1. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Ramon Costa Castelló Advanced Control of Energy Systems (ACES) Instituto de Organización y Control (IOC) Universitat Politècnica de Catalunya (UPC) Barcelona, Spain Repetitive control : Power Electronics Applications

2. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Contents Repetitive Control Basics –Introduction –Periodic Signals –Performance –Discrete Time –The Odd-Harmonic case –Control Scheme Cascade Approach Plug-in Approach The active filter application –Introduction –Basic Concept –Architecture –Control Problem –Experimental Setup –Experimental Results

3. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction A key topic in classical control theory is the Internal Model Principle (IMP). –B. Francis and W. Wonham, “Internal Model Principle in control theory,” Automatica, vol. 12, pp. 457–465, 1976. This principle states that if a certain signal must be tracked or rejected without steady-state error, the generator must be inside the control loop, in the controller, or in the plant itself.

4. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction : Type Concept Standard classical control subjects include the IMP concept implicitly when they introduce the system-type concept. The type concept can only be applied to polynomial signals (step, ramp, and parabola) whose generator has the form in the Laplace domain.

5. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction : Type Concept (II)

6. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction : Systems with periodical disturbances or references In practice, many real systems have to handle tracking and rejecting periodic signals. Magnet power supply for a proton synchrotron (Nakano and others)

7. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction : Systems with periodical disturbances or references (II) Demonstration of the Internal Model Principle by Digital Repetitive Control of an Educational Laboratory Plant. Ramon Costa- Castelló and Jordi Nebot and Robert Griñó.IEEE Transactions on Education. Vol. 48, No.1, Pages 73- 80 (February 2005). ISSN : 0018-9359.

8. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction : Power Electronics Inverter : Generating a 50/60 Hz signal from dc one (Tracking a reference signal) Active filter : Compensation of harmonic signals (Rejecting periodic signals)

9. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Periodical Signals Any periodical signal can be written as: The control loop should include:

10. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Periodical Signals : Generator Yamamoto, Y. (1993). Learning control and related problems in infinite- dimensional systems. In: Proceedings of the 1993 European Control Conference. pp. 191-222.

11. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Periodical Signals : Generator I

12. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Periodical Signals : Generator II +

13. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Periodical Signals : Generator III

14. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Performance C(s) P(s) Open Loop Transfer Function Sensitivity Function Complementary Sensitivity Function

15. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Digital Case

16. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Digital Case II +

17. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Odd-Harmonic Case Digital repetitive plug-in controller for odd-harmonic periodic references and disturbances Robert Griñó and Ramon Costa- Castelló. Automatica. Volume 41, Issue 1,Pages 153-157(January 2005)

18. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Odd-Harmonic Case II N=3 odd harmonic N=3 traditional

19. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Scheme Cascade form Plug-in Form

20. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Scheme : Cascade form P(z)

21. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Scheme : Plug-in Approach Repetitive Controller

22. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Scheme : Plug-in Approach II

23. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Scheme : Plug-in Approach III

24. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Plug-in Approach : Stability Conditions 1.First stability Condition : The System without the Repetitive Controller must be stable. 2.Second stability Condition 3.Third stability Condition :

25. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Plug-in Approach : Filter F(z) should fulfill the second stability condition. Usually, a low-pass null-phase FIR filter is used. To assure unitary gain a DC frequency the parameters must fulfill : No causality problems exist because that the filter is in cascade with a N periods delay. The filter reduces the open-loop gain at those frequencies at which uncertainty exists (robustness). Unfortunately it slightly moves the open-loop pole positions in z-plane (precision loose).

26. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Plug-in Approach : G x (z) A common approach to design G x (z) is Unfortunately, this approach cannot be applied to non- minimum-phase plants. Another approach is to cancel minimum-phase zeros and compensate the phase for the non minimum-phase ones: k r is fixed by a trade-off between robustness and transient response.

27. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Contents Repetitive Control Basics √ –Introduction –Periodic Signals –Performance –Discrete Time –The Odd-Harmonic case –Control Scheme Cascade Approach Plug-in Approach The active filter application –Introduction –Basic Concept –Architecture –Control Problem –Experimental Setup –Experimental Results

28. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Introduction Proliferation of nonlinear loads ->This fact has deteriorated the power quality of electrical power systems. More stringent requirements proposals IEC-61000-3-{2,4} and IEEE-519.

29. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Basic Concepts Linear Load Nonlinear Load Active Filter

30. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Architecture : Complete Picture Full Bridge Boost Converter

31. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Problem: Control Goals Current in phase with the voltage waveform: Constant average value of the voltage at the DC bus capacitor:

32. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Architecture : Boost Converter r L C r L C

33. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Architecture : Boost Converter II The averaged model

34. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Problem: Current Control loop ZOH, T

35. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Problem: Voltage Loop Current loop in steady state r=0

36. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Problem: Voltage Loop PI

37. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Control Problem: Proposed Scheme Two control loops : –Current loop : Digital Repetitive Control –Voltage loop : Classical PI Control Boost Converter Repetitive Controller PI Controller Odd-Harmonic Digital Repetitive Control of a Single-Phase Current Active Filter. Ramon Costa-Castelló, Robert Griñó & Enric Fossas IEEE Transactions on Power Electronics. Volume: 19, Issue: 4, Year: July 2004. E.Page(s):1060- 1068.

38. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Setup Active filter parameters: –Capacitor: 6600 uF, 450 V DC –Inductor: 0.8 mH –parasitic resistance: 0.04 Ohm –IGBT: 1200 V, 100 A Feedback paths (sensors): –Network voltage: voltage transformer (220V/15V) –Network current: Hall-effect sensor (TECSA-HA-050053) (50A) –DC bus voltage: AD-215BY isolation amplifier Control hardware: –ADSP-21161 floating-point DSP –ADMC-200 coprocessor: A/D channels and PWM generation

39. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Setup : General view

40. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental setup : IGBT drivers

41. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental setup : Control hardware

42. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Results: Nonlinear Load

43. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Results: No-Load

44. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Results: Full NL load

45. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Results: Full NL load

46. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Results: Full load to No-load

47. Repetitive Control: Power Electronics Applications. Jornadas de Ingeniería de Control Zaragoza Mayo 2005 Experimental Results: No-load to full load