Field Oriented Control Foc Matlab

International Journal of Power Electronics and Drive Systems (IJPEDS)

Journal Homepage: Http://Ijpeds.Iaescore.Com

A field-oriented control method using the virtual currents for

The Induction Motor Drive

Cuong Dinh Tran1, Tien Xuan Nguyen2, Phuong Duy Nguyen3

Accepted Oct 15, 2021

An improving field-oriented control technique without current sensors is proposed to control rotor speed for an induction motor drive. The estimated stator currents based on the slip frequency are used instead of feedback current signals in the field-oriented control (FOC) loop. The reference signals and the estimated currents through computation steps are used to generate the control voltage for the switching inverter. Simulations were performed in Matlab/Simulink environment at rated speed and low-speed range to demonstrate the method's feasibility. Through simulation results, the FOC method using virtual sensors has proved its effectiveness in ensuring the stable operation of the induction motor drive (IMD) over a wide speed range.

Virtual Sensor

This is an open access article under the CC BY-SA license.

Power System Optimization Research Group

19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam

:Rotor_Flux Angle

1.

Introduction

Asynchronous motor, which operates based on the electromagnetic induction principle, is one of the most popular electric machine types with a wide variety of industrial applications. Based on inverter technology and microprocessor technology development, the induction motor (IM) drive using modern control algorithms has expanded its operation scope into speed control applications . Scalar control and

2096

vector control are the two major branches of IMD's speed control application. The Scalar control (Scl) method's basic principle is to keep the flux as a constant value when controlling the speed by adjusting the stator voltage according to the operating speed (V/f). Typical scalar methods with advantages of simple control algorithm, fast response, medium hardware are suitable for applications that do not require high precision -.

Field-oriented control (FOC) is a typical modern control method in the vector control method group. FOC method is suitable for applications requiring high precision in speed and torque control , . FOC technique converts the IM's complicated non-linear control structure into a linear control structure similar to the DC motor control technique. The three-phase stator current in the FOC technique is divided into two orthogonal components, including “isx” and “isy” in the [x, y] rotating coordinate system, as in Figure 1. The “isx” component is used to keep the rotor flux as a constant value, and the “isy” component is applied to adjust the IM's torque -. Therefore the stator current plays a crucial role in the speed control of the FOC technique. If there is any failure of the current sensors during the operation, the performance of IMD's can be severely affected, which can cause the collapse of the total system -.

Stability and reliability always are essential criteria of speed control in IMD systems. Therefore, in recent years, FOC methods without current sensors, called current sensorless (CSL), has been focused on research. Generally, virtual current signals are used instead of the measured current signals supplied to the FOC control loop in the CSL technique. The aim of CSL controllers is to ensure the stable operation of the IMD system in controlling the rotor speed without feedback current signal from sensors in various operating conditions.

In Barba et al. , the speed of IMD is controlled by the FOC method without any current sensors. In this method, an observer based on the typical Luenberger form receives current DC-link signals and the feedback rotor speed to estimate the reference voltages for motor speed control. The success of the method is determined through the stable operation of IMD under normal conditions. In , a fault-tolerant control is presented as a solution against the failure of current sensors. The estimated line-current generated from a Luenberger observer is used to replace the measured stator current to calculate the electrical torque and stator flux vector for the direct torque controller of IMD. Using estimated line-currents has ensured stable operation of IMD under current sensor fault states. In , A new CSL method is applied for estimating the stator current from the rotor flux variable and voltage signal in [α, β] coordinate. In this way, the speed of IM is controlled through the FOC loop with only a feedback speed signal of the encoder. The IMD system without current sensors could work stably and reliably under various operating conditions. Authors in have proposed a method for virtual stator current estimation to replace the function of the measured currents in the speed control of IMD. The virtual current signals in this paper are estimated from the voltage signal of the DC bus and the feedback signal of the encoder. The proposed method has proven highly reliable when operating efficiently under load and no-load conditions over a wide speed range.

This paper proposes the virtual stator currents based on the slip frequency instead of feedback current signals in the FOC technique. The estimation algorithm uses machine parameters and virtual currents to generate the predicted voltage supplied to the inverter switching control. The feasibility of the technique will be demonstrated in various operating conditions in the Matlab/Simulink environment.

Figure 1. Vector Control Diagram

2.

Foc Method Using The Virtual Current

In this section, the operational structure of IMD systems using the FOC strategy is introduced in general. The mathematical equation of IMD is presented in detail in the rotating coordinate system. Then, a FOC method without current sensors (virtual currents) is proposed for the speed control of the IMD.



A field-oriented control method using the virtual currents for the induction motor drive (Cuong Dinh Tran)

2.1. Foc Technique In Rotating Coordinate System

The FOC works based on projections on the axes of the [x, y] rotating coordinate system corresponding to rotor flux angle and rotor flux speed -. The isx-component is used for controlling the magnetic current to keep the rotor flux as a setting value. The isy-component controls the electrical torque of IMD to obtain the setting motor speed. The operation mechanism of the IMD system using the typical FOC strategy is shown in the block diagram in Figure 2.

There are three sensors used in the typical FOC method for motor speed control, including a pair of current sensors and a speed encoder. Two-phase current signals in the [a, b, c] coordinate is transformed to the [α, β] stationary coordinate by using Clark's formulas in the FOC controller, as shown in (1).

0

.

(1)

Next step, Park's formulas are used to convert current vector components from [α, β] to [x, y] coordinate, as shown in (2).

Sin

.

(2)

The iSα, iSβ components combining a feedback motor speed signal is applied to determine the magnetic current and rotor flux angle. The PI controllers use the deviation of the reference and actual signals to generate the reference voltage in [x, y] rotating coordinate. The reverse Park's formulas are applied to convert this reference signal into the [α, β] stationary coordinate. Finally, the reference voltage is transformed back to the [a, b, c] coordinate for the switching control pulse of the inverter.

2.2. Current sensorless technique based on the rotor slip speed (Virtual currents) The relationship between voltage, current, and flux signals in IM is non-linear. The dynamic equations of IM in [x, y] rotating coordinate are described in detail as shown in:

𝜔𝑒 : Flux_Speed

The rotor flux is kept as a constant value and has the same direction as the x-axis of the coordinate corresponding to the FOC technique. The feature of rotor flux in the [x, y] rotating coordinate system, as

(7)

Using (7) into (3)-(6), we can receive in (8)-(10):

𝑇𝑅 : Rotor_Time Constant

From (8)-(10), we can determine the stator current components on the [x-y] axis through in:

(12)

The rotor slip speed can be determined as the following:

(13)

Due to the magnetic current is keep as a constant value in the FOC technique; therefore, we can apply the reference magnetic currents (im, isx) and reference voltage on the y-axis to replace the actual signals in the differential equations. As a result, we can obtain the estimated equations for virtual stator currents

(16)

The block diagram of the FOC used the virtual stator current is shown in Figure 3. AS shown in (14), (15), (16) are applied in the “Virtual current estimator block” for generating the estimated stator current instead of feedback current signals from sensors. The reference voltages, reference currents, and the rotor speed signal are used as the input signals of the estimator. The PI controllers use the reference signals and the estimated signals to modulate the control voltage for the switching inverter. As a result, the speed control using FOC strategy of IMD is implemented with only a speed sensor in the drive system. The simulations

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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