012 may 2012RST Digital control: structure and
calculationRST calculation: control structurennnnnnz t z t z t t Tz
s z s z s s Sz r z r z r r R + + + = + + + = + + + =.........2211
02211 02211 0SRHfbSTHffy R r T u S== = A combination of FFW and FBK
actionsthat can be tuned separatelyREGULATIONR B S AS Ady + =POPCA3
POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may
2012SRHfbSTHffy R r T u S== = ) ( ) ( ) ( ) ( ) (1 1 1 1 1 = + z P
z R z B z S z AdesREGULATIONR B S AS Ady + =R B S AT Bry + =
TRACKING) 1 () 1 () 1 () (1BPBz PTdesdes=RST calculation:
Diophantine Equation3 . 0100 222 22= =+ + s sSample Ts=100us2 - 1
--2 -1z 0.963 + z 1.959 - 1z 0.001924 + z 0.001949-2 -1z 0.963 + z
1.959 - 1 =desPGetting the desired polynomialp x M z P z R z B z S
z Ades= = + ) ( ) ( ) ( ) ( ) (1 1 1 1 1Calculating R and S:
Diophantine EquationMatrix form:POPCA3 POPCA3 Desy Desy Hamburg 20
to 23 Hamburg 20 to 23rd rdmay 2012 may 2012p x M z P z R z B z S z
Ades= = + ) ( ) ( ) ( ) ( ) (1 1 1 1 1((((((((((
=nB nAnB nAb ab b a ab ab ab aM0 0 0 0 ... 00 00 10 00 ... ... 0
0 ... 0 12 21 12 21 1nB+d nAnA+nB+dMatrix form:j j 0 ,..., 0 ,
,..., , 1,..., , , ,..., , 111 0 1nPTnR nSTp p pr r r s s x==RST
calculation: fixed polynomialsController TF is:) () (11=z Sz RHfbj
) ( 1) (1 * 11 z S zz RR B S AS Ady + =Add integratorAdd 2 zeros
more on S j j R B S AS z z z A + + + * 221111 1 POPCA3 POPCA3 Desy
Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may 2012R of
part fixed ) (S of part fixed ) () ( ) ( ) ( ) ( ) ( ) ( ) (111 1 1
1 1 1 1=== + z Hrz Hsz P z R z Hr z B z S z Hs z AdesCalculating R
and S: Diophantine EquationIntegrator active on step reference and
step disturbance.Attenuation of a 300Hz disturbanceRST equivalent
for PID controllersPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg
20 to 23rd rdmay 2012 may 2012RST equivalent for PID controllersRST
equivalent of PID controller: continuous PID design3 . 0100 222 22=
=+ += s s ABConsider a II order system:, , , , 20 0 020 02 2 2 2 2
32 21 .111 + + + = + + + + += + = = += ==||
\| ++ =s s s Ki s Kp s Kd sHsy PID Den HclPIDcHsy PIDHsy
PIDHclPIDcTd Kp KdTiKpKiTd sTi sKp PIDPole Placement forcontinuous
PIDPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd
rdmay 2012 may 2012, , , , 20 0 020 02 2 2 2 2 32 21 .111 + + + = +
+ + + += + = = += ==||
\| ++ =s s s Ki s Kp s Kd sHsy PID Den HclPIDcHsy PIDHsy
PIDHclPIDcTd Kp KdTiKpKiTd sTi sKp PIDRST equivalent of PID
controller: continuous PID design3 . 0100 222 22= =+ += s s
ABConsider a II order system:Td Kp KdTiKpKiNTdsTd sTi sKp PIDf
==|||
\| + ++ =111, , 20 0 023002200 02 21 2 1 += = + =KdKiKpPOPCA3
POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may
2012, , 20 0 023002200 02 21 2 1 += = + =KdKiKpRST equivalent of
PID: s to z substitution) ( ) (1 1 = z R z T) 1 ( ) (1R z T =All
control actions on errorProportional on error;Int+deriv on
outputPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd
rdmay 2012 may 2012Choose R and S coeffs such that the 2 TFare
equal) () () (12211 02211 011 = + + + += z PIDdz s z s sz r z r rz
Sz R, , , , , 2 12 111112 1 02 1 011111 + + + += =((
+ + + + + =z s z s sz r z r rSRz Td Ts N Ts N Tdz Td NzzTiTsKp
PIDd o = 0 forward Euler o = 1 backward Euler o = 0.5 TustinRST
equivalent of PID: pole placement in zChoose desired poles8 . 0150
222 22= =+ + s sSample Ts=100us2 - 1 --2 -1z 0.963 + z 1.959 - 1z
0.001924 + z 0.001949-2 -1z 0.963 + z 1.959 - 1 =desPChoose fixed
parts for R and SPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg
20 to 23rd rdmay 2012 may 20121 11= =Hr z HsChoose fixed parts for
R and S) ( ) ( ) ( ) ( ) ( ) ( ) (1 1 * 1 1 1 * 1 1 = + z P z R z
Hr z B z S z Hs z AdesCalculating R and S: Diophantine EquationRST
equivalent of PID: pole placement in zThe 3 regulators behave
verysimilarlyPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to
23rd rdmay 2012 may 2012Increasing KdManual Tuning with Ki, Kd
andKp is still possibleRS for regulation, T for TrackingPOPCA3
POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may
2012RS for regulation, T for TrackingRS for regulation, T for
tracking, , 9 . 0 / 940 5 . 1 20 0 020 0 020 0= = = + + + = s r s s
s PdesPaux Pdes R B S Hs AHs = + =*: Equation e
Diophantinintegrator ] 1 1 [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==S AR BHolAfter the D. Eq solved we
get the following open loop TF:e=942r/s,=0.9e=1410r/s,=1Pure
delaye=31400r/s,=0.004Closed Loop TF without T0.844z^-2) +
1.836z^-1 - (1 ) 0.8682z^-1 - (1 ) 0.8819z^-1 - (1) 0.9875z^-1 + (1
z^-1 0.0019487= + =R B S ABHclREGULATIONPOPCA3 POPCA3 Desy Desy
Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may
2012e=1410r/s,=1e=1260r/s,=1) 1 ( BPaux PdesT= TRACKING1)
0.9875z^-1 + (1 z^-1 0.50314= + =R B S AB THclT polynomial
compensate most ofthe system dynamicSystems with delaysPOPCA3
POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may
2012Systems with delaysSystems with delaysII order system with pure
delaymss rs seABs33 . 0/ 100 222 22== =+ += Sample Ts=1ms2 - 1 --5
-4z 0.6859 + z 1.368 - 1z 0.149 + z 0.1692Continuous timePID is
muchslower than beforePOPCA3 POPCA3 Desy Desy Hamburg 20 to 23
Hamburg 20 to 23rd rdmay 2012 may 2012Continuous timePID is
muchslower than beforeSystems with delaysPredictive controlsPOPCA3
POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may
2012Diophantine Equation) ( ) ( ) ( ) ( ) ( ) (1 1 1 101 1 = + z P
z A z R z B z z S z Aauxd1 11= =Hr z HsChoose fixed parts for R and
SRST at work with POPSPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23
Hamburg 20 to 23rd rdmay 2012 may 2012RST at work with POPSRST at
work with POPSVout Controller Imag or Bfield
controlPpk=60MWIpk=6kAVpk=10kVPOPCA3 POPCA3 Desy Desy Hamburg 20 to
23 Hamburg 20 to 23rd rdmay 2012 may 2012RST at work with POPS:
Vout ControlLfiltCfCdmpRdmpVinVoutIind ImagIcfIcdmpIII order output
filter2 - 1 -2 - 1 --2 -11ms Ts 22 22z 0.3897 + z 1.142 - 1z 0.3897
+ z 1.142 - 1z 0.1043 + z 0.143185 . 0150 22 = = =+ +=desd cPs s
Decide desired dynamicsPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23
Hamburg 20 to 23rd rdmay 2012 may 2012HF zeroresponsible
foroscillations2 - 1 -2 - 1 --2 -11ms Ts 22 22z 0.3897 + z 1.142 -
1z 0.3897 + z 1.142 - 1z 0.1043 + z 0.143185 . 0150 22 = = =+
+=desd cPs s ) ( ) ( ) ( ) ( ) ( ) (1 1 1 1 1 1 = + z P z P z R z B
z S z Azeros desSolve Diophantine EquationCalculate T to eliminate
all dynamics) 1 () () (11Bz Pz Tdes=R B S AT Bry + =Eliminate
process well dumped zeros0.8053 - z =zerosPRST at work with POPS:
Vout ControlPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to
23rd rdmay 2012 may 2012Identification of output filter with a
stepWell not very nice performance.There must be something odd
!!!Put this back in the RSTcalculation sheetRST at work with POPS:
Vout ControlIn reality the response is a bit less nice but still
very good.POPCA3 POPCA3 Desy Desy Hamburg 20 to 23 Hamburg 20 to
23rd rdmay 2012 may 2012Ref following ------Dist rejection
------Performance to date (identified with initial
stepresponse):Ref following: 130HzDisturbance rejection: 110HzRST
at work with POPS: Imag ControlMagnet transfer function for Imag:O
==+ =32 . 096 . 01magmagmag mag magmagRH LR L s VIPS magnets deeply
saturate:The RST controller was badly oscillating at the flattop
because the gain of the system was changedPOPCA3 POPCA3 Desy Desy
Hamburg 20 to 23 Hamburg 20 to 23rd rdmay 2012 may 201226Gev
without Sat compensationThe RST controller was badly oscillating at
the flattop because the gain of the system was changedRST at work
with POPS: Imag ControlPOPCA3 POPCA3 Desy Desy Hamburg 20 to 23
Hamburg 20 to 23rd rdmay 2012 may 201226Gev with Sat
compensationRST at work with POPS: Bfield ControlMagnet transfer
function for Bfield:5 . 232 . 096 . 01=O == +
=magmagmagmagmagmagmagmagmagKRH LKLRK sVBTsampl=3ms.Ref following:
48HzDisturbance rejection: 27HzPOPCA3 POPCA3 Desy Desy Hamburg 20
to 23 Hamburg 20 to 23rd rdmay 2012 may 2012Error
