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Int. J. Intelligent Enterprise, Vol. 4, Nos. 1/2, 2017

Modelling and simulation DC-DC power converter buck for mobile applications using MATLAB/Simulink Kaoutar Bendaoud* and Salah-ddine Krit Laboratory of Engineering Sciences and Energy, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Agadir BP/638, Morocco Email: [email protected] Email: [email protected] *Corresponding author

Jalal Laassiri Laboratory of Mathematic informatics and Applications, Mohamed V University, Agdal Rabat BP/1014, Morocco Email: [email protected]

Lahoucine El Maimouni Laboratory of Engineering Sciences and Energy, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Agadir BP/638, Morocco Email: [email protected] Abstract: Switched mode DC-DC converters are some of the simplest power electronic circuits which convert one level of electrical voltage into another level by switching action. These converters have received an increasing deal of interest in many areas. This is due to their wide applications like power supplies for personal computers, office equipment, appliance control, telecommunication equipment, DC motor drives, automotive, aircraft, etc. The analysis, design, control and stabilisation of switching converters are the main factors that need to be considered (Verma et al., 2013). In brief, DC/DC converters are used to generate multiple DC levels for powering the circuits in a device, they are also used to reduce ripples, i.e., they carry out two main functions: modify the voltage level (step-up or step-down), regulate voltage. This paper first reviews the commonly used DC-DC converters in portable power device, namely, buck and boost converters, and then a model for a buck converter using MATLAB/Simulink is illustrated and simulated in both open loop mode and using a PID controller. Keywords: DC/DC converters; mobile applications; MATLAB/Simulink; buck and boost converters; PID controller.

Copyright © 2017 Inderscience Enterprises Ltd.

Modelling and simulation DC-DC power converter buck Reference to this paper should be made as follows: Bendaoud, K., Krit, S-d., Laassiri, J. and El Maimouni, L. (2017) ‘Modelling and simulation DC-DC power converter buck for mobile applications using MATLAB/Simulink’, Int. J. Intelligent Enterprise, Vol. 4, Nos. 1/2, pp.76–87. Biographical notes: Kaoutar Bendaoud graduated in Electronics and Automatics Engineering from the National School of Applied Science of Tangier, Morocco in 2015. She is currently a PhD candidate at the Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco. Her research interests include linear regulators, DC-DC power converters, and switching converters for mobile applications. Salah-ddine Krit received his BS and PhD in Microectronics Engineering from the Sidi Mohammed Ben Abdellah University, Fez, Morroco Institute in 2004 and 2009, respectively. During 2002 to 2008, he is also an Engineer Team Leader in audio and power management integrated circuits (ICs) research, design, simulation and layout of analogue and digital blocks dedicated for mobile phone and satellite communication systems using CMOS technology. He is currently a Professor of Informatics-Physics with Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Agadir, Morroco. His research interests include wireless sensor networks (software and hardware), computer engineering and wireless communications. Jalal Laassiri received his Bachelor’s in Mathematics and Informatics in 2001 and his Master’s (DESA) in Computer Sciences and Engineering from the Faculty of Sciences, University Mohammed V, Rabat, Morroco in 2005. He received his PhD in Computer Sciences and Engineering from the University of Mohammed V, Rabat, Morocco in June, 2010. He was a Visiting Scientific with the Imperial College London in London, UK. He is a member of the International Association of Engineers (IAENG). He joined the Faculty of Sciences of Kénitra, Department of Computer Science, Ibn Tofail University, Morocco, as a Professor in October 2010, His current research interests include software and systems engineering, UML-OCL, and B-method. Lahoucine El Maimouni received his PhD in Electronics in 2005 from the Institute of Electronics, Microelectronics and Nanotechnology (IEMN) University of Valenciennes, Valenciennes, France. In 2006, he joined the Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco. In 2011, he received his Habilitation à Diriger des Recherches (HDR) from the Faculty of Sciences, Ibn Zohr University, Agadir. At present, his research activities are focused on acoustic wave propagation in piezoelectric structures, BAW resonators, piezoelectric sensor, acoustic wave resonators and filters for RF-MEMS, and audiovisual techniques for image and sound. This paper is a revised and expanded version of a paper entitled ‘Design and simulation DC-DC power converters buck and boost for mobile applications using MATLAB/Simulink’ presented at International Conference on Engineering & MIS, Agadir, Morocco, 22–24 September 2016.

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Introduction

The emergence of integrated circuit around 1964 due to transistor’s miniaturisation facilitated a great revolution of electronics which allowed the emergence of various portable applications. Consequently, mobile equipment industry has known strong growth and mobiles integrate more and more functionalities in smaller volumes. In other words, battery-powered mobile equipment has become an important pillar of the electronic consumer market. However, all these mobile equipment have the same major weakness: their battery provides a limited operating time, which can only be increased in two ways. First, the energy density of the battery can be increased by developing new battery chemistries. Second, the battery energy can be used more efficiently by improving energy management. We will focus on the latter, and especially on voltage conversion, which is used in mobile equipment. A way used to optimise the battery run-time consists in inserting a DC-DC converter between the battery and supplied load. In recent years, these converters have received an increasing deal of interest in many areas of applications due to maintain the voltage supplied to the load constant from no load to full load with high conversion efficiency (Mude and Sahu, 2012). DC/DC converters are important in portable electronic devices such as cellular phones and laptop computers, which are supplied with power from batteries primarily. Such electronic devices often contain several sub circuits, each with its own voltage level requirement different from that supplied by the battery or an external supply (sometimes higher or lower than the supply voltage). DC-DC converters provide smooth acceleration control, high efficiency, and fast dynamic response (Rashid, 2004). Buck and boost converters are ones of the basic DC-DC converters. They have a broad applicable background because of the simple circuit structure and good control effort. In general, they have two basic mode of work operation, i.e., continuous inductor current mode (CCM) and discontinuous inductor current mode (DCM) (Tse, 1994). CCM is that the inductor current is always greater than zero without interruption of current in a switch period; however, DCM is that the inductor current is zero during the switch-off some time (Jiang et al., 2009). This paper presents a brief overview of the operation of DC-DC buck and boost converters, then presents modelling of buck converter using MATLAB/Simulink.

2

DC-DC voltage converters role

At present, mobiles are composed of several integrated circuits. Figure 1 illustrates their distribution. Namely, circuits used to transmit and receive data through the antenna, circuit manages digital parts like memories, microcontroller and processor, circuits incorporate analogue/digital circuits and battery management functions. Since the constraints are very different for each of these circuits, they are realised in a technology adapted to their functions. Every integrated circuit needs a constant supply voltage. However, the only way to store electrical energy in portable equipment is in DC energy reservoirs (e.g., batteries, accumulators and capacitors), which all suffer from the same drawback: their voltage decreases when they discharge (Rao et al., 2003). The voltage delivered must be regulated and adapted to voltage requested by integrated circuits in mobile devices (Panigrahi et al., 2001). This makes the integration of DC-DC converters for mobile

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systems essential. In brief, the role of DC-DC voltage regulators will be to generate several regulated voltages, stable and constant in time, from the single, variable and distorted voltage that delivers the rechargeable battery to power integrated circuits. I.e., DC-DC converter must provide a regulated dc output voltage even subjected to load and input voltage variation (Kumutha et al., 2015). Current needs are cost reduction and miniaturisation which manifest in the development of new integrated DC-DC voltage regulators structures purely CMOS. Figure 1

3

Integrated circuits of a mobile phone

DC-DC converters operating principle

3.1 Boost converter Boost converter is one of the simplest but most useful power converters. It is a step-up converter that converts an unregulated DC input voltage to a regulated dc output at a lower voltage. Figure 2 shows the basic circuit configuration used in the buck converter. As can be seen, it consists of a power MOSFET switch Q, flywheel diode D, inductor L, output capacitor C, and load resistance R. The inductor L acts as energy storage element that keeps the current flowing while the diode facilitates inductor current wheeling during the OFF time of the MOSFET. Filter made of capacitor (C) is normally added to the output of the converter to reduce output voltage ripple (Erickson and Maksimovic, 2004). Usually, P-channel MOSFET (PMOS) is preferred to be used as switch instead of NMOS, because if the NMOS is employed as a MOSFET switch since both the gate and the source are connected to the voltage supply then it would be hard to drive it (Kazimierczuk, 2008). In order to improve power efficiency, the diode is usually replaced by an n-channel MOSFET (NMOS) because voltage drop in conducted MOSFET is very low comparison to conducted diode. In this case, it is referred to a synchronous boost converter. The operation of a buck converter can be divided into two times according to the state of MOSFET switch. During ON state, the current through the inductance increases linearly. The voltage across the diode is negative, no current passes through it. The off-state begins when MOSFET switch Q is blocked. The diode becomes conductive.

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It ensures continuity of the current in the inductor. The current through the inductor decreases. As mentioned previously, it can operate in continuous conduction mode (CCM) or in discontinuous conduction mode (DCM), depending on the waveform of inductor current (Kazimierczuk, 2008). Figure 2

Boost converter (see online version for colours)

Figure 3

Waveforms of current and voltage in CCM (see online version for colours)

3.2 CCM vs. DCM If the value of the inductance is reduced to the critical point, the valley current will decay and finally become zero at the end of the duty cycle. A further decrease in L will cause the current to fall to zero even before the completion of the OFF period of the converter. The current builds up from an initial zero value during TON in the next converter cycle.

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This operation of the converter is called discontinuous load current mode. If the current is non-zero for all the chopper period, the converter is said to be operating in continuous load current mode. This is achieved by appropriate selection of converter switching frequency or inductance value, or both (Mahesh Gowda et al., 2014). Figure 3 shows waveforms of current and voltage in CCM for a boost converter while Figure 4 presents them in DCM. Figure 4

Waveforms of current and voltage in DCM (see online version for colours)

3.3 Buck converter Buck converter is a step down converter which converts unregulated DC input voltage to a regulated DC output voltage. Figure 5 shows the basic configuration of a buck converter. The buck converter is operated by turning the MOSFET ON and OFF at a high switching frequency. During the ON state, the MOSFET is turned ON for a time interval TON and the diode is OFF, then IL begins to grown exponentially across inductance L. The OFF state TOFF begins when MOSFET is turned off and IL is at its peak value Ipk. The decay of IL causes an induced voltage L didtL to appear across the inductance, then the diode becomes forward-biased and causes the current flow to continue and decay exponentially. The output voltage is given by: Vout = DVin

(1)

where the duty cycle D is given by: D=

TON TON + TOFF

(2)

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Figure 5

Buck converter with feed back controller (see online version for colours)

Figure 6

Block diagram of a PID controller

3.4 PID controller Proportional-integral-derivative (PID) controller (Figure 6) has been used for several decades in industries for process control applications. PID involves three separate parameter, the proportional, the integral and derivatives. By tuning the three constants in PID controller algorithm, the controller can provide control action designed for specific process requirement. First, the PID controller works in a closed-loop system. The variable (e) represents the tracking error, the difference between the desired input value (R) and the actual output. This error signal (e) will be sent to the PID controller, and the controller computes both the derivative and the integral of this error signal. The signal (u) just past the controller is now equal to the proportional gain (Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the error plus the derivative gain (Kd) times the derivative of the error where, this signal (u) will be sent to the plant, and the new output will be obtained. This new output will be sent back to the sensor again to find the new error signal (e). The controller takes this new error signal and computes its

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derivative and its integral again. This process goes on and on, this signal (u) is obtained as follows (Rathi and Ali, 2016):

∫

u (t ) = K p e(t ) + K i e(t )dt + K d Figure 7

4

de(t ) dt

(3)

Model diagram of buck converter using Simulink

Modelling of DC-DC buck converter using Simulink

Differential equations of inductor current iL and capacitor voltage out v as a variable respectively are established according to KVL and KCL theory (Erickson and Maksimovic, 2004). The inductor is given by: diL + RL iL + Vout dt

(4)

1 (Vin D − RL iL − Vout ) dt L

(5)

Vin D = L

Then

∫

iL =

Applying KCL at the capacitor node we get: C=

dVC = iL − iout dt

(6)

Then VC =

1 ( iL − iout ) dt C

∫

(7)

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And Vout = VC + RL ( iL − iout )

(8)

where RC is the effective series resistance of the capacitor. The Simulink model for buck converter based on the above equation is shown in Figure 7 (Sigalo and Osikibo, 2016).

4.1 Modelling of PWM waveforms generator using Simulink Power width modulation (PWM) signal is the most typical control signal applied on a switch in switching DC converters. It is usually a signal with fixed frequency. Simulink model of PWM generator is illustrated in Figure 8. Figure 8

Model diagram PWM generator using Simulink

Figure 9

Buck converter subsystem

As shown in Figure 9, inputs are represented by the duty cycle and a repeating sequence which provides a saw-tooth waveforms of time values (0 1/fs). The magnitude of this repeating sequence is subtracted from the duty cycle to yield a mirrored version of the saw tooth waveform whose amplitude ranges from D to D – 1. The resulted waveform possesses a positive value whenever the required PWM signal is high and a negative value where the PWM pulse is low. This fact is exploited to generate the PWM pulses by using a Relay block that is configured to switch on (Output = 1) and off (Output = 0) during the zero crossings (Mahesh Gowda et al., 2014).

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4.2 Subsystems Each of the power electronic models represents subsystems within the simulation environment. These blocks have been developed so they can be interconnected in a consistent and simple manner for the construction of complex systems. The subsystems are masked, meaning that the user interface displays only the complete subsystem, and user prompts gather parameters for the entire subsystem. Relevant parameters can be set by double-clicking a mouse or pointer on each subsystem block, then entering the appropriate values in the resulting dialogue window (Sigalo and Osikibo, 2016). Figure 9 shows the subsystem for a buck converter.

5

Simulation

Converters are designed and simulated using MATLAB/Simulink environment. Simulation has been carried out for various changes in load value and input values. Figure 10 and Figure 11 show respectively results on output voltage and output current for open loop DC/DC buck converter. Figure 10 Results on output voltage for open loop buck converter (see online version for colours)

Figure 11 Results on output current for open loop buck converter (see online version for colours)

Simulation shows that in open loop mode, converter system is sensitive to parameter variations and external load disturbances, the output current and voltage tracking contains overshoot and system has long settling time. In closed-loop mode, the default PID controller offered by Simulink is used. The simulation results of output voltage and current for buck converter with PID controller are shown in Figure 12 and Figure 13.

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Figure 12 Output voltage for buck converter using PID controller (see online version for colours)

Figure 13 Output current for buck converter using PID controller (see online version for colours)

Results show that using PID controller offer better output tracking ability, thus improving output voltage and current regulation. The system is insensitive to parameter variations and external load disturbances; PID controller gives stable operation to DC-DC converters.

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Conclusions

In this paper, we illustrated the role of DC/DC converters in mobile applications, we provided a brief overview of the operation of both buck and boost converters and proceeded t model buck converter using only Simulink blocks. The designed buck converter operates effectively when PID controller is used. The controller realises a better output tracking with minimal overshoot, and improves converter efficiency.

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References Erickson, R.W. and Maksimovic, D. (2004) Fundamentals of Power Electronics, 2nd ed., Kluwer Academic Publishers. Jiang, W., Zhou, Y-f. and Chen, J-n. (2009) ‘Modeling and simulation of boost converter in CCM and DCM’, 2nd International Conference on Power Electronics and Intelligent Transportation System. Kazimierczuk, M.K. (2008) Pulse-width Modulated DC-DC Power Converters, Wiley. Kumutha, M.A.S., Vasugi, M. and Dharmaprakash, R. (2015) ‘Voltage ripple reduction of buck converter using sliding mode control technique’, Middle-East Journal of Scientific Research (Sensing, Signal Processing and Security), Vol. 23, No. 23, pp.83–88. Mahesh Gowda, N.M., Kiran, Y. and Parthasarthy, S.S. (2014) ‘Modelling of buck DC-DC converter using Simulink’, International Journal of Innovative Research in Science, Engineering and Technology, July, Vol. 3, No. 7, pp.14965–14975. Mude, N.R. and Sahu, A. (2012) ‘Adaptive control schemes for DC-DC buck converter’, International Journal of Engineering Research and Applications, Vol. 2, No. 3, pp.463–467. Panigrahi, D., Chiasserini, C., Dey, S., Rao, R., Raghunathan, A. and Lahiri, K. (2001) ‘Battery life estimation of mobile embedded systems’, in 14th International Conference on VLSI Design, 3–7 January, pp.57–63. Rao, R., Vrudhula, S. and Rakhmatov, D. (2003) ‘Battery modeling for energy-aware system design’, Computer, December, Vol. 36, No. 12, pp.77–87, IEEE Computer Society. Rashid, M.H. (2004) Power Electronics – Circuits, Devices, and Applications, Pearson, Prentice Hall, London. Rathi, K. and Ali, M.S. (2016) ‘Design and simulation of PID controller for power electronics converter circuits’, International Journal of Innovative and Emerging Research in Engineering, Vol. 3, No. 2, pp.26–31. Sigalo, M. and Osikibo, L. (2016) ‘Design and simulation of DC-DC voltage converters using MATLAB/Simulink’, American Journal of Engineering Research, February, Vol. 5, No. 2, pp.229–236. Tse, C.K. (1994) ‘Flip Bifurcation and chaos in three-state boost switching regulators’, IEEE Transactions on Circuits and Systems, Vol. 41, No. 1, pp.16–23. Verma, S., Singh, S.K. and Rao, A.G. (2013) ‘Overview of control techniques for DC-DC converters’, Research Journal of Engineering Sciences, August, Vol. 2, No. 8, pp.18–21.

Int. J. Intelligent Enterprise, Vol. 4, Nos. 1/2, 2017

Modelling and simulation DC-DC power converter buck for mobile applications using MATLAB/Simulink Kaoutar Bendaoud* and Salah-ddine Krit Laboratory of Engineering Sciences and Energy, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Agadir BP/638, Morocco Email: [email protected] Email: [email protected] *Corresponding author

Jalal Laassiri Laboratory of Mathematic informatics and Applications, Mohamed V University, Agdal Rabat BP/1014, Morocco Email: [email protected]

Lahoucine El Maimouni Laboratory of Engineering Sciences and Energy, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Agadir BP/638, Morocco Email: [email protected] Abstract: Switched mode DC-DC converters are some of the simplest power electronic circuits which convert one level of electrical voltage into another level by switching action. These converters have received an increasing deal of interest in many areas. This is due to their wide applications like power supplies for personal computers, office equipment, appliance control, telecommunication equipment, DC motor drives, automotive, aircraft, etc. The analysis, design, control and stabilisation of switching converters are the main factors that need to be considered (Verma et al., 2013). In brief, DC/DC converters are used to generate multiple DC levels for powering the circuits in a device, they are also used to reduce ripples, i.e., they carry out two main functions: modify the voltage level (step-up or step-down), regulate voltage. This paper first reviews the commonly used DC-DC converters in portable power device, namely, buck and boost converters, and then a model for a buck converter using MATLAB/Simulink is illustrated and simulated in both open loop mode and using a PID controller. Keywords: DC/DC converters; mobile applications; MATLAB/Simulink; buck and boost converters; PID controller.

Copyright © 2017 Inderscience Enterprises Ltd.

Modelling and simulation DC-DC power converter buck Reference to this paper should be made as follows: Bendaoud, K., Krit, S-d., Laassiri, J. and El Maimouni, L. (2017) ‘Modelling and simulation DC-DC power converter buck for mobile applications using MATLAB/Simulink’, Int. J. Intelligent Enterprise, Vol. 4, Nos. 1/2, pp.76–87. Biographical notes: Kaoutar Bendaoud graduated in Electronics and Automatics Engineering from the National School of Applied Science of Tangier, Morocco in 2015. She is currently a PhD candidate at the Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco. Her research interests include linear regulators, DC-DC power converters, and switching converters for mobile applications. Salah-ddine Krit received his BS and PhD in Microectronics Engineering from the Sidi Mohammed Ben Abdellah University, Fez, Morroco Institute in 2004 and 2009, respectively. During 2002 to 2008, he is also an Engineer Team Leader in audio and power management integrated circuits (ICs) research, design, simulation and layout of analogue and digital blocks dedicated for mobile phone and satellite communication systems using CMOS technology. He is currently a Professor of Informatics-Physics with Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Agadir, Morroco. His research interests include wireless sensor networks (software and hardware), computer engineering and wireless communications. Jalal Laassiri received his Bachelor’s in Mathematics and Informatics in 2001 and his Master’s (DESA) in Computer Sciences and Engineering from the Faculty of Sciences, University Mohammed V, Rabat, Morroco in 2005. He received his PhD in Computer Sciences and Engineering from the University of Mohammed V, Rabat, Morocco in June, 2010. He was a Visiting Scientific with the Imperial College London in London, UK. He is a member of the International Association of Engineers (IAENG). He joined the Faculty of Sciences of Kénitra, Department of Computer Science, Ibn Tofail University, Morocco, as a Professor in October 2010, His current research interests include software and systems engineering, UML-OCL, and B-method. Lahoucine El Maimouni received his PhD in Electronics in 2005 from the Institute of Electronics, Microelectronics and Nanotechnology (IEMN) University of Valenciennes, Valenciennes, France. In 2006, he joined the Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco. In 2011, he received his Habilitation à Diriger des Recherches (HDR) from the Faculty of Sciences, Ibn Zohr University, Agadir. At present, his research activities are focused on acoustic wave propagation in piezoelectric structures, BAW resonators, piezoelectric sensor, acoustic wave resonators and filters for RF-MEMS, and audiovisual techniques for image and sound. This paper is a revised and expanded version of a paper entitled ‘Design and simulation DC-DC power converters buck and boost for mobile applications using MATLAB/Simulink’ presented at International Conference on Engineering & MIS, Agadir, Morocco, 22–24 September 2016.

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Introduction

The emergence of integrated circuit around 1964 due to transistor’s miniaturisation facilitated a great revolution of electronics which allowed the emergence of various portable applications. Consequently, mobile equipment industry has known strong growth and mobiles integrate more and more functionalities in smaller volumes. In other words, battery-powered mobile equipment has become an important pillar of the electronic consumer market. However, all these mobile equipment have the same major weakness: their battery provides a limited operating time, which can only be increased in two ways. First, the energy density of the battery can be increased by developing new battery chemistries. Second, the battery energy can be used more efficiently by improving energy management. We will focus on the latter, and especially on voltage conversion, which is used in mobile equipment. A way used to optimise the battery run-time consists in inserting a DC-DC converter between the battery and supplied load. In recent years, these converters have received an increasing deal of interest in many areas of applications due to maintain the voltage supplied to the load constant from no load to full load with high conversion efficiency (Mude and Sahu, 2012). DC/DC converters are important in portable electronic devices such as cellular phones and laptop computers, which are supplied with power from batteries primarily. Such electronic devices often contain several sub circuits, each with its own voltage level requirement different from that supplied by the battery or an external supply (sometimes higher or lower than the supply voltage). DC-DC converters provide smooth acceleration control, high efficiency, and fast dynamic response (Rashid, 2004). Buck and boost converters are ones of the basic DC-DC converters. They have a broad applicable background because of the simple circuit structure and good control effort. In general, they have two basic mode of work operation, i.e., continuous inductor current mode (CCM) and discontinuous inductor current mode (DCM) (Tse, 1994). CCM is that the inductor current is always greater than zero without interruption of current in a switch period; however, DCM is that the inductor current is zero during the switch-off some time (Jiang et al., 2009). This paper presents a brief overview of the operation of DC-DC buck and boost converters, then presents modelling of buck converter using MATLAB/Simulink.

2

DC-DC voltage converters role

At present, mobiles are composed of several integrated circuits. Figure 1 illustrates their distribution. Namely, circuits used to transmit and receive data through the antenna, circuit manages digital parts like memories, microcontroller and processor, circuits incorporate analogue/digital circuits and battery management functions. Since the constraints are very different for each of these circuits, they are realised in a technology adapted to their functions. Every integrated circuit needs a constant supply voltage. However, the only way to store electrical energy in portable equipment is in DC energy reservoirs (e.g., batteries, accumulators and capacitors), which all suffer from the same drawback: their voltage decreases when they discharge (Rao et al., 2003). The voltage delivered must be regulated and adapted to voltage requested by integrated circuits in mobile devices (Panigrahi et al., 2001). This makes the integration of DC-DC converters for mobile

Modelling and simulation DC-DC power converter buck

79

systems essential. In brief, the role of DC-DC voltage regulators will be to generate several regulated voltages, stable and constant in time, from the single, variable and distorted voltage that delivers the rechargeable battery to power integrated circuits. I.e., DC-DC converter must provide a regulated dc output voltage even subjected to load and input voltage variation (Kumutha et al., 2015). Current needs are cost reduction and miniaturisation which manifest in the development of new integrated DC-DC voltage regulators structures purely CMOS. Figure 1

3

Integrated circuits of a mobile phone

DC-DC converters operating principle

3.1 Boost converter Boost converter is one of the simplest but most useful power converters. It is a step-up converter that converts an unregulated DC input voltage to a regulated dc output at a lower voltage. Figure 2 shows the basic circuit configuration used in the buck converter. As can be seen, it consists of a power MOSFET switch Q, flywheel diode D, inductor L, output capacitor C, and load resistance R. The inductor L acts as energy storage element that keeps the current flowing while the diode facilitates inductor current wheeling during the OFF time of the MOSFET. Filter made of capacitor (C) is normally added to the output of the converter to reduce output voltage ripple (Erickson and Maksimovic, 2004). Usually, P-channel MOSFET (PMOS) is preferred to be used as switch instead of NMOS, because if the NMOS is employed as a MOSFET switch since both the gate and the source are connected to the voltage supply then it would be hard to drive it (Kazimierczuk, 2008). In order to improve power efficiency, the diode is usually replaced by an n-channel MOSFET (NMOS) because voltage drop in conducted MOSFET is very low comparison to conducted diode. In this case, it is referred to a synchronous boost converter. The operation of a buck converter can be divided into two times according to the state of MOSFET switch. During ON state, the current through the inductance increases linearly. The voltage across the diode is negative, no current passes through it. The off-state begins when MOSFET switch Q is blocked. The diode becomes conductive.

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It ensures continuity of the current in the inductor. The current through the inductor decreases. As mentioned previously, it can operate in continuous conduction mode (CCM) or in discontinuous conduction mode (DCM), depending on the waveform of inductor current (Kazimierczuk, 2008). Figure 2

Boost converter (see online version for colours)

Figure 3

Waveforms of current and voltage in CCM (see online version for colours)

3.2 CCM vs. DCM If the value of the inductance is reduced to the critical point, the valley current will decay and finally become zero at the end of the duty cycle. A further decrease in L will cause the current to fall to zero even before the completion of the OFF period of the converter. The current builds up from an initial zero value during TON in the next converter cycle.

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This operation of the converter is called discontinuous load current mode. If the current is non-zero for all the chopper period, the converter is said to be operating in continuous load current mode. This is achieved by appropriate selection of converter switching frequency or inductance value, or both (Mahesh Gowda et al., 2014). Figure 3 shows waveforms of current and voltage in CCM for a boost converter while Figure 4 presents them in DCM. Figure 4

Waveforms of current and voltage in DCM (see online version for colours)

3.3 Buck converter Buck converter is a step down converter which converts unregulated DC input voltage to a regulated DC output voltage. Figure 5 shows the basic configuration of a buck converter. The buck converter is operated by turning the MOSFET ON and OFF at a high switching frequency. During the ON state, the MOSFET is turned ON for a time interval TON and the diode is OFF, then IL begins to grown exponentially across inductance L. The OFF state TOFF begins when MOSFET is turned off and IL is at its peak value Ipk. The decay of IL causes an induced voltage L didtL to appear across the inductance, then the diode becomes forward-biased and causes the current flow to continue and decay exponentially. The output voltage is given by: Vout = DVin

(1)

where the duty cycle D is given by: D=

TON TON + TOFF

(2)

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Figure 5

Buck converter with feed back controller (see online version for colours)

Figure 6

Block diagram of a PID controller

3.4 PID controller Proportional-integral-derivative (PID) controller (Figure 6) has been used for several decades in industries for process control applications. PID involves three separate parameter, the proportional, the integral and derivatives. By tuning the three constants in PID controller algorithm, the controller can provide control action designed for specific process requirement. First, the PID controller works in a closed-loop system. The variable (e) represents the tracking error, the difference between the desired input value (R) and the actual output. This error signal (e) will be sent to the PID controller, and the controller computes both the derivative and the integral of this error signal. The signal (u) just past the controller is now equal to the proportional gain (Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the error plus the derivative gain (Kd) times the derivative of the error where, this signal (u) will be sent to the plant, and the new output will be obtained. This new output will be sent back to the sensor again to find the new error signal (e). The controller takes this new error signal and computes its

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derivative and its integral again. This process goes on and on, this signal (u) is obtained as follows (Rathi and Ali, 2016):

∫

u (t ) = K p e(t ) + K i e(t )dt + K d Figure 7

4

de(t ) dt

(3)

Model diagram of buck converter using Simulink

Modelling of DC-DC buck converter using Simulink

Differential equations of inductor current iL and capacitor voltage out v as a variable respectively are established according to KVL and KCL theory (Erickson and Maksimovic, 2004). The inductor is given by: diL + RL iL + Vout dt

(4)

1 (Vin D − RL iL − Vout ) dt L

(5)

Vin D = L

Then

∫

iL =

Applying KCL at the capacitor node we get: C=

dVC = iL − iout dt

(6)

Then VC =

1 ( iL − iout ) dt C

∫

(7)

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And Vout = VC + RL ( iL − iout )

(8)

where RC is the effective series resistance of the capacitor. The Simulink model for buck converter based on the above equation is shown in Figure 7 (Sigalo and Osikibo, 2016).

4.1 Modelling of PWM waveforms generator using Simulink Power width modulation (PWM) signal is the most typical control signal applied on a switch in switching DC converters. It is usually a signal with fixed frequency. Simulink model of PWM generator is illustrated in Figure 8. Figure 8

Model diagram PWM generator using Simulink

Figure 9

Buck converter subsystem

As shown in Figure 9, inputs are represented by the duty cycle and a repeating sequence which provides a saw-tooth waveforms of time values (0 1/fs). The magnitude of this repeating sequence is subtracted from the duty cycle to yield a mirrored version of the saw tooth waveform whose amplitude ranges from D to D – 1. The resulted waveform possesses a positive value whenever the required PWM signal is high and a negative value where the PWM pulse is low. This fact is exploited to generate the PWM pulses by using a Relay block that is configured to switch on (Output = 1) and off (Output = 0) during the zero crossings (Mahesh Gowda et al., 2014).

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4.2 Subsystems Each of the power electronic models represents subsystems within the simulation environment. These blocks have been developed so they can be interconnected in a consistent and simple manner for the construction of complex systems. The subsystems are masked, meaning that the user interface displays only the complete subsystem, and user prompts gather parameters for the entire subsystem. Relevant parameters can be set by double-clicking a mouse or pointer on each subsystem block, then entering the appropriate values in the resulting dialogue window (Sigalo and Osikibo, 2016). Figure 9 shows the subsystem for a buck converter.

5

Simulation

Converters are designed and simulated using MATLAB/Simulink environment. Simulation has been carried out for various changes in load value and input values. Figure 10 and Figure 11 show respectively results on output voltage and output current for open loop DC/DC buck converter. Figure 10 Results on output voltage for open loop buck converter (see online version for colours)

Figure 11 Results on output current for open loop buck converter (see online version for colours)

Simulation shows that in open loop mode, converter system is sensitive to parameter variations and external load disturbances, the output current and voltage tracking contains overshoot and system has long settling time. In closed-loop mode, the default PID controller offered by Simulink is used. The simulation results of output voltage and current for buck converter with PID controller are shown in Figure 12 and Figure 13.

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Figure 12 Output voltage for buck converter using PID controller (see online version for colours)

Figure 13 Output current for buck converter using PID controller (see online version for colours)

Results show that using PID controller offer better output tracking ability, thus improving output voltage and current regulation. The system is insensitive to parameter variations and external load disturbances; PID controller gives stable operation to DC-DC converters.

6

Conclusions

In this paper, we illustrated the role of DC/DC converters in mobile applications, we provided a brief overview of the operation of both buck and boost converters and proceeded t model buck converter using only Simulink blocks. The designed buck converter operates effectively when PID controller is used. The controller realises a better output tracking with minimal overshoot, and improves converter efficiency.

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References Erickson, R.W. and Maksimovic, D. (2004) Fundamentals of Power Electronics, 2nd ed., Kluwer Academic Publishers. Jiang, W., Zhou, Y-f. and Chen, J-n. (2009) ‘Modeling and simulation of boost converter in CCM and DCM’, 2nd International Conference on Power Electronics and Intelligent Transportation System. Kazimierczuk, M.K. (2008) Pulse-width Modulated DC-DC Power Converters, Wiley. Kumutha, M.A.S., Vasugi, M. and Dharmaprakash, R. (2015) ‘Voltage ripple reduction of buck converter using sliding mode control technique’, Middle-East Journal of Scientific Research (Sensing, Signal Processing and Security), Vol. 23, No. 23, pp.83–88. Mahesh Gowda, N.M., Kiran, Y. and Parthasarthy, S.S. (2014) ‘Modelling of buck DC-DC converter using Simulink’, International Journal of Innovative Research in Science, Engineering and Technology, July, Vol. 3, No. 7, pp.14965–14975. Mude, N.R. and Sahu, A. (2012) ‘Adaptive control schemes for DC-DC buck converter’, International Journal of Engineering Research and Applications, Vol. 2, No. 3, pp.463–467. Panigrahi, D., Chiasserini, C., Dey, S., Rao, R., Raghunathan, A. and Lahiri, K. (2001) ‘Battery life estimation of mobile embedded systems’, in 14th International Conference on VLSI Design, 3–7 January, pp.57–63. Rao, R., Vrudhula, S. and Rakhmatov, D. (2003) ‘Battery modeling for energy-aware system design’, Computer, December, Vol. 36, No. 12, pp.77–87, IEEE Computer Society. Rashid, M.H. (2004) Power Electronics – Circuits, Devices, and Applications, Pearson, Prentice Hall, London. Rathi, K. and Ali, M.S. (2016) ‘Design and simulation of PID controller for power electronics converter circuits’, International Journal of Innovative and Emerging Research in Engineering, Vol. 3, No. 2, pp.26–31. Sigalo, M. and Osikibo, L. (2016) ‘Design and simulation of DC-DC voltage converters using MATLAB/Simulink’, American Journal of Engineering Research, February, Vol. 5, No. 2, pp.229–236. Tse, C.K. (1994) ‘Flip Bifurcation and chaos in three-state boost switching regulators’, IEEE Transactions on Circuits and Systems, Vol. 41, No. 1, pp.16–23. Verma, S., Singh, S.K. and Rao, A.G. (2013) ‘Overview of control techniques for DC-DC converters’, Research Journal of Engineering Sciences, August, Vol. 2, No. 8, pp.18–21.