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

2. POPCA3 Desy Hamburg 20 to 23 rd 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

3. POPCA3 Desy Hamburg 20 to 23 rd 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

4. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST Digital control: structure and calculation

5. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST calculation: control structure A combination of FFW and FBK actions that can be tuned separately REGULATION TRACKING

6. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST calculation: Diophantine Equation Sample Ts=100us Getting the desired polynomial Calculating R and S: Diophantine Equation nB+dnA nA+nB+d Matrix form:

7. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST calculation: fixed polynomials Controller TF is: Add integrator Add 2 zeros more on S Calculating R and S: Diophantine Equation Integrator active on step reference and step disturbance. Attenuation of a 300Hz disturbance

8. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST equivalent for PID controllers

9. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST equivalent of PID controller: continuous PID design Consider a II order system: Pole Placement for continuous PID

10. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST equivalent of PID controller: continuous PID design Consider a II order system:

11. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST equivalent of PID: s to z substitution Choose R and S coeffs such that the 2 TF are equal  = 0 forward Euler  = 1 backward Euler  = 0.5 Tustin All control actions on error Proportional on error; Int+deriv on output

12. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST equivalent of PID: pole placement in z Choose desired poles Sample Ts=100us Choose fixed parts for R and S Calculating R and S: Diophantine Equation

13. POPCA3 Desy Hamburg 20 to 23 rd 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

14. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RS for regulation, T for Tracking

15. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RS for regulation, T for tracking 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 REGULATION TRACKING T polynomial compensate most of the system dynamic

16. POPCA3 Desy Hamburg 20 to 23 rd may 2012 Systems with delays

17. POPCA3 Desy Hamburg 20 to 23 rd may 2012 Systems with delays II order system with pure delay Sample Ts=1ms Continuous time PID is much slower than before

18. POPCA3 Desy Hamburg 20 to 23 rd may 2012 Systems with delays Predictive controls Diophantine Equation Choose fixed parts for R and S

19. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST at work with POPS

20. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST at work with POPS Vout ControllerImag or Bfield control Ppk=60MW Ipk=6kA Vpk=10kV

21. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST at work with POPS: Vout Control III order output filter HF zero responsible for oscillations Decide desired dynamics Solve Diophantine Equation Calculate T to eliminate all dynamics Eliminate process well dumped zeros

22. POPCA3 Desy Hamburg 20 to 23 rd 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

23. POPCA3 Desy Hamburg 20 to 23 rd 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.

24. POPCA3 Desy Hamburg 20 to 23 rd may 2012 RST at work with POPS: Imag Control Magnet transfer function for Imag: 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

25. POPCA3 Desy Hamburg 20 to 23 rd may 2012 26Gev with Sat compensation RST at work with POPS: Imag Control

26. POPCA3 Desy Hamburg 20 to 23 rd may 2012 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. POPCA3 Desy Hamburg 20 to 23 rd 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 !

28. POPCA3 Desy Hamburg 20 to 23 rd may 2012 Thanks for the attention Questions?

29. POPCA3 Desy Hamburg 20 to 23 rd may 2012 Towards more complex systems (test it before !!!)

30. POPCA3 Desy Hamburg 20 to 23 rd 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

31. POPCA3 Desy Hamburg 20 to 23 rd may 2012 Unstable filter+magnet+delay Aux Poles for Robusteness lowered the freq to about 50Hz @-3dB (not Optimized) Choose Pdes as 2 nd order system 100Hz well dumped