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Digital Implementation of Analog Controllers: Basic Power Supply Control

This document discusses the digital implementation of analog controllers, focusing on basic power supply control. It addresses essential tasks and methods for achieving them, including discretization techniques and their effects on controller performance. Key aspects such as maintaining zero steady-state error using integral action, anti-windup measures, and suppression of dc-link disturbances are explored. The implementation of PI controllers, including gain tuning and sampling time considerations, for magnetic power supplies is also detailed, emphasizing the importance of balancing performance and operational constraints.

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Digital Implementation of Analog Controllers: Basic Power Supply Control

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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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