RST Digital Controls POPCA 3 Desy Hamburg 20

RST Digital Controls POPCA 3 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 • “Advanced PID Control”: Karl J. Astrom; Tore Hagglund; • “Elementi di automatica”: Paolo Bolzern POPCA 3 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 POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST Digital control: structure and calculation POPCA 3 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 POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST calculation: Diophantine Equation Getting the desired polynomial Sample Ts=100 us Calculating R and S: Diophantine Equation Matrix form: n. B+d n. A+n. B+d POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST calculation: fixed polynomials Controller TF is: Add integrator Add 2 zeros more on S Integrator active on step reference and step disturbance. Attenuation of a 300 Hz disturbance Calculating R and S: Diophantine Equation POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST equivalent for PID controllers POPCA 3 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 POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST equivalent of PID controller: continuous PID design Consider a II order system: POPCA 3 Desy Hamburg 20 to 23 rd may 2012

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 POPCA 3 Desy Hamburg 20 to 23 rd may 2012 = 0. 5 Tustin

RST equivalent of PID: pole placement in z Choose desired poles Sample Ts=100 us Choose fixed parts for R and S Calculating R and S: Diophantine Equation POPCA 3 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 POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RS for regulation, T for Tracking POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RS for regulation, T for tracking REGULATION After the D. Eq solved we get the following open loop TF: =942 r/s =0. 9 =31400 r/s =0. 004 Closed Loop TF without T Pure delay =1260 r/s =1 =1410 r/s =1 TRACKING T polynomial compensate most of the system dynamic POPCA 3 Desy Hamburg 20 to 23 rd may 2012

Systems with delays POPCA 3 Desy Hamburg 20 to 23 rd may 2012

Systems with delays II order system with pure delay Sample Ts=1 ms Continuous time PID is much slower than before POPCA 3 Desy Hamburg 20 to 23 rd may 2012

Systems with delays Predictive controls Diophantine Equation Choose fixed parts for R and S POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST at work with POPS POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST at work with POPS Vout Controller Imag or Bfield control Ppk=60 MW Ipk=6 k. A Vpk=10 k. V POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST at work with POPS: Vout Control III order output filter Decide desired dynamics Eliminate process well dumped zeros Solve Diophantine Equation Calculate T to eliminate all dynamics POPCA 3 Desy Hamburg 20 to 23 rd may 2012 HF zero responsible for oscillations

RST at work with POPS: Vout Control Well… not very nice performance…. There must be something odd !!! Identification of output filter with a step Put this back in the RST calculation sheet POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST at work with POPS: Vout Control In reality the response is a bit less nice… but still very good. Performance to date (identified with initial step response): Ref following: 130 Hz Disturbance rejection: 110 Hz POPCA 3 Desy Hamburg 20 to 23 rd may 2012 Ref following -----Dist rejection ------

RST at work with POPS: Imag Control Magnet transfer function for Imag: PS magnets deeply saturate: The RST controller was badly oscillating at the flat top because the gain of the system was changed 26 Gev without Sat compensation POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST at work with POPS: Imag Control 26 Gev with Sat compensation POPCA 3 Desy Hamburg 20 to 23 rd may 2012

RST at work with POPS: Bfield Control Tsampl=3 ms. Ref following: 48 Hz Disturbance rejection: 27 Hz Magnet transfer function for Bfield: Error<0. 4 Gauss Error<1 Gauss POPCA 3 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 ! POPCA 3 Desy Hamburg 20 to 23 rd may 2012

Thanks for the attention Questions? POPCA 3 Desy Hamburg 20 to 23 rd may 2012

Towards more complex systems (test it before !!!) POPCA 3 Desy Hamburg 20 to 23 rd may 2012

Unstable filter+magnet+delay 150 Hz Ts=1 ms 1. 2487 (z+3. 125) (z+0. 2484) -------------------z^3 (z-0. 7261) (z^2 - 1. 077 z + 0. 8282) POPCA 3 Desy Hamburg 20 to 23 rd may 2012

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