Repetitive control : Power Electronics. Applications

Transcription

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

2 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 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 , 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 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 Introduction : Type Concept (II)

6 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 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 (February 2005). ISSN :

8 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 Periodical Signals Any periodical signal can be written as: The control loop should include:

10 Periodical Signals : Generator Yamamoto, Y. (1993). Learning control and related problems in infinitedimensional systems. In: Proceedings of the 1993 European Control Conference. pp

11 Periodical Signals : Generator I

12 Periodical Signals : Generator II T p +

13 Periodical Signals : Generator III

14 Performance C(s) P(s) Open Loop Transfer Function Sensitivity Function Complementary Sensitivity Function

15 Digital Case

16 Digital Case II ( ) R z T p = z + N 1 T p 1 z N = N T s 2π j i N 2π z = e ω = i i i N T p

17 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 (January 2005)

18 Odd-Harmonic Case II N=3 traditional N=3 odd harmonic Imaginary Axis Pole-Zero Map Real Axis

19 Control Scheme Cascade form Plug-in Form

20 Control Scheme : Cascade form P(z)

21 Control Scheme : Plug-in Approach Repetitive Controller z N F( z) Gx ( z) Gc ( z) Gp ( z)

22 Control Scheme : Plug-in Approach II

23 Control Scheme : Plug-in Approach III

24 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 : Gx ( z) Gc F( z) < 1 ( z)

25 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 Plug-in Approach : G x (z) A common approach to design G x (z) is Unfortunately, this approach cannot be applied to nonminimum-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 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 Introduction Proliferation of nonlinear loads ->This fact has deteriorated the power quality of electrical power systems. More stringent requirements proposals IEC {2,4} and IEEE-519.

29 Basic Concepts v s i s Linear Load Active Filter Nonlinear Load

30 Architecture : Complete Picture Full Bridge Boost Converter

31 Control Problem: Control Goals Current in phase with the voltage waveform: ( ) * sin s d r i = I ω t Constant average value of the voltage at the DC bus capacitor: * x = V 2 0 d

32 Architecture : Boost Converter u r L r L & = 1 C x& = x 1 x 1 Vs x2 L x1+ x2 + r x1 = v s x C 2 1 & = 1 C x& = x L x1 x2 + r x1 = v s 2 1 u Vs x2 C

33 Architecture : Boost u & + + = = 1 C x& 2 = x1 Converter II L x1 x2 r x1 v s & L x1 = ux2 r x1+ v s C x& = ux & 2 1 L x1 = u x2 r x1+ v s C x& = u x 2 1 & u = 1 C x& = x L x1 x2 + r x1 = v s 2 1 u = { 1,1} The averaged model u = [ 1,1]

34 Control Problem: Current L x& = u x r x + v Control loop s x = V 2 d L x& = u V r x + V 1 d 1 V x ( ) 1 s = r = G ( ) ( ) p s u s L d s + 1 r s G () ( 1 ( ) 1 ) p s Gp z = z Z s ZOH, T

35 Control Problem: Voltage Loop C x y = x 2 C y& = u x x & = u x ( ) 2 2 x1 () t = Id sin ( ωrt) al cos( l ωrt) + blsin ( l ωrt) l= Iload Current loop in steady state k+ 1 T k 2 2 ET k 2 ( d 1) ( l l ) ( d 1) C y = r kt I b + a + b + I b l 2 r=0 ( k+ 1) T ET k C y = I b kt 2 ( ) d 1

36 Control Problem: Voltage Loop 2 V d 2 PI E T z 2 1 y b 1

37 Control Problem: Proposed Two control loops : Scheme Current loop : Digital Repetitive Control Voltage loop : Classical PI Control I d sin ( ωr t) Repetitive Controller PI Controller Boost Converter 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 E.Page(s): x 2 x 1 V d * I s I l

38 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 ) (50A) DC bus voltage: AD-215BY isolation amplifier Control hardware: ADSP floating-point DSP ADMC-200 coprocessor: A/D channels and PWM generation

39 Experimental Setup : General view

40 Experimental setup : IGBT drivers

41 Experimental setup : Control hardware

42 Experimental Results: Nonlinear Load

43 Experimental Results: No-Load

44 Experimental Results: Full NL load

45 Experimental Results: Full NL load

46 Experimental Results: Full load to No-load

47 Experimental Results: No-load to full load