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==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
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==Robust Modeling and Simulation State Space Model Based BLDC Motor Fed Universal Actuation System==
  
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Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
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Abstract:  
  
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An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself. -->==
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This paper deals with mathematical modeling of Permanent magnet brushless DC (BLDC) motor in MATLAB-SIMULINK environment. Modeling of BLDC motor carried in transfer function, transfer equations and state space model to verify the performance as actuators. Mathematical switches to control electronic commutation of BLDC motor based on signals of Hall Effect position sensor using three-phase inverter drive. Performance of the simplified mathematical inverter fed BLDC motor under steady state and dynamic conditions analyzed. Due to the switching losses during PWM generation generates low ripple content in torque of BLDC motor which described and eliminated through state space model. Comparison made of proposed modeling of BLDC motor with motor parameters like back-EMF, stator current and speed of BLDC motor, proposed work suggests the state space modeling holds a superior method for design of BLDC motor during high dynamic load performance and operating ranges.    
  
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Keywords: BLDC motor, Transfer equation, MATLAB, Simulink, transfer function, State space model
  
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1          Introduction
  
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BRUSHLESS dc motor recommended high and low power applications due to their advantages of high-efficiency, high torque/inertia ratio, variable speed operation, and low electromagnetic interference (EMI)<sup>1</sup>. A BLDC motor is silent operation, compact form, high torque-speed characteristics reliability and low maintenance<sup>2</sup>. Stator with three-phase winding arranged in trapezoidal nature excited with permanent magnets on the rotor. BLDC motor adds advantage of brush-less in commutator arrangement and an electronic based commutation of hall based position sensors used as a feedback signals<sup>4-5</sup>. the limitations met in BLDC motor due for variable speed operation over last decades continuing technology development in power semiconductors, microprocessors, adjustable speed drivers control schemes and permanent-magnet brushless electric motor production joined to enable reliable, cost-effective solution for a broad range of adjustable speed applications<sup>6-8</sup>. However, modelling of BLDC is a challenge to any users due its stator winding in trapezoidal nature and rotor magnets position needs to be sensed at every instant to operate particular switches in ON and OFF condition<sup>9-12</sup>. A Hall Effect sensor is used to provide rotor magnets information and corresponding decoding signals to ON –OFF PWM signals. It is necessary to model actuator with effective dynamic performance system and less ripple harmonics<sup>13-16</sup>.  The proposed BLDC motor modelling is carried in MATLAB simulink environment. MATLAB is an efficient tool for modelling an electrical systems and it is necessary to design BLDC motor i.e actuator for desire performance in overall systems. Modelling of BLDC motor in MATLAB is proposed in this paper with three modelling methods state space model, state transfer equations and transfer functions. Modelling of BLDC motor is carried with three subsystems Modelling of Inverter, Modelling of Motor and Modelling of Decoder.
  
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==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
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Fig. 1.    Structure of BLDC motor
  
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Most of the documents in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific publications in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.
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2           Modelling of BLDC motor
  
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Brushless DC motors modeling with three main parts: Stator, Rotor and Hall Sensor as shown in fig.1.  a three-phase BLDC motor has three stator phases that are excited two at a time to create a rotating electric field as represented in fig.2. The excitation on the stator must be sequenced in a specific manner while knowing the exact position of the rotor magnets.
  
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2.1 Subsections
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(1)
  
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Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
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(2)
  
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(3)
  
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2.2 General guidelines
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WhereV<sub>ab,</sub> V<sub>bc</sub>  and, V<sub>ca</sub> are the stator phase voltages; R is the stator resistance per phase; i<sub>a</sub> ,i<sub>b</sub> and i<sub>c</sub> are the stator phase currents; L areinductance of phases; It has been assumed that resistance of all the winding are equal. It also has been assumed that if there no change in the rotor reluctance with angle because of a no salient rotor and then
  
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Some general guidelines that should be followed in your manuscripts are:
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BLDC motor model is electromagnetic torque and current of motor. The other is a mechanical part, which generates revolution of motor. Under the above assumption, the electrical part of BLDC motor can be represented as
  
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*  Avoid hyphenation at the end of a line.
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(4)
  
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*  Symbols denoting vectors and matrices should be indicated in bold type. Scalar variable names should normally be expressed using italics.
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)                                   (5)
  
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*  Use decimal points (not commas); use a space for thousands (10 000 and above).
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)                                    (6)
  
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*  Follow internationally accepted rules and conventions. In particular use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI.
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The stator phase currents are constrained to be balanced
  
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I<sub>a</sub>+I<sub>b</sub>+I<sub>c</sub>=0                                               (7)
  
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2.3 Tables, figures, lists and equations
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(8)
  
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Please insert tables as editable text and not as images. Tables should be placed next to the relevant text in the article. Number tables consecutively in accordance with their appearance in the text and place any table notes below the table body. Be sparing in the use of tables and ensure that the data presented in them do not duplicate results described elsewhere in the article.
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The phase back EMF in the PMBLDC motor is trapezoidal in nature and is the function of the speed )  ω m and rotor position angle θras shown in fig.3 From this, the phase back EMF’S can be expressed as.
  
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Graphics may be inserted directly in the document and positioned as they should appear in the final manuscript.
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(9)
  
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Number the figures according to their sequence in the text. Ensure that each illustration has a caption. A caption should comprise a brief title. Keep text in the illustrations themselves to a minimum but explain all symbols and abbreviations used. Try to keep the resolution of the figures to a minimum of 300 dpi. If a finer resolution is required, the figure can be inserted as supplementary material
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(10)
  
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For tabular summations that do not deserve to be presented as a table, lists are often used. Lists may be either numbered or bulleted. Below you see examples of both.
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Figure.2 Brushless DC motor drive system
  
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1. The first entry in this list
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Figure.3 Trapezoidal back EMF of three phase BLDC motor
  
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2. The second entry
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3. PWM current controller
  
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2.1. A subentry
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PWM Current Controller generation is dependable to generate three phase reference currents, to generate PWM Current Controller block to compare reference current and observed current. Current error generates fed to build up required PWM signals for switching power electronics switches to drive BLDC motor as shown in fig.7 a MATLAB-SIMULINK model.
  
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3. The last entry
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Figure.7 PWM current controller
  
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* A bulleted list item
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4          Modelling of BLDC motor
  
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* Another one
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4.1 Modelling of BLDC motor in Transfer function
  
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You may choose to number equations for easy referencing. In that case they must be numbered consecutively with Arabic numerals in parentheses on the right hand side of the page. Below is an example of formulae that should be referenced as eq. (1].
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BLDC motor parameter equation is derived in a transfer function block in a behavior to deliver desired current, back-EMF speed and torque motor characteristics. The complete MATLAB model is modeled in Fig.8 with the load torque is tested for different load applying conditions to verify the proposed modeling procedure is suitable as a motor. Back-EMF generation for three phases is simulated using corresponding theta and gamma values manipulated from motor position information as represents in fig.9.  
  
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Figure.8 BLDC motor modeling in transfer function
  
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2.4 Supplementary material
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FIGURE.9 BACK EMF GENERATION OF SIMULINK BLOCKS
  
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Supplementary material can be inserted to support and enhance your article. This includes video material, animation sequences, background datasets, computational models, sound clips and more. In order to ensure that your material is directly usable, please provide the files with a preferred maximum size of 50 MB. Please supply a concise and descriptive caption for each file. -->==
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4.2        Modelling of BLDC motor in Transfer Equation
  
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BLDC motor is modeled using transfer equations with voltage and current equations with inverter and gate decoder circuits. Motor model is based on input parameters of Van,Vbn,Vcn and load torque(Tl) as shown in equations(1-3,8) to generate voltage with corresponding back-EMF (Ea, Eb,Ec). To generate angle back-EMF a look up based logic is used with motor back-EMF constant (Ke) as described in Table.II. Total electromagnetic torque is become conversant with by summing electrical and mechanical torque with product of torque constant (Kl). The mechanical side motor modeling is carried in a transfer equations based modeling as parameter rotor inertia, static and rotor dynamic torque constant as mentioned in Table. II. The complete modeling of BLDC motor with inverter gate drive and back-EMF generations in transfer equations is shown in fig.10 to form transfer function and modeled using MATLAB-SIMULINK
  
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Figure.10 Modeling Of BLDC Motor in Transfer Equations
  
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4.3        Modelling of BLDC motor in State space modelling
  
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==3 Bibliography<!--
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BLDC motor equations is modeled in state space form and fed through a state space block sets MATLAB simulink model as in fig. 11 with corresponding input voltage variables and output variables as velocity, theta angle and  current. The state space model equations variables model is implemented, by considering: the stator phase resistances and inductance described as per data sheets faulhaber motor. In modeling of inverter a mathematical switches is considered neglecting the hysteresis and eddy current losses.  
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Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the document is [1], the second [2], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen
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You should ensure that all references are cited in the text and that the reference list. References should preferably refer to documents published in Scipedia. Unpublished results should not be included in the reference list, but can be mentioned in the text. The reference data must be updated once publication is ready. Complete bibliographic information for all cited references must be given following the standards in the field (IEEE and ISO 690 standards are recommended). If possible, a hyperlink to the referenced publication should be given. See examples for Scipedia’s articles [1], other publication articles [2], books [3], book chapter [4], conference proceedings [5], and online documents [6], shown in references section below. -->==
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Figure.11 Modeling of BLDC motor in state space
  
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4.4 Simulation results and discussions
  
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The proposed BLDC motor is simulated as per data sheets tables as shown in table. II. The design of BLDC motor is verified using parameters listed in Table.II and modeled in MATLAB SIMULINK environment to verify design analysis of Brushless DC motor. A Faulhaber BLDC motor (Series-2444024B)<sup>18</sup> and Motor driver rated current 6A peak have been taken for simulation with BLDC motor is set value of 10000rpm speed and simulated performance of motor at no load and loaded condition  is presented.
  
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Table.II BLDC motor parameters
  
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==4 Acknowledgments<!-- Acknowledgments should be inserted at the end of the document, before the references section. -->==
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{| class="MsoTableGrid"
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 +
  |
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<nowiki>  </nowiki>'''Motor  parameter'''
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 +
  |
 +
<nowiki>  </nowiki>'''Symbol'''
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 +
  |
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<nowiki>  </nowiki>'''Values'''
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 +
  |
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<nowiki>  </nowiki>'''Units''' 
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|-
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<nowiki>  </nowiki>Nominal Voltage
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 +
  |
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<nowiki>  </nowiki>Vn
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 +
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<nowiki>  </nowiki>24
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 +
  |
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<nowiki>  </nowiki>Volt 
 +
 +
|-
 +
  |
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<nowiki>  </nowiki>Terminal resistance
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 +
  |
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<nowiki>  </nowiki>R
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 +
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<nowiki>  </nowiki>1.16
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 +
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<nowiki>  </nowiki>Ohms 
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|-
 +
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<nowiki>  </nowiki>Output power
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 +
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<nowiki>  </nowiki>P<sub>2max</sub>
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 +
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<nowiki>  </nowiki>101
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 +
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<nowiki>  </nowiki>Watts 
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 +
|-
 +
  |
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<nowiki> </nowiki>Speed constant
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 +
  |
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<nowiki>  </nowiki>Kn
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 +
  |
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<nowiki>  </nowiki>475
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 +
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<nowiki>  </nowiki>Rpm/V 
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 +
|-
 +
  |
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<nowiki>  </nowiki>Current constant
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 +
  |
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<nowiki>  </nowiki>Ki
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 +
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 +
<nowiki>  </nowiki>0.050
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 +
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<nowiki>  </nowiki>A/mNm 
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 +
|}
  
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Figure.12 Output waveform of BLDC motor model in transfer functions
  
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Figure.13 output waveforms of BLDC motor model in state space model
  
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Faulhaber BLDC Motor with model 3564B series is designed in MATLAB based on transfer function, state space modeling and transfer equations in open-loop condition and results is presented in fig.13. The Motor characteristic of each modeling method is tabulated below in Table.III.
  
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==5 References<!--[1] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: http://www.scipedia.com/ucode.
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TABLE.III '''BLDC Motor modelling comparison'''
  
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[2] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Volume number, first page-last page.
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{| class="MsoTableGrid"
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 +
  | 
 +
 
 +
  |
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<nowiki>  </nowiki>'''Transfer Function'''
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 +
  |
 +
<nowiki>  </nowiki>'''Transfer equations'''
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 +
  |
 +
<nowiki>  </nowiki>'''State Space  Modeling''' 
 +
 +
|-
 +
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<nowiki>  </nowiki>'''Speed (11300rpm)'''
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 +
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<nowiki>  </nowiki>4000 range
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 +
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 +
<nowiki>  </nowiki>Achieved
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 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|-
 +
  |
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<nowiki>  </nowiki>'''Dynamic Characteristics'''
  
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[3] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.
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   '''(settling time  to reach rated speed)'''
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 +
  |
 +
<nowiki>  </nowiki>Slow
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 +
  |
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<nowiki>  </nowiki>Moderate
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 +
  |
 +
<nowiki>  </nowiki>Fast 
 +
 +
|-
 +
  |
 +
<nowiki>  </nowiki>'''Back EMF (Pure Trapezoidal)'''
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|-
 +
  |
 +
<nowiki>  </nowiki>'''Current (quasi Square)'''
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|-
 +
  |
 +
<nowiki>  </nowiki>'''PWM Current control (IaIbIc )'''
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|-
 +
  |
 +
<nowiki>  </nowiki>'''Hysterias   Current control (IaIbIc )'''
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|-
 +
  |
 +
<nowiki>  </nowiki>'''PWM  Current  control (Idc )'''
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|-
 +
  |
 +
<nowiki>  </nowiki>'''Hysterias current Controller(Idc )'''
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>N.A
 +
 
 +
  |
 +
<nowiki>  </nowiki>Achieved 
 +
 +
|}
  
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[4] Author of Part, D. (Year). Title of chapter or part. In A. Editor & B. Editor (Eds.), Title: Subtitle of book (edition, inclusive page numbers). Place of publication: Publisher.
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From the results obtained from three modeling techniques of BLDC motor in Sim-power system has better performance compared with others. Powergui block in MATLAB has automatically converted the MATLAB-model into average model in SIMULINK which is not possible in transfer function and State-space modeling of BLDC motor.  
  
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[5] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.
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5. Conclusion
  
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[6] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: http://www.scipedia.com/document.pdf.  
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The performance evaluation results show that, such a modelling is very useful in studying the drive system before taking up the dedicated controller design, accounting the relevant dynamic parameters of the motor. The paper presents an implementation of BLDC motor dynamic model, by using the transfer functions, transfer equations and state space modeling using MATLAB-SIMULINK in which all methods performed well and every method has its drawbacks. An inverter mathematical model is also simulated in MATLAB-SIMULINK with corresponding encoder, current controller, hall sensor and back-EMF generation. Motor parameters of real BLDC motor is used and verified as per values in the data sheet. From the results obtained from three modeling techniques of BLDC motor, state space modeling worked well, it is efficient methods to model BLDC motor. By adopting BLDC motor modeling in state space form will be a potential advantage in many actuation system applications.
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-->==
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'''References'''
 +
 
 +
[1]         S. Chen, G. Liu and L. Zhu, "Sensorless Startup Strategy for a 315-kW High-Speed Brushless DC Motor With Small Inductance and Nonideal Back EMF," in ''IEEE Transactions on Industrial Electronics'', vol. 66, no. 3, pp. 1703-1714, March 2019.
 +
 
 +
[2]         B. V. R. Kumar and K. S. Kumar, "Design of a new Dual Rotor Radial Flux BLDC motor with Halbach array magnets for an electric vehicle," 2016 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Trivandrum, 2016, pp. 1-5.
 +
 
 +
[3]         R. Manikandan and R. Arulmozhiyal, "Modeling and simulation of fuzzy based BLDC fed vertically rotating one DOF robot arm position control system," ''2016 10th International Conference on Intelligent Systems and Control (ISCO)'', Coimbatore, 2016, pp. 1-7.
 +
 
 +
[4]         R.Manikandan, and R.Arulmozhiyal, 2016, “Intelligent Position Control of a Vertical Rotating Single Arm Robot Using BLDC Servo Drive”, Journal of Power Electronics, vol.16, no.1, pp. 205-216, ISSN (Print): 1598-2092, ISSN (Online): 2093-4718.
 +
 
 +
[5]         Muniraj M. and Arulmozhiyal R., Modeling and simulation of control actuation system with fuzzy-PID logic controlled brushless motor drives for missiles glider applications, The Scientific World Journal,Hindawi Publishing Corporation, 2015, 1-11, 2015.
 +
 
 +
[6]         Arulmozhiyal R., Murali M. and Manikanadan R., Modeling and simulation of control actuation system, ARPN Journal of Engineering and Applied Sciences, 10(4), 1778-1782, 2015.
 +
 
 +
[7]         J. Shao, "An Improved Microcontroller-Based Sensorless Brushless DC (BLDC) Motor Drive for Automotive Applications," in ''IEEE Transactions on Industry Applications'', vol. 42, no. 5, pp. 1216-1221, Sept.-Oct. 2006.
 +
 
 +
[8]         J. De Viaene, F. Verbelen, S. Derammelaere and K. Stockman, "Energy-efficient sensorless load angle control of a BLDC motor using sinusoidal currents," in ''IET Electric Power Applications'', vol. 12, no. 9, pp. 1378-1389, 11 2018.
 +
 
 +
[9]         PadmarajaYedamale, "Brushless DC (BLDC) Motor Fundamentals", Microchip Technology Inc., 2003. 
 +
 
 +
[10]       S. Baldursson, "BLDC Motor Modelling and Control - A MATLAB/Simulink Implementation", Master Thesis, May, 2005.
 +
 
 +
[11]       B. Tibor, V. Fedák and F. Durovský, "Modeling and simulation of the BLDC motor in MATLAB GUI," ''2011 IEEE International Symposium on Industrial Electronics'', Gdansk, 2011, pp. 1403-1407.
 +
 
 +
doi: 10.1109/ISIE.2011.5984365
 +
 
 +
[12]       Singh, C. P.; Kulkarni, S. S.; Rana, S. C.andKapilDeo, “State-Space Based Simulink Modeling of BLDC Motor and its Speed Control using Fuzzy PID Controller”, International Journal of Advances in Engineering Science and Technology, Vol. 2 , No. 3, 2013, pp. 359-369.
 +
 
 +
[13]       Tashakori, A.; Ektesabi, M. and Hosseinzadeh, N., “Modeling of BLDC Motor with Ideal Back-EMF for Automotive Applications”, In Proceedings of the World Congress on Engineering 2011, WCE 2011, July 6-8, 2011, London, U.K.
 +
 
 +
[14]       A. A. Laczko, M. V. Zaharia, M. M. Radulescu and S. Brisset, "Modeling and simulation of a brushless DC permanent-magnet generator-based wind energy conversion system," ''Ecological Vehicles and Renewable Energies (EVER), 2015 Tenth International Conference on'', Monte Carlo, 2015, pp. 1-7.
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 +
[15]       J. Gebauer, D. Fojtík and P. Podešva, "Modeling of the electronic variable pitch drive," ''Carpathian Control Conference (ICCC), 2015 16th International'', Szilvasvarad, 2015, pp. 138-141.
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doi: 10.1109/CarpathianCC.2015.7145062.
 +
 
 +
[16]       FaulhaberMiniatureDriveSystems,www.faulhaber.com
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[17]       Copeland Brian R., “The Design of PID Controllers using Ziegler Nichols Tuning”, March 2008.
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[18]       Pan S., Edelberg K. and Hedrick J.K., Discrete AdaptiveSliding Control of Automotive Powertrains, 2014American Control Conference (ACC), Portland,Oregon, USA, 2014.
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Revision as of 07:08, 30 June 2020

Robust Modeling and Simulation State Space Model Based BLDC Motor Fed Universal Actuation System

Abstract:

This paper deals with mathematical modeling of Permanent magnet brushless DC (BLDC) motor in MATLAB-SIMULINK environment. Modeling of BLDC motor carried in transfer function, transfer equations and state space model to verify the performance as actuators. Mathematical switches to control electronic commutation of BLDC motor based on signals of Hall Effect position sensor using three-phase inverter drive. Performance of the simplified mathematical inverter fed BLDC motor under steady state and dynamic conditions analyzed. Due to the switching losses during PWM generation generates low ripple content in torque of BLDC motor which described and eliminated through state space model. Comparison made of proposed modeling of BLDC motor with motor parameters like back-EMF, stator current and speed of BLDC motor, proposed work suggests the state space modeling holds a superior method for design of BLDC motor during high dynamic load performance and operating ranges.    

Keywords: BLDC motor, Transfer equation, MATLAB, Simulink, transfer function, State space model

1          Introduction

BRUSHLESS dc motor recommended high and low power applications due to their advantages of high-efficiency, high torque/inertia ratio, variable speed operation, and low electromagnetic interference (EMI)1. A BLDC motor is silent operation, compact form, high torque-speed characteristics reliability and low maintenance2. Stator with three-phase winding arranged in trapezoidal nature excited with permanent magnets on the rotor. BLDC motor adds advantage of brush-less in commutator arrangement and an electronic based commutation of hall based position sensors used as a feedback signals4-5. the limitations met in BLDC motor due for variable speed operation over last decades continuing technology development in power semiconductors, microprocessors, adjustable speed drivers control schemes and permanent-magnet brushless electric motor production joined to enable reliable, cost-effective solution for a broad range of adjustable speed applications6-8. However, modelling of BLDC is a challenge to any users due its stator winding in trapezoidal nature and rotor magnets position needs to be sensed at every instant to operate particular switches in ON and OFF condition9-12. A Hall Effect sensor is used to provide rotor magnets information and corresponding decoding signals to ON –OFF PWM signals. It is necessary to model actuator with effective dynamic performance system and less ripple harmonics13-16.  The proposed BLDC motor modelling is carried in MATLAB simulink environment. MATLAB is an efficient tool for modelling an electrical systems and it is necessary to design BLDC motor i.e actuator for desire performance in overall systems. Modelling of BLDC motor in MATLAB is proposed in this paper with three modelling methods state space model, state transfer equations and transfer functions. Modelling of BLDC motor is carried with three subsystems Modelling of Inverter, Modelling of Motor and Modelling of Decoder.

Fig. 1.    Structure of BLDC motor

2           Modelling of BLDC motor

Brushless DC motors modeling with three main parts: Stator, Rotor and Hall Sensor as shown in fig.1.  a three-phase BLDC motor has three stator phases that are excited two at a time to create a rotating electric field as represented in fig.2. The excitation on the stator must be sequenced in a specific manner while knowing the exact position of the rotor magnets.

(1)

(2)

(3)

WhereVab, Vbc  and, Vca are the stator phase voltages; R is the stator resistance per phase; ia ,ib and ic are the stator phase currents; L areinductance of phases; It has been assumed that resistance of all the winding are equal. It also has been assumed that if there no change in the rotor reluctance with angle because of a no salient rotor and then

BLDC motor model is electromagnetic torque and current of motor. The other is a mechanical part, which generates revolution of motor. Under the above assumption, the electrical part of BLDC motor can be represented as

(4)

)                                   (5)

)                                    (6)

The stator phase currents are constrained to be balanced

Ia+Ib+Ic=0                                               (7)

(8)

The phase back EMF in the PMBLDC motor is trapezoidal in nature and is the function of the speed )  ω m and rotor position angle θras shown in fig.3 From this, the phase back EMF’S can be expressed as.

(9)

(10)

Figure.2 Brushless DC motor drive system

Figure.3 Trapezoidal back EMF of three phase BLDC motor

3. PWM current controller

PWM Current Controller generation is dependable to generate three phase reference currents, to generate PWM Current Controller block to compare reference current and observed current. Current error generates fed to build up required PWM signals for switching power electronics switches to drive BLDC motor as shown in fig.7 a MATLAB-SIMULINK model.

Figure.7 PWM current controller

4          Modelling of BLDC motor

4.1 Modelling of BLDC motor in Transfer function

BLDC motor parameter equation is derived in a transfer function block in a behavior to deliver desired current, back-EMF speed and torque motor characteristics. The complete MATLAB model is modeled in Fig.8 with the load torque is tested for different load applying conditions to verify the proposed modeling procedure is suitable as a motor. Back-EMF generation for three phases is simulated using corresponding theta and gamma values manipulated from motor position information as represents in fig.9.

Figure.8 BLDC motor modeling in transfer function

FIGURE.9 BACK EMF GENERATION OF SIMULINK BLOCKS

4.2        Modelling of BLDC motor in Transfer Equation

BLDC motor is modeled using transfer equations with voltage and current equations with inverter and gate decoder circuits. Motor model is based on input parameters of Van,Vbn,Vcn and load torque(Tl) as shown in equations(1-3,8) to generate voltage with corresponding back-EMF (Ea, Eb,Ec). To generate angle back-EMF a look up based logic is used with motor back-EMF constant (Ke) as described in Table.II. Total electromagnetic torque is become conversant with by summing electrical and mechanical torque with product of torque constant (Kl). The mechanical side motor modeling is carried in a transfer equations based modeling as parameter rotor inertia, static and rotor dynamic torque constant as mentioned in Table. II. The complete modeling of BLDC motor with inverter gate drive and back-EMF generations in transfer equations is shown in fig.10 to form transfer function and modeled using MATLAB-SIMULINK

Figure.10 Modeling Of BLDC Motor in Transfer Equations

4.3        Modelling of BLDC motor in State space modelling

BLDC motor equations is modeled in state space form and fed through a state space block sets MATLAB simulink model as in fig. 11 with corresponding input voltage variables and output variables as velocity, theta angle and  current. The state space model equations variables model is implemented, by considering: the stator phase resistances and inductance described as per data sheets faulhaber motor. In modeling of inverter a mathematical switches is considered neglecting the hysteresis and eddy current losses.

Figure.11 Modeling of BLDC motor in state space

4.4 Simulation results and discussions

The proposed BLDC motor is simulated as per data sheets tables as shown in table. II. The design of BLDC motor is verified using parameters listed in Table.II and modeled in MATLAB SIMULINK environment to verify design analysis of Brushless DC motor. A Faulhaber BLDC motor (Series-2444024B)18 and Motor driver rated current 6A peak have been taken for simulation with BLDC motor is set value of 10000rpm speed and simulated performance of motor at no load and loaded condition  is presented.

Table.II BLDC motor parameters

Motor parameter

Symbol

Values

Units

Nominal Voltage

Vn

24

Volt

Terminal resistance

R

1.16

Ohms

Output power

P2max

101

Watts

Speed constant

Kn

475

Rpm/V

Current constant

Ki

0.050

A/mNm

Figure.12 Output waveform of BLDC motor model in transfer functions

Figure.13 output waveforms of BLDC motor model in state space model

Faulhaber BLDC Motor with model 3564B series is designed in MATLAB based on transfer function, state space modeling and transfer equations in open-loop condition and results is presented in fig.13. The Motor characteristic of each modeling method is tabulated below in Table.III.

TABLE.III BLDC Motor modelling comparison

Transfer Function

Transfer equations

State Space Modeling

Speed (11300rpm)

4000 range

Achieved

Achieved

Dynamic Characteristics 

  (settling time  to reach rated speed)

Slow

Moderate

Fast

Back EMF (Pure Trapezoidal)

Achieved

Achieved

Achieved

Current (quasi Square)

N.A

N.A

Achieved

PWM Current control (IaIbIc )

N.A

Achieved

Achieved

Hysterias  Current control (IaIbIc )

Achieved

Achieved

Achieved

PWM  Current control (Idc )

N.A

N.A

Achieved

Hysterias current Controller(Idc )

N.A

N.A

Achieved

From the results obtained from three modeling techniques of BLDC motor in Sim-power system has better performance compared with others. Powergui block in MATLAB has automatically converted the MATLAB-model into average model in SIMULINK which is not possible in transfer function and State-space modeling of BLDC motor.

5. Conclusion

The performance evaluation results show that, such a modelling is very useful in studying the drive system before taking up the dedicated controller design, accounting the relevant dynamic parameters of the motor. The paper presents an implementation of BLDC motor dynamic model, by using the transfer functions, transfer equations and state space modeling using MATLAB-SIMULINK in which all methods performed well and every method has its drawbacks. An inverter mathematical model is also simulated in MATLAB-SIMULINK with corresponding encoder, current controller, hall sensor and back-EMF generation. Motor parameters of real BLDC motor is used and verified as per values in the data sheet. From the results obtained from three modeling techniques of BLDC motor, state space modeling worked well, it is efficient methods to model BLDC motor. By adopting BLDC motor modeling in state space form will be a potential advantage in many actuation system applications.

References

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