Permanent Magnet Synchronous Motor Pmsm Matlab

Shenzhen, Guangdong

#These authors contributed equally. Abstract—Permanent magnet synchronous motors (PMSM) are widely used due to their numerous benefits. It is critical to get rotor position and speed information in order to operate the motor accurately. Sensorless control techniques have emerged as a popular study area both at home and overseas. The sliding mode observer (SMO) may indirectly detect rotor position and has the benefits of easy implementation and efficient algorithms.

In this study, a mathematical model for sensorless control of a PMSM is developed using SMO, vector control, and other techniques. With a surface-mounted PMSM as the study object, a mathematical model for sensorless control of PMSM is developed. PMSM's sliding mode observer model is built in the matlab/simulink environment. Experiments demonstrate that the system can track the rotor position and speed of the motor precisely and fulfill the requirements of sensorless vector control of PMSM.

Keywords—permanent magnet synchronous motor, vector

I. Introduction

At present, PMSM is extensively utilized in industries because to its simple construction, high power factor, high power density, high accuracy, high efficiency, high torque, and ease of heat dissipation and maintenance . Compared with induction motors, PMSM has permanent magnets that can provide a continuous magnetic field in the air gap, and the current of the stator is solely utilized to generate torque, which makes PMSM have a higher power factor under the same output conditions. Compared with the winding - rotor synchronous motor (SM), the rotor windings of PMSM do not require DC excitation, minus the brush and sliding ring, so its cost is reduced .

Traditional PMSM control methods mainly include open loop control method , vector control(VC) method and DTC method. VC is not dependent on motor parameters and has good robustness. It has the disadvantage of irregular operation, resulting in large pulsations in the output current waveform .

Accurate control of PMSM requires not only appropriate control methods, but also accurate acquisition of rotor position

Information

.

Control,

electromagnetic sensors, photoelectric encoders, speed generators to determine the magnetic pole location and speed of the rotor, mechanical sensors like and are most frequently utilized. , in order to control motor torque and speed. But adding mechanical sensors will make the motor bigger and more expensive, making the system more susceptible to interference and reducing the stability . The goal of PMSM sensorless position control is to rebuild the motor's back electromotive force by monitoring the three-phase AC voltage and current of the stator, and then estimate the the rotor's position. and the motor speed to achieve closed- loop control . The advantages of sensorless control are improved control accuracy and anti-interference ability.

Intelligent Algorithm , And Smo Method Are The

primary sensorless control techniques. In recent years, the advantages of SMO based sliding mode control (SMC) have gradually become prominent.

The SMO method obtains an estimate of the internal state of a particular system by measuring only the inputs and outputs of the actual system , and can replicate the disturbance to achieve complete compensation of the disturbance. Thanks to the above characteristics, SMO has good transient performance, fast dynamic response, insensitivity to system parameter changes and external interference, and strong robustness . Is an easy to implement and commonly used robust control strategy, and can effectively target nonlinear systems with interference .

The research content is carried out with the acquisition of rotor position as the core. In order to determine the rotational speed, the model reference adaptive system approach suggested in reference is based on stability theory.The Lyapunov equation and the Popov superstability theory ensure the asymptotic convergence of state and speed. According to reference , the electromagnetic torque was calculated using a stator current observer with rotor back electromotive force adaptive for the pole impact of permanent magnet brushless DC motors that stands out. Literature creates a composite control approach that combines sliding mode reference adaptive control (MRAC) with an extended state observer (ESO) to view the whole disturbance.. In literature , full-dimensional observer is used to calculate load disturbance and estimate location error. Experimental data indicate that this approach performs well at low speeds, although the technique is challenging to implement .

In this paper, to address the chattering issue, a customized sliding mode plane, a high-order sliding mode, or a fuzzy control and filter combination are used of the sliding model method in the sliding mode method , which makes up for the issue that the traditional SMO's vibrations make it difficult

Required

performance. To achieve the speed control system's smooth transition from the independent control mode to the automatic mode, the sliding mode controller's speed following feature is used .

A. Model Building

In this study, a SMO based on rotor position estimation of arctangent function is used, and Figure 1 displays a block schematic of it in its entirety.Clark transformation and Park transformation are used. Clark transform is the transformation

) Under The Stationary Coordinate System. Park

transformation is the transformation of the current or voltage under the stationary coordinate system to the current (

) Under The Synchronous Rotation Coordinate

system. Clark inverse and Park inverse are also used. Before establishing the mathematical model, the following assumptions are made: the core magnetic saturation of the motor is negligible; eddy as well as hysteresis losses are often small, and the motor's three-phase current is a symmetrical sine wave current.

At present, most traditional SMO algorithms are designed based on the stationary coordinate system (α-β), so The

 Is The

electric angular velocity of the stator; uand uis the voltage of the stator;i andiis the current of the stator; e and eis the extended back electromotive force (EMF), which satisfies

F

is the magnetic chain of a permanent magnet. Fig. 1. Overall control block diagram based on SMO

B. Three-Phase Voltage-Source Inverter Model

The SVPWM technology not only improves the voltage utilization rate of the voltage-type inverter and the motor's capability for dynamic reaction, but also reduces the current harmonic wave and torque pulsation of the motor .

Therefore, the SVPWM algorithm is used as the voltage inverter control algorithm in this paper. Its theoretical basis is the principle of average equivalence, which properly combines the basic voltage vectors in a switching cycle T, so that the average voltage in a cycle is equal to the desired voltage vector. The purpose is to control the direction of the magnetic chain vector by adjusting the voltage vector's direction, and subsequently the rotor's rotation speed and orientation. There are six basic voltage vectors in a typical two-level three-phase voltage source inverter (001, 010, 011, 100, 101, 110) and two zero vectors (000, 111), respectively denoted as V1 , V2 , V3 , V4 , V5 , V6 , V0 , V7 .The six basic voltage vectors divide a 360° circular space vector into six equal sectors, each of which is 60°, and are denoated as sectors Ⅰ to Ⅵ. So as long as the given voltage vector is within the output range, it can be synthesized by two adjacent voltage vectors, that is to say, the synthesis of the given vector can be

Completed By Controlling The Turn-On Time Of The

corresponding switching tube . Of course, in order to minimize the switching loss, we use the seven-section SVPWM algorithm for control.Before the control, we also need to know the number of sectors. However, knowing this is not enough, we also need to calculate the working time of each switch tube and the switching time point .Once you've done that, you can start taking control.

C. Solve For Position And Velocity

As can be seen, the extended reverse electric potential contains information about the orientation and speed of the motor rotor.So we only need to obtain the extended reverse electromotive force accurately to calculate the required information. In order to make more use of the SMO to monitor the extended reverse electromotive force, the equation in (1)

(3)

In a conventional SMO, the formula system utilized to

Bv Is

the observer's regulated voltage input. By deducting (3) from, the error equation for stator current

Is The

sliding mode gain. In the experiment, after several adjustments, its value is 145. Slipform surface is reached when the observer's state

, And The Observers

maintains on the slipform plane..At this point the control quantity can be seen as the equivalent control quantity, namely:

(7)

To get continuous extended back-EMF estimations , a low

(8)

Where, is the time constant of the low-pass filter. However, the addition of low-pass filtering affects the amplitude and phase of the estimates of the extended inEMF.

To obtain a more accurate positional information of the rotor, it is necessary to obtain it by arctangent function method and

C

 is the cutoff frequency of a low-pass filter. With a switching frequency of 10kHz, the cutoff frequency of about 20khz is adopted, which is adjusted to 30khz in the actual



. The differential operation of can be used to determine the rotational speed information (9).

D. Smo Control Method For Sensorless Pmsm

The table-stick three-phase PMSM is studied in this study along with the PMSM vector control approach. Using the synchronous rotation index and the electromagnetic torque

Qi Is

the sole way to regulate the amount of the electromagnetic torque. and the implementation is simple.

E. Speed Inner Loop Regulator Setting

In this study, speed internal loop and current internal loop regulators were applied. To make parameter computations easier, the motor equations of motion for a three-phase PMSM

T Is The Load

torque. The "active damping" principle, which is used to construct the velocity loop PI regulator's parameters, is defined as:

(12)

When the motor is assumed to be started under no-load

(13)

To meet bandwidth requirements β, the poles need to be shifted so that a transfer function of velocity with respect to Q-axis current could well be acquired, as follows：

(14)

By applying Laplace transform to (13) and comparing it

(15)

Since the traditional PI regulator is used in this paper, the controller expression of the velocity loop is as follows:

(16)

Thus, the formula below can be used to obtain the PI

(17)

After plugging in the motor parameters and experimental debugging, it is found that the most basic deviation pi

Qi Generate

cross-coupled electromotive forces in axis q and d

Qu Represents The Voltage Of The Axes D And Q

following current decoupling.



In this paper, a conventional current in-loop regulator is combined with a feed-forward decoupling control strategy for

Represents Current Internal Loop

regulator’s proportionate gain, accordingly.

K

represents the integral gain of current internal loop regulator’s , accordingly. If feed-forward decoupling control techniques are utilised, the regulator parameters within the current loop can only be made fully independent if the actual motor parameters used are the same as those predicted by the model.This is because I-order systems are frequent in automated control theory. The integrated three-phase PMSM's convex pole effect is also taken into consideration and the effect of the model error on the system cannot be ignored. Therefore, in order to make the designed motor model more generalisable, a tabulated control strategy is chosen for the parameter design. It has the advantages of poor model accuracy and unresponsiveness to changes in the parameters, basic design, a single parameter, and straightforward computation.

In order to calculate better, the internal model control block diagram needs equivalent transformation.As shown in

(B) Equivalent Block Diagram

Fig. 2. Equivalent transformation block diagram for internal mode control

(22)

Where I is the identity matrix.

, If The System'S Feedback Connection Is

absent, the system transfer function is as follows:

(23)

As a result, the system is only stable if and when

( )

G s are stable.

, The Current Loop Of The Control

system may be classified as a first-order process since the motor's electromagnetic time constant is much less than its mechanical time constant, the definition is as follows:

, L Is The Inductance, R Is The

resistance. By substituting (24) into (22), you may get the internal

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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