MEASUREMENT RESULTS OF BUCK CONVERTER PROTOTYPE DIGITALLY CONTROLLED BY ALGORITHM USING LAW OF CONSERVATION OF ENERGY - PROJECT BUMBLEBEE J. KACZMAREK, A. MAZUREK TECHNICAL UNIVERSITY OF KOSZALIN UNIVERSITY, POLAND KEYWORDS: DC/DC converters, Digital control, Law of conservation of energy ABSTRACT: Last year, during MIXDES 2007 conference authors presented 3 articles devoted to new approach to the digital control of DC/DC converters. In this paper authors present results of first tests of Buck converter prototype controlled by algorithm that uses law of conservation of energy. Control algorithm is executed by DSP processor that’s usually used in energoelectronics.
INTRODUCTION In recent years intensive research of energy conversion devices are conducted, particularly of DC/DC converters. From analyzes of converters models presented in literature and from controlling methods that use PID regulators [1], it can be concluded that those devices cannot fulfil ascending requirements that stand before newest converters. Control devices for converters described in literature are usually implemented as digital PID regulators that were developed by transmittance from domain s to z. These solutions are usually effective in the close vicinity of projected bias point, and its change causes worsening of stabilized output voltage properties. It’s necessary to consider not only work mode (CCM, DCM), but also changes of bias point of the device. Main factors that influence bias point are: changes in loads resistance and changes in input voltage value [1]. The solution to those problems could be (at least in wide range), the use of other DC/DC converters control methods. In articles [2-10] authors presented original new concept of controlling DC/DC converters using law of conservation of energy. The result of implementation of this method is universal mathematical description, which is independent of converters work mode (CCM, DCM/CCM, DCM), and even of its type. Stabilization of output voltage is indirect, and realized by controlling the amount of energy accumulated in converter and the amount of energy consumed by load. The equivalent of reference voltage is reference energy Eref, which could be defined as the sum of energy accumulated in converter and consumed by load in single work cycle, defined by following equation [2]:
E
2 V2 Vref ref ( n ) 1 C V 2 1 L T 2 2 RO ( nT ) RO ( nT ) (1) ref ref
where:
Eref (n) – reference energy, Vref C
– required output voltage, – capacitor capacity,
L RO T __
– inductors inductance, – converters load resistance in cycle n (n – converters cycle number), – duration of converters cycle, converters work cycle is time interval , – underlined statement defines the energy accumulated in converter in steady state.
Energy accumulated in converter at the beginning of cycle n can be described using following dependency [2]: E ( n ) 1 C V 2 ( nT ) 1 L I 2 ( nT ) (2) 2 2 L P0 C where: EP0(n) – energy accumulated in the converter at the beginning of cycle n, at time nT, VC(nT) – voltage drop on capacitor at the beginning of current work cycle, IL(nT) – inductors current at the beginning of the actual cycle. At the beginning of every cycle reference energy is compared to the energy accumulated in converters elements EP0. In this way the amount of energy E X is calculated, that should be taken from power source V Z in single work cycle, which is described by equation [2]: Vref 2 E (n) 1 C V 2 V 2(nT) 1 L I 2(nT) ... 2 2 ref X C Ro2(nT) L Vref 2 ... T R (nT) O
((3)
where: EX(n) – amount of energy that should be taken from power source VZ in cycle n.
Amount of energy that the converter takes from power source (buck, buck - boost) during ON phase is described by following dependency [2]: nT t (4) EZ ( n ) nT on VZ (t ) I L (t ) dt where: ton – duration of ON phase in cycle n, EZ(n) – energy taken from source in cycle n, VZ(t) – power source voltage during current cycle. Based on calculated value of energy EX(n) and actual bias point of the converter control device calculates duration of ON phase. The result of comparison of dependencies describing EZ(n) and EX(n) the main equation describing regulation mechanism is leaded out [2]: nT t 2 2 nT on VZ (t ) I L (t ) dt 12 C Vref VC (n T ) ... 2 Vref Vref ... 12 L I 2 ( n T ) T R (n ) RO (n ) L O
V ( nT ) V ( nT ) L A Z , 2L Z
( nT ) I
L
( nT ),
C 2 V V 2 ( nT ) ... ref C 2 L 2 ... I I 2 ( nT ) ... ref L 2 2 ... V I ( nT ) T , ref ref
C
(6)
I ( nT ) ref Ro ref V ( nT ) C Properties and way of implementation of this equation in DSP processor were described in paper [3,6,7]. Presented method can be realized in the following sequence of operations: Measurement of state variables VZ, IL, IRo i VC at time of beginning of new work cycle, and calculation of equation (5) coefficients. Calculation of ON phase duration. V
I
( nT )
In order to verify presented method, a prototype of Buck converter with output power of 100W was developed. In the converter deliberately no additional input and output distortion filters were implemented, and high ESR resistance capacitors were used. It allowed checking the immunity of control device to the EMI distortions generated by converter. Controlling was realized by using so called starter kit EZDSP 320F28335 equipped with DSP processor 320F28335 manufactured by TI company designed for energoelectronics applications. The view of laboratory setup with prototype device is presented in Błąd! Nie można odnaleźć źródła odwołania.. Results of conducted research are presented in the following part of the article.
(5)
Equation (5) allows calculation of ON phase duration ton, in such way, that in single work cycle sum of energy accumulated in converter won’t change. In this way control device will extort required value of output voltage. Implementation of equation (5) in digital devices requires following simplifications: we assume that rise of inductor current is linear, and we discard input voltage changes that occur during single work cycle (input voltage is measured only at the beginning of the cycle). With these assumptions integrator in equation (5) can be replaced by discreet equation [2,3]: 2 B t A ton on C 0 where :
B V
LABORATORY SETUP
Fig. 1. View of laboratory setup with prototype device.
MEASUREMENT DEVICE Proposed control method requires measuring of four values: input voltage, output voltage, inductor and load current. Voltage drops were measured using resistance divider and buffer amplifier. Current measurement was realized by use of measurement resistor and differential amplifier. Because of range of individual values and allowed values of measured signal at the input of A/D converter measured voltages were suppressed in 1:10 rate, and currents at 1:6. It’s derived from assumption that, maximum voltage input equals VZ=24V, and inductor current can reach 16A, when the maximum input voltage of A/D converter cannot surpass 2.5V. These limits are the cause of significant distortions that hamper the work of control device at the small signal levels. Distortion level in converter fluctuated in range of 50-100mV, and at the time of switching the key transistor of Buck converter it even reached 300mV. Especially adverse is conducting measurements during switching of the transistors. (This effect is relevant during converters functioning at low levels of input voltage and small current consumption, for example at bias point: VZ=4.4V, VOUT=2.5V i Ro=3.3Ω). At this bias point voltage describing VZ level measured by A/D converter had amplitude of 0.44V, and voltages measured by A/D converter describing the inductor and load current in steady state were at the 125mV level. This problem was solved by use of the technique of so
called oversampling of A/C acquisition. Measurements were conducted only when the unsteady states caused by key transistor switching didn’t occur. But the use of this technique wasn’t always possible. Influence of the discussed phenomenon is illustrated by Fig. 10 and Fig. 12. Significant reduction of those distortions can be achieved by introducing a low-pass filter to the measurement device or by digital signal processing. In screen shots Fig. 2, Fig. 3 voltage waveform describing average inductor current IL=3A before and after filtering is shown.
behavior of converter at different bias points during steady state. Power consumed by load changes form 1,8W up to 96W. • Green line is the value of output voltage, which average value measured by oscilloscope is displayed in lower left corner. • Yellow line – PWM control signal waveform.
Fig. 4. Authors method - Vref=10V, Ro=1.1Ω Vz=19.5V. Fig. 2. Voltage waveform at the inductor current measurement device output (average value of inductor current: 3A).
Through limitation of oscilloscope bandwidth to 1.25MHz and through the use of embedded digital lowpass filter significant distortion limitation was achieved (as shown in Fig. 3).
Fig. 5. Magnification of Fig. 4
Fig. 3. Voltage waveform at the inductor current measurement device output after filtering.
EXEMPLARY PWM AND OTPUT VOLTAGE SIGNAL WAVEFORMS DURING STEADY STATE The functioning of Buck converter controlled through the use of authors method is illustrated by PWM and output voltage Vout waveforms, that are shown in th following screen shots Fig. 4 - Fig. 12. They show
Fig. 6. Authors method Vref=10V, Vz=19.5V, Ro=3.3Ω.
Fig. 7. Authors method Vref=10V, Vz=12V, Ro=3.3Ω.
Fig. 10. Authors method - Vref=5V, Vz=8V, Ro=1.1Ω – Oscillations caused by imposition of switching of the transistor from ON phase to OFF phase with measurement of output voltage Vout. ON phase is prolonged because of lower load resistance in comparison to Fig. 9
Fig. 8. Authors method Vref=5V, Vz=14.5V, Ro=1.1Ω
Fig. 11. Authors method Vref=2.5V, Vz=20V, Ro=3.3Ω.
Fig. 9. Authors method Vref=5V, Vz=8V, Ro=3.3Ω – Lack of oscillations, change of ON/OFF phase occurs before the measurement of output voltage and current. Measurement aren’t distorted by change of converters work cycle.
Fig. 12. Authors method Vref=2.5V, Vz=4.2V Ro= 3.3Ω – Oscillations of control PWM signal caused by too smal time distance between switching of the converters controlling transistor and the measurement of output voltage and current. Oscilograph was taken at the very low value of signal measured by A/D converter of the DSP processor (distortions reach 30% of measured signal).
CONVERTERS UNSTEADY STATE – PROTOTYPE MEASUREMENT RESULTS A converter functioning was monitored by measurement system based on multifunction A/D measurement device (12 bit 100ksamples for channel) and LabView software. To enhance the precision of the measurement, external triggering of measurement start has been used by using (synchronized with PWM) voltage impulse generated by DSP processors hardware. Figures show signal samples measured at the every time of beginning of a converters new work cycle - nT.
Fig. 15. Comparison of authors method with proportional controlling of PWM signal filling , filling depends on proportions between VZ and Vref voltages. Measurement conditions were as follows: Vref (reference voltage) 5V, Vz=14V, Ro=3.3Ω.
Fig. 15 shows comparison of converters output voltage waveform controlled by regulator functioning according to authors method with simplest proportional control of PWM1. One should notice not only the speed of changes of the output voltage in proposed method, but also lack of oscillations of output voltage, independently of converters load resistance (Fig. 13, Fig. 14, Fig. 15). Fig. 13. Buck converter start – using authors algorithm.
SUMMARY The goal of measurement was verification of new concept of digital control of DC/DC converters that uses law of conservation of energy. Test measurement results confirm earlier results of simulations presented in other authors papers [2-9]. Control device shows significant immunity for distortions generated by converter. Proposed solution is characterized by high dynamics and lack of oscillations of output voltage. Wide range of bias point changes had slight influence on output voltage value. Conducted test measurements confirmed in practice the rightness of concept.
THE AUTHORS
Fig. 14. Start of Buck converter controlled by authors algorithm. Reference voltage values are respectively: 2.5V, 5V and 10V.
Jacek Kaczmarek Faculty of Electronic Systems E-mail:
[email protected] Faculty of Electronic Systems Electronic Department Technical University of Koszalin. ul. Śniadeckich 11 Koszalin Poland Andrzej Mazurek E-mail:
[email protected] Faculty of Electronic Systems Electronic Department Technical University of Koszalin. ul. Śniadeckich 11 Koszalin Poland
1
Proportional controlling of PWM signal filling: filling depends on proportions between VZ and Vref voltages.
REFERENCES [1] Siew-Chong Tan, Y. M. Lai, Chi K. Tse, And Martin K. H. Cheung:An, “Adaptive Sliding Mode Controller For Buck Converter In Continuous Conduction Mode.”, 0-7803-8270-6/04/ (C) 2004 IEEE [2] J. Kaczmarek, A. Mazurek, “New Concept Of Dc/Dc Converters Digital Control Based On Law Of Onservation Of Energy – Project “Bumblebee””, Proceedings Of The 14 Th International Conference Mixed Design Of Intergrated Circuits And Systems - Mixdes 2007 Ciechocinek, Poland 21-31 June, 2007, Pages 586591 ISBN 83-922632-4-3 [3] J. Kaczmarek, A. Mazurek, ”Compensation Of Calculations Duration On Converters Output Voltage In Digitally Controled Converters Based On Law Of Conservation Of Energy - Project “Bumblebee”” – Proceedings Of The 14 Th International Conference Mixed Design Of Intergrated Circuits And Systems - Mixdes 2007 Ciechocinek, Poland 21-31 June, 2007, Pages 412 – 417 ISBN 83-922632-4-3 [4] J. Kaczmarek, A. Mazurek, “Comparison Of Classic Dc/Dc Converters With Converters Equipped With Analog-Digital Regulator Based On Law Of Conservation Of Energy (Bumblebee Type)”, Proceedings Of The 14 Th International Conference Mixed Design Of Intergrated Circuits And Systems - Mixdes 2007 Ciechocinek, Poland 21-31 June, 2007, Pages 564-569 ISBN 83-9226324-3 [5] J. Kaczmarek, A. Mazurek, “Nowa Idea Sterowania Przetwornicami Dc/Dc”, VI Krajowa Konferencja Elektroniki Darłowo, Czerwiec 2007, Pages 403408 [6] J. Kaczmarek, A. Mazurek, “Nowa Koncepcja Cyfrowego Sterowania Przetwornicami Dc/Dc.”, VI Krajowa Konferencja Elektroniki Darłowo, Czerwiec 2007, Pages 409-414 [7] J. Kaczmarek, A. Mazurek, “Wpływ Czasu Obliczeń Algorytmu w Nowej Metodzie Sterowania Napięciem Wyjściowym Przetwornicy Dc/Dc”, VI Krajowa Konferencja Elektroniki Darłowo, Czerwiec 2007, Pages 415-420 [8] J. Kaczmarek, A. Mazurek, “Porównanie Nowej Metody Sterowania Przetwornicami Dc/Dc Z Metodą Sterowania Wykorzystującą Kontrolę Prądu Cewki.”, VI Krajowa Konferencja Elektroniki Darłowo, Czerwiec 2007, Pages 421426 [9] J. Kaczmarek, A. Mazurek, “Nowa Idea Sterowania Przetwornicami Dc/Dc, Elektronika 11/2007”, Pages 114-117 ISSN 0033-2089 [10] J. Kaczmarek, A. Mazurek, “Porównanie Nowej Metody Sterowania Przetwornicami Dc/Dc z Metodą Sterowania Wykorzystującą Kontrolę Prądu Cewki”, Elektronika 11/2007 , Pages 84-86 ISSN 0033-208
