Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Ramon Costa Castelló Advanced Control of Energy Systems (ACES) Institut d’Organització i Control (IOC) Universitat Politècnica de Catalunya (UPC) Barcelona, Spain Odd-Harmonic Digital Repetitive Control and its application to Active filters control

NTU Nayang, February 15h 2006 Contents Repetitive Control Basics –Introduction –Periodic Signals –Discrete Time –Control Scheme –The Odd-Harmonic case The active filter application –Introduction –Basic Concept –Single phase –Control Problem –Experimental Setup –Experimental Results

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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, 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.

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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.

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Introduction : Type Concept (II)

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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)

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Introduction : Systems with periodical disturbances or references (II) Virtual Laboratory

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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)

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Periodical Signals Any periodical signal can be written as: The control loop should include:

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Periodical Signals : Generator Yamamoto, Y. (1993). Learning control and related problems in infinite- dimensional systems. In: Proceedings of the 1993 European Control Conference. pp

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Periodical Signals : Generator I

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Periodical Signals : Generator II +

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Periodical Signals : Generator III

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Digital Case

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Digital Case II +

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Scheme Cascade form Plug-in Form

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Scheme : Cascade form P(z)

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Scheme : Plug-in Approach Repetitive Controller

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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 :

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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).

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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.

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Odd-Harmonic Case N Repetitive controller is order N because it needs to “learn” the N samples defining one period.

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Odd-Harmonic Case (I) A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = - f(x) for all x in the domain of f. Most signals in power electronics are odd symmetric.

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Odd-Harmonic Case (II) N The second semi period can be obtained form the first one

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Odd-Harmonic Case (III) 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)

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Odd-Harmonic Case (IV) N=3 odd harmonic N=3 traditional Demo

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Odd-Harmonic Case (V) Less order (less delay). The closed loop system is faster. Robustness –Gain is only introduced where needed –Waterbed Many industrial systems include a transformer (a derivator in their open- loop transfer function). Traditional RC many not be internally stable. Cannot compensate even harmonics !!!

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Contents Repetitive Control Basics √ –Introduction –Periodic Signals –Discrete Time –Control Scheme –The Odd-Harmonic case The active filter application –Introduction –Basic Concept –Single phase –Control Problem –Experimental Setup –Experimental Results

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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.

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Basic Concepts Linear Load Nonlinear Load Active Filter

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Architecture : Complete Picture (Single Phase) Full Bridge Boost Converter

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Problem: Control Goals Current in phase with the voltage waveform: Constant average value of the voltage at the DC bus capacitor:

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Architecture : Boost Converter r L C r L C

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Architecture : Boost Converter II The averaged model

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Problem: Current Control loop ZOH, T

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Problem: Voltage Loop Current loop in steady state r=0

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Control Problem: Voltage Loop PI

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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 E.Page(s):

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 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

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: Nonlinear Load

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: No-Load

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: Full NL load

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: Full load to No-load

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: No-load to full load

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Architecture : Complete Picture (Three Phase) Active Filter AC current sensors AC voltage sensors DC voltage sensor

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Architecture : Control Scheme RC Signal Analyzer Mode selection

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Architecture : Working Modes Branch Equilibration (all net branches have the same active current) Harmonic Compensation Reactive Compensation

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Setup : General view

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental setup : IGBT drivers

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental setup : Control hardware

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental setup

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: Load Current

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: No Load Current

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: Complete compensation

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Experimental Results: Complete compensation

Odd-Harmonic Digital Repetitive Control and its application to Active filters control NTU Nayang, February 15h 2006 Thank you very much