Direct Torque Control Dtc Matlab

American Journal of Applied Sciences 5 (8): 1083-1090, 2008

1083

Simulink Model of Direct Torque Control of Induction Machine

Selangor De, Malaysia

Abstract: Direct torque control (DTC) is one of the most excellent control strategies of torque control in induction machine. It is considered as an alternative to the field oriented control (FOC) or vector control technique. These two control strategies are different on the operation principle but their objectives are the same. They aim to control effectively the torque and flux. Torque control of an induction machine based on DTC strategy has been developed and a comprehensive study is present in this research. The performance of this control method has been demonstrated by simulations performed using a versatile simulation package, Matlab/Simulink. Several numerical simulations have been carried out in a steady state and transient operation on a speed control mode.

Key words: Direct torque control, induction machine, vector control, Matlab/Simulink

For Many Years, Induction Machine Have Provided

the most common form of electromechanical drive for industrial, commercial and domestic applications that can operate at essentially constant speed. Induction

Machines Have Simpler And More Rugged Structure,

higher maintainability and economy than DC motors. They are also robust and immune to heavy loading.

Basically, There Are Two Types Of Instantaneous

electromagnetic torque-controlled AC drives used for

Control In The Field Rotating Reference Using Pwm

inverter control.

Flux Control In The Stator Fixed Reference Frame

using direct control of the inverter switching.

Induction Machine. It Was Introduced In Japan By

Takahashi (1984) and also in Germany by Depenbrock

(1985). Dtc Of Induction Machine Has Increasingly

become the best alternative to field orientation methods or vector control.

A Block Diagram Of A Dtc System For An Induction

machine is shown in Fig. 1,. The DTC scheme is very

Simple; In Its Basic Configuration It Consists Of

hysteresis controllers, torque and flux estimator and a Fig. 1: Direct torque control of induction machine switching table. The configuration is much simpler than

The Vector Control System Due To The Absence Of

coordinate transformation between stationary frame and synchronous frame and PI regulators. It also does not need a pulse width modulator and a position encoder,

Without Using The Current Regulation Loop. Dtc

scheme uses a stationary d-q reference frame (fixed to the stator) having its d-axis aligned with the stator q- axis. Torque and flux are controlled by the stator voltage space vector defined in this reference frame.

The Basic Concept Of Dtc Is To Control Directly

both the stator flux linkage (or rotor flux linkage, or magnetizing flux linkage) and electromagnetic torque of machine simultaneously by the selection of optimum

1084

inverter switching modes. The use of a switching table for voltage vector selection provides fast torque response, low inverter switching frequency and low harmonic losses without the complex field orientation

By Restricting The Flux And Torque Errors Within

respective flux and torque hysteresis bands with the

Optimum Selection Being Made. The Dtc Controller

consists of two hysteresis comparator (flux and torque) to select the switching voltage vector in order to

Maintain Flux And Torque Between Upper And Lower

limit. The main objective of this paper is to develop the simulink model of direct torque control of induction machine based on the mathematical modelling.

The Develop Torque Control Of Inverter Fed

induction machine is carried out by hysteresis control of magnitude stator flux and torque that selects one of the six non-zero and two zero inverter voltage vectors shown in Fig. 2. The selection is made in order to maintain torque and flux error inside the hysteresis band in which the errors are indicated by ∆Te and ∆Ψs

S As The

combination of switches status of the inverter are given

7

Fig. 2: Inverter output voltage vectors and voltage

Rotates At

the desired frequency ωs inside a specified band. If the stator ohmic drops are neglected, the stator voltage impresses directly the stator flux in accordance

Therefore The Variation Of The Stator Flux Space

vector due to the application of the stator voltage vector

Ss

V during a time interval of ∆t can be approximated as:

(6)

Torque Control: The electromagnetic torque given by equation (7) is a sinusoidal function ofγ , the angle

As Shown In Fig. 3. Since The

rotor flux changes slowly, the rapid variation of stator

Flux Space Vector Will Produce A Variation In The

developed torque because of the variation of the angle

V Has To Be

selected to obtain stronger rotation speed of ωs. The actual value of stator flux can be expressed as:

Indicate The Measured Stator Voltage

and current respectively. The electromagnetic torque is calculated by means of

(10)

Switching Table: On the basis of the torque and flux hysteresis status and of the stator flux switching sector,

Inverter Voltage Vector To Apply To The Induction

machine from the Table 1. The outputs of the switching table are the settings for the switching devices of the inverter. Figure 4 shows the relation of inverter voltage vector and the stator flux switching sectors.

V (111)

Table 1: Switching table of inverter voltage vectors

To Study The Performance Of The Developed Dtc

model, a closed loop torque control of the drive is simulated using Matlab/Simulink simulation package. The block diagram of the simulink model is shown in Fig. 5.

Start-Up With No Load: Torque Control Dynamic

performance of developed DTC model is evaluated by applying a step input of amplitude 30 Nm after 0.4 ms to torque reference while the stator flux reference is maintained at 1 Wb. The width of the hysteresis band is adjusted to ±0.01 Wb for the flux comparator and ±0.01 Nm for the torque comparator. Maximum step size of

0.1 Ms Is Used In This Simulation. The Obtained

responses are shown in Fig. 6.

The Equation Of Torque For No Load Running With

single inertia and negligible friction is shown below:

From Fig. 6(A), The Estimated Electromagnetic

torque remains at zero at period before 0.4 ms, so the rotor does not rotate. At t=0.4 ms, a step of 30 Nm is

1086

Fig. 5: Developed model of direct torque control of induction machine applied to the torque reference and the electromagnetic

Torque Immediately Increases To Reach The Demand

torque. This causes the rotor to accelerate at a rate dictated by the rotor inertia. From the torque response, the acceleration is given

The Rotor Speed Response In Fig. 6(B) Behaves

linearly during start-up. This is validating the equation of the speed for no load running with single inertia and

The

corresponding acceleration of the rotor speed can be

Both Of The Above Acceleration Calculations Based

on the estimated torque and the speed response are differ only by 2.8%. Thus, the small difference in percentage can verify the accuracy of the developed model.

In This No Load Situation, The Rotor Speed Would

eventually accelerate to synchronous speed of 147.8 rad/s. There is 5.9% difference with the calculated of

Rad/S. The Response Is Shown In

Fig. 7.

Figure 6(C) Shows The Stator Flux Magnitude

response has risen to its final value of 1.0 Wb that is equal to the stator flux reference. The stator flux magnitude is also constrained within its hysteresis band of ±0.01 Wb as shown in Fig. 6(d). The locus of the stator fluxes is presented in Figure 6(e). Since the stator

Flux Magnitude Is Constantly Maintained In The

hysteresis band, the locus draws the figure of a circle.

In Dtc Scheme, A Direct Control Of The Stator

current is not present and this may determine over current when a step variation of torque and flux are applied to the input command. Figure 6(f) and 6(g)

Uncontrolled Current During Start-Up, The Machine

exceeds the rated current with stator current amplitude,

Si

> 80 A as shown in Fig. 6(g). It can be noted that

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

Related Journal Articles & DOI Links

Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).

Why Choose Us?

Bangalore guidance for robotics, Spectre and autonomous systems projects.