A New Approach of Sensorless Control Methodology for Achieving Ideal Characteristics of Brushless DC Motor Using MATLAB/Simulink Santanu Mondal
Arunabha Mitra
Debjyoti Chowdhury
Elec. & Instru. Engg. Techno India Salt Lake , Kolkata
[email protected]
App. Elec. & Instru. Engg. Heritage Institute of Technology, Kolkata arunabha.official @gmail.com
App. Elec. & Instru. Engg. Heritage Institute of Technology, Kolkata
[email protected]
Abstract—This paper describes a new mathematical model of permanent magnet brushless dc motor (PMBLDC) with sensorless commutated drive on MATLAB/Simulink based platform. The main challenges in sensorless BLDC commutation techniques compared with sensored drive lies in identification of first commutation point and minimization of torque ripple. In this work, an ideal back-EMF generation methodology has been designed and implemented in order to incline the system with the ideal one. As a result, a significant reduction in torque ripple is achieved. The characteristics of this model give satisfactory outputs over a wide range of controlled speed variation from 700 to 14000 rpm. Moreover, the torque and speed characteristic provide a high torque even at low speed. The strength of the sensorless commutation technique used here is established by performance analysis of the simulated design. Keyword—Brushless dc motor; back-EMF; ZCD; electronic commutation technique; Sensorless drive
I. INTRODUCTION The use of permanent magnet BLDC motor is expanding day by day in different applications especially in computer, aerospace, military, automotive, industrial and household appliances as it holds high efficiency, torque, compactness over intact operating range and can be easily controlled due to proportional variation of torque with input voltage [1]. The electronic commutation circuitry in BLDC motor requires a three phase inverter, rotor position sensors (for starting and providing the proper commutation sequence to stator windings) [2]. The main limitation of such sensored drive circuit not only increases the cost and size of the motor but also needs special mechanical arrangement for mounting the position sensors (Hall sensors) [3]. Moreover, these Hall sensors are temperature sensitive as they lose sensing capability at the temperature beyond 120 ºC. To overcome this, sensorless drive of BLDC motor is introduced [4-6]. In this sensorless commutation technique, both the hardware complexity due to position sensors as well as energy and space consumption of associated circuitry are reduced. In sensorless BLDC motor, the trapezoidal back-EMF is used to detect the instantaneous position of rotor. The back-EMF waveforms generated from the stator go through a zero
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Madhurima Chattopadhyay App. Elec. & Instru. Engg. Heritage Institute of Technology, Kolkata madhurima.chattopadhyay @heritageit.edu
crossing detector [7]. The output of the zero crossing detector (ZCD) is a square wave pulse and it is generated every time the trapezoidal back-EMF changes its phase. Principally, four types of sensorless control methods can be found [8]. They are (i) Back-EMF Sensing method, (ii) Back-EMF Integration method, (iii) Flux Linkage-Based method, and (iv) Detection of freewheeling diode conduction method. Among these four techniques, we have adapted back-EMF sensing method owing to ease of implementation. In this sensorless commutation technique, three zero crossing detectors (ZCD) are employed with simple ON-OFF logical operation. During each commutation cycle, two out of the three phases remain conducting while the third phase is used to determine the back emf through ZCD. This back-EMF signal of the floating winding is used to determine the commutation sequence of power devices in the three phase inverter [9, 10]. This paper introduces the sensorless drive of BLDC motor in Section I followed by mathematical modelling in Section II. Section III deals with implementation of simulation model in MATLAB/Simulink. The output results of the simulated model are discussed in Section IV. Finally Section V concludes the work. II. DESCRIPTION AND MODELLING OF THE DRIVE SYSTEM In this model, a three phase, four pole, star connected trapezoidal back-EMF type BLDC motor and three phase inverter is considered. Fig.1 shows the basic block diagram of Sensorless drive of BLDC motor [11]. Figure 2 shows sixswitch inverter with equivalent circuit of BLDC Motor [10]. The gating signals in the inverter circuit, given to the MOSFET are sequenced at 60º intervals which is explained by Table I where each MOSFET conducts for a duration of 120º [12, 13]. During modeling, we assume that there are no power losses in the inverter and 3-phase motor winding.
Fig.1. Basic Block diagram of Sensorless drive of BLDC Motor by back-EMF detection method.
Applying Kirchhoff’s voltage law for the three phase stator winding circuit and we get:
Fig.2. Equivalent circuit of BLDC Motor fed six-switch inverter [6]
0 0 0
0 0
0
(1) (7) (2) (3) where Va, Vb and Vc are the respective three phase voltages of the stator winding, Ra, Rb and Rc are the stator resistances, ia , ib and ic are the stator phase currents, La , Lb and Lc are the self-inductances, Mab, Mac, Mba, Mbc, Mca and Mcb are the mutual inductances and ea, eb and ec are the three phase back-EMFs. In a 3-phase BLDC motor, the back-EMF is a function of the rotor position. The back-EMF of each phase has a difference of 120º, thus equation of each phase should be as follows:
The stator self-inductances and mutual inductances are independent of the rotor position. Hence, assuming all the selfinductances to be equal, we represent them by L (i.e., La = Lb = Lc = L). Similarly, all mutual inductances of three different phases can be considered to be equal and be denoted by M. As we have considered a balanced three phase system, all the phase resistances are equal and thus, are represented by R. Rearranging equation (7) we obtain: 0 0 0
0 0
0 (8)
. .
(4)
. .
(5)
. .
(6)
where k is back-EMF constant, and is the rotor position.
is angular speed of rotor,
From equations (1), (2) and (3), a complete BLDC model can be written as: TABLE I. Rotor Position (Degree) 0-60
SIX STEP SWITCHING SEQUENCE Switch Closed Q1
Q5
Phase Currents Ia
Ib
Ic
+
-
Off -
60-120
Q1
Q6
+
Off
120-180
Q2
Q6
Off
+
-
180-240
Q2
Q4
-
+
Off
240-300
Q3
Q4
-
Off
+
300-360
Q3
Q5
Off
-
+
The electromagnetic torque equation is given as: . .
2 3
. . . .
(9)
The equation of motion for simple system is given as: (10)
III. IMPLEMENTATION OF BLDC MOTOR IN MATLAB/SIMULINK According to the mathematical model, the complete motor drive is simulated in MATLAB/ Simulink environment. The entire drive is divided into several functional blocks such as BLDC motor, PI controller and inverter with commutation logic. By the logical combination of these blocks, the simulation model of BLDC motor drive is implemented. The block representing BLDC motor is the main part of simulation, which generates simulated outputs corresponding to rotor speed and electromechanical torque. The main attribute of this model is the implementation of a true back-
EMF generator block that incorporates one dimensional interpolation of input values using a specific table. The piecewise linear method is selected to produce the trapezoidal back-EMF waveform, which divides one period of 0°-360° into six commutation stages. Fig. 3 and Fig.4 show back-EMF zero crossing detector and the entire model of BLDC motor implemented in MATLAB/Simulink platform respectively. IV. SIMULATION RESULTS The proposed simulation in this present work is established in the MATLAB / Simulink environment. The parameters of BLDC motor for simulation study are shown in Table II. The output results like rotating speed, back-EMFs, three-phase current of stator winding and electromagnetic torque are shown in Fig. 5, Fig. 6, Fig. 7 and Fig. 8 correspondingly. These figures assure swiftness in start-up of the designed motor. Fig. 5 illustrates variation of rotor speed for different preferred rpm which confirms a smooth achievement of desired rpm with a settling time less than 0.02 sec. The simulated model generates a smooth response over a wide variation (700 - 14000 rpm) of speed. It has been observed from Fig. 5 that in low speed (
