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RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012

RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012. Fulvio Boattini CERN TEEPC. Bibliography. “Digital Control Systems”: Ioan D. Landau; Gianluca Zito “Computer Controlled Systems. Theory and Design”: Karl J. Astrom ; Bjorn Wittenmark

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RST Digital Controls POPCA3 Desy Hamburg 20 to 23 rd may 2012

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  1. RST Digital Controls POPCA3 Desy Hamburg 20 to 23rd may 2012 Fulvio Boattini CERN TE\EPC

  2. Bibliography • “Digital Control Systems”: Ioan D. Landau; GianlucaZito • “Computer Controlled Systems. Theory and Design”: Karl J. Astrom; Bjorn Wittenmark • “Advanced PID Control”: Karl J. Astrom; Tore Hagglund; • “Elementidiautomatica”: Paolo Bolzern

  3. SUMMARY • 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

  4. RST Digital control: structure and calculation

  5. RST calculation: control structure A combination of FFW and FBK actions that can be tuned separately REGULATION TRACKING

  6. RST calculation: Diophantine Equation Getting the desired polynomial Sample Ts=100us Calculating R and S: Diophantine Equation Matrix form: nB+d nA nA+nB+d

  7. RST calculation: fixed polynomials Controller TF is: Calculating R and S: Diophantine Equation Integrator active on step reference and step disturbance. Attenuation of a 300Hz disturbance Add integrator Add 2 zeros more on S

  8. RST equivalent for PID controllers

  9. RST equivalent of PID controller: continuous PID design Pole Placement for continuous PID Consider a II order system:

  10. RST equivalent of PID controller: continuous PID design Consider a II order system:

  11. RST equivalent of PID: s to z substitution All control actions on error Proportional on error; Int+deriv on output Choose R and S coeffs such that the 2 TF are equal  = 0 forward Euler  = 1 backward Euler  = 0.5 Tustin

  12. RST equivalent of PID: pole placement in z Choose desired poles Sample Ts=100us Calculating R and S: Diophantine Equation Choose fixed parts for R and S

  13. 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

  14. RS for regulation, T for Tracking

  15. RS for regulation, T for tracking REGULATION After the D. Eq solved we get the following open loop TF: =942r/s =0.9 =31400r/s =0.004 Closed Loop TF without T Pure delay =1410r/s =1 =1260r/s =1 TRACKING T polynomial compensate most of the system dynamic

  16. Systems with delays

  17. Systems with delays II order system with pure delay Sample Ts=1ms Continuous time PID is much slower than before

  18. Systems with delays Predictive controls Choose fixed parts for R and S Diophantine Equation

  19. RST at work with POPS

  20. RST at work with POPS Vout Controller Imag or Bfield control Ppk=60MW Ipk=6kA Vpk=10kV

  21. RST at work with POPS: Vout Control III order output filter HF zero responsible for oscillations Decide desired dynamics Eliminate process well dumped zeros Solve Diophantine Equation Calculate T to eliminate all dynamics

  22. 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

  23. RST at work with POPS: Vout Control In reality the response is a bit less nice… but still very good. Ref following ------ Dist rejection ------ Performance to date (identified with initial step response): Ref following: 130Hz Disturbance rejection: 110Hz

  24. RST at work with POPS: Imag Control PS magnets deeply saturate: Magnet transfer function for Imag: 26Gev without Sat compensation The RST controller was badly oscillating at the flat top because the gain of the system was changed

  25. RST at work with POPS: Imag Control 26Gev with Sat compensation

  26. RST at work with POPS: Bfield Control Magnet transfer function for Bfield: Tsampl=3ms. Ref following: 48Hz Disturbance rejection: 27Hz Error<0.4Gauss Error<1Gauss

  27. 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 !

  28. Thanks for the attention Questions?

  29. Towards more complex systems (test it before !!!)

  30. Unstable filter+magnet+delay 150Hz Ts=1ms 1.2487 (z+3.125) (z+0.2484) -------------------------------------- z^3 (z-0.7261) (z^2 - 1.077z + 0.8282)

  31. Unstable filter+magnet+delay Choose Pdes as 2nd order system 100Hz well dumped Aux Poles for Robusteness lowered the freq to about 50Hz @-3dB (not Optimized)

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