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Paul Scherrer Institut

Hans Jäckle. Paul Scherrer Institut. Basic powersupply control – Digital implementation of analog controllers. PSI,. 31. Oktober 2014. Topics. Digital implementation of analog controllers Part 1: Basic Powersupply Controller

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Paul Scherrer Institut

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  1. Hans Jäckle Paul Scherrer Institut Basic powersupply control – Digital implementation of analog controllers PSI, PSI, 31. Oktober 2014

  2. Topics Digital implementation of analog controllers Part 1: Basic Powersupply Controller - Essential Tasks of a basic powersupply controller and how to achieve them Part 2: Discretization - Paths to discrete controller - Methods of discretization - Effects of SamplingTime

  3. Tasks of controller Achieve zero steady-state error -> Integral action

  4. PI Controller • Ki = 1 / TMagnet • -> experimentally (step response in open loop) • -> Ki = RMagnet / LMagnet • Kp can be found manually, starting value: Kp_init = RMagnet / UDC_Link * ωCL / Ki

  5. Tasks of controller Achieve zero steady-state error -> Integral action keep operation of controller linear (avoid limitations) -> Limit diRef / dt -> Anti-Windup

  6. dI/dt Limiter • Keeps the controller in the linear regime by preventing actuator saturation • Anti-Windup is a remedy in case of actuator saturation

  7. Tasks of controller Achieve zero error -> Integral action Stay in linear region -> Limit diRef / dt -> Anti-Windup Suppress dc-link voltage disturbances (e.g. 300Hz Ripple) ->feedforward the dc-link disturbances

  8. DC-Link Feedforwards

  9. DC-Link Feedforward

  10. DC-Link Feedforward + Delay Example: fPWM = 20kHz PWM-Delay = 1/(4* fPWM) = 12.5us Measurement delay = 20us Control cycle = 10us Total delay = 42.5us -> min. gain: -20dB

  11. Tasks of controller Achieve zero error -> Integral action Stay in linear region -> Limit diRef / dt -> Anti-Windup Suppress dc-link voltage disturbances ->feedforward the dc-link disturbances Protect Output Filter Resistor -> Output limiter Reduce measurement noise -> Lowpass-filter for the measured value Reduce overshoot -> Lowpass-filter for the reference value

  12. Beyond PI Compensation of higher order plant dynamics e.g. the output filter 2-DOF structure to seperately tune reference tracking and disturbance rejection

  13. PI Analog:

  14. Paths to discrete controller

  15. Types of discretizations Area based approximations: Forward difference Backward difference Trapezoidal (Tustin, bilinear) Response Invariant transforms: Step response (zero-order hold) Ramp response Impulse response Pole-zero mapping

  16. Area based approximations Forward Euler: Backward Euler: Trapezoidal:

  17. PI Analog: Discrete:

  18. Approximations z <--> s Source: Theorie der Regelungstechnik, Hugo Gassmann

  19. Bode plot of integrators

  20. How to choose sampling time too large -> loss of information too small -> loss of precision (numerical issues) / computational overload No absolute truth -> rules of thumb: 10x faster than Shannons sampling theorem Fs = 10 – 30x system bandwidth Loss of phase margin not more than 5°-15° compared to the continuous system

  21. Summary PI controller for magnet powersupplies is a good choice: can be manually tuned (only two parameters Kp & Ki) good static performance (zero error) reasonable dynamic performance Fast enough sampling rate allows to regard the discrete PI controller as a (quasi-)continous controller. High frequency behaviour not compensated (output filter resonance)

  22. PSI, PSI, 31. Oktober 2014

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