Buck Boost Converter Matlab Simulink

International Journal of Engineering and Advanced Technology (IJEAT)

And Sciences Publication

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Abstract: This article presents the converter circuit analysis, mathematical modeling followed by deriving its average state space equations. The model so obtained is simulated in MATLAB in open loop and closed loop configuration and changes in the output are observed. Specifically, Buck & Boost converters with & without its controller at steady state and study of their transient responses to the changing inputs with a controller design and its implementation on SIMULINK model is presented here. The method used to control the output of the converter is Proportional and Integral error correction that is a PI controller which is used to reduce errors and stabilize the variable input fed to the Buck or Boost converters. The tool used to design the controller parameters is PID Tuner application in in MATLAB. The analyses plots derived using the tool lets us examine the controller performance in time and frequency domain. The advantage of the tool used is, it allows user to interactively refine the performance of the controller to adjust loop bandwidth and phase margin or to favor a set-point tracking or disturbance rejection. The designed converters are analyzed in current mode control and voltage mode control to switch on/off. The long term goal is to have a sophisticated controller design for buck & boost converters for the application where variable input is fed to them, so as to allow its simulation to fully understand how the converters behave when controller is implemented. The model tested here are of the similar nature that are being used in standalone solar or wind energy generation & distribution systems. The variable nature of the input tested here with Buck & Boost converters reflects the variable nature of the output of the renewable energy sources and that broaden the scope of these converters to be implanted with such standalone energy systems.

Keywords: Boost Converter, Buck converter, Current Control

I. Introduction

The voltage-mode controlled regulator, the PWM signal is generated by applying a control voltage to one comparator input and a saw-tooth voltage of fixed frequency, generated by the clock, to the other. The duty cycle of the PWM signal is proportional to the control voltage and determines the percentage of the time that the switching element conducts.

The control voltage is derived from the difference between the actual-output voltage and the desired-output voltage. Manuscript received on April 21, 2021.

Revised Manuscript received on April 29, 2021. Manuscript published on April 30, 2021.

* Correspondence Author

© The Authors. Published by Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) The more efficient control scheme that finds a wide application is current mode control. In this type of control the Inductor current is used as a feedback state. The current-mode control technique derives the PWM ramp by adding a second loop feeding back the inductor current. This feedback signal comprises two parts: the AC-ripple current, and the DC or average value of the inductor current. An amplified form of the signal is routed to one input of the PWM comparator while the error voltage forms the other input. It will generate PWM pulses, which will act as a controlling signal to the power electronic devices. The advantage is the ease to control and integrate. The voltage transformation in dc-dc converter is achieved by using the technique of PWM (pulse width modulation). The power needed for pulse train is very small and can be neglected.

There are different combinations of switching devices using different energy storing elements used as switching regulators.

The

unregulated dc input to an accurate and desired dc output voltage. Based on the control and regulation of the voltage/current at the output terminals from an input source, the switching regulators can be divided as: Isolated & Non-isolated converters. The transfer of the energy from the input to the output side is done using electromagnetic field. This can be achieved using a mutually coupled magnetic component thereby isolating the input and the output. So this type of DC-DC converter cannot be used where it is desired to have the ground terminal of input and output at different potentials (for example, in case of gate drive circuit of an inverter's devices). Also, if the transformation ratio between

The Input & Output Voltage Is Too Large/Low, The

on-time/off-time of the device becomes comparable to the device turn-on/turn-off time. Therefore, in such cases, isolated type DC-DC converters are more advantageous.

There is no isolation in between the input and the output, i.e. the current flows through a common path during the operation from the source to the load. The selection of converters from a variety of switching system available in the market is based on certain parameters (cost, performance, characteristics) which are determined by the user and the system application.

This paper will limit its consideration to the first two types of non-isolated converters (Buck & Boost). This paper

Farha Naz

Closed loop Buck & Boost Converter Mathematical Modeling, Analysis and Simulation using MATLAB

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mathematical modeling followed by deriving its average state space equations. The model so obtained is simulated in MATLAB in open loop and closed loop configuration and changes in the output is observed. PI controller is used here to reduce the errors. These DC-to-DC power converters steps up/down the voltage (while stepping down/up the current) from its input (supply) to its output (load). The DC input to a buck or boost converter can be from many sources as well as batteries, such as rectified AC from the supply mains, or DC from solar panels, fuel cells, dynamos and DC generators.

A. Buck Or Step-Down Converter

In the step-down or buck converter, average dc output voltage Vo is less than the input unregulated dc voltage Vs. Thus, it is a voltage step-down and current step-up converter.

A simplified circuit diagram is shown in figure below.

Fig.1 Buck Converter

The transfer function for the buck converter is derived by equating the voltage-time product of the inductance in the ON and OFF conditions. The products so obtained for ON and OFF conditions must be the same because of the energy conservation principle.

Energy equations during ON condition: EIN = (VIN –VOUT) tON Energy equations during OFF condition: EOUT = VOUT tOFF

A) Voltage Control Mode

The controller manipulates the error term depending on the type of controller that is being used. The output of the controller is the new value of the duty cycle which is used as an input to the power stage and modulates the switching devices so as to close the control loop and provide a regulated and stable output voltage.

B) Current Control Mode

In this type of control the peak of the output filter inductor current is controlled to a set point value. This set point value is determined by the output of the controller and varies on a cycle-by-cycle basis.

Initially, the switching device is turned on with no pre-determined duty cycle given by the clock pulse which sets the S-R latch. The sensed inductor current is then compared with the desired current by means of a current comparator.

When the sensed inductor current intersects with the desired current, the current sense comparator resets the S-R latch, which turns off the switching device.

Therefore, the duty cycle is not set by the controller and is determined by the rise of the inductor current during the on-time. The modulation of the duty cycle differs significantly from that of voltage mode control, and as such, the design of the compensator differs also.

Fig.3 Buck Converter Current Control Loop

The DC gain for the current mode buck converter is: The power stage output filter consists of an inductor and a capacitor that normally forms a double pole due to resonance formed between the inductor and capacitor. In current mode control, the inductor’s current is controlled on a cycle-by-cycle basis, and therefore the inductor acts as a constant current source.

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This implies that the plant power stage no longer contains the double pole present when operating under voltage mode control and the plant power stage now only contains a single plant pole. This control method results in a single plant pole at lower frequencies. This removes the crossover frequency restriction around the double pole found in voltage-mode controlled converters and therefore allows for easier stabilizing of converters with a right-half plane zero.

B. Boost Or Step-Up Converter

In the step-up or boost converter, average dc output voltage Vo is more than the input unregulated dc voltage Vs. Thus, it is a voltage step-up and current step-down converter. A simplified circuit diagram is shown in figure below.

Fig.4 Boost Converter

The transfer function for the boost converter is derived by equating the voltage-time product of the inductance in the ON and OFF conditions. The products so obtained for ON and OFF conditions must be the same because of the energy conservation principle.

Energy equations during ON condition: EIN = VIN tON Energy equations during OFF condition: EOUT = (VOUT-VIN)tOFF

A) Voltage Control Mode

Voltage-mode control which is also called as the duty-cycle control contains a single loop and adjusts the duty cycle directly in response to changes in output voltage.

Fig.5 Boost Converter Voltage Control Mode

The equation for the control-to-output transfer function is: The boost converter adds a new complexity to the control problem which is caused by the fact that when the boost converter switch is turned on for a longer period of time, the inductor is disconnected from the load for a longer period of time which makes the output initially drop, even though the control command is trying to make it increase.

B) Current Control Mode

Current-mode control which is also called as current

Programmed Mode Or Current-Injected Control Is A

multiple-loop control method that contains two loops (an inner current loop and an outer voltage loop). There are several types of current mode control methods, and the most popular method is fixed-frequency peak-current-mode control with fixed-slope compensation ramp. The technique is called current-mode control because the inductor current is directly controlled, whereas the output voltage is controlled indirectly by the current loop. A control reference is used to regulate the peak current of the converter directly. Figure shows the schematic of the boost converter with current-mode

C. Inductor And Capacitor Behavior

The basic concept of operation is that every time the switch is closed, current builds up in the inductor. When the switch is opened, the current can't stop instantly and so it's forced to flow into the capacitor until the current dissipates. If the switch is closed again, the diode ensures that the capacitor won't discharge back through the switch. This process of opening and closing the switch can be repeated many times with each cycle adding more charge onto the capacitor until a limiting value of voltage is attained.

A) Inductor Property

Inductor stores energy in the form of magnetic field, and electric current is responsible for it. Therefore electric current flowing through the inductor cannot change suddenly. An applied voltage will cause current through the inductor to build up over time at a rate inversely proportional to its inductance (L1). That process is governed by the equation:

A Matlab Code Was Developed Which Simulates The

behaviour and makes the plot with the title "Initialization Period" which is given in figure. It can be seen that with the components chosen, the whole initialization process is in less than 1/100th of a second, so one may not be able to observe it easily without a storage scope. To reach 99% of the steady state current took just about 5 milliseconds.

We Can Find The Recommended Inductor Values In A

datasheet. An inductor is chosen from this range. The higher the value of L, the higher is the maximum output current because of the reduced ripple current. In general, the lower the inductor value, the smaller is the solution size. The inductor must always have a higher current rating than the maximum current because as the current increases the inductance decreases. If no inductor range is provided, the following equation is a good estimation for the right inductor: A good estimation for the inductor ripple current is 20% to 40% of the output current.

B) Capacitor Property

Capacitor stores energy in the form of electric field, and voltage across it, is responsible for the stored energy. Therefore voltage across capacitor cannot change suddenly.

Now let's say that after letting the system initialize with the switch closed (ON), the switch is now opened (OFF). The capacitor becomes important at this stage because the only possible path for the current to flow is forward through the diode and into the capacitor. Voltage across the capacitor will build up over time at a rate proportional to the current and

Inversely Proportional To The Capacitance (C1)

With the help of a voltmeter, the voltage across the capacitor is measured so that one can track the behaviour of the capacitor as the voltage changes. Note that voltmeter actually allows some current to flow. We usually can neglect this, but here in this case, it is considered as it is to be modelled. Let's say the voltmeter acts like a resistor with fixed resistance of Rload.

A Matlab Code Was Developed That Simulates The

circuit's behaviour and makes another plot which is entitled "Switch Opened after Initialization Period".

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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