A New Single Current Strategy for High-Performance Brushless DC ...

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Abstract—For closed-loop current control of brushless dc. (BLDC) motors, instantaneous phase currents are measured using appropriate current sensors.
A New Single Current Strategy for High-Performance Brushless DC Motor Drives M. R. Feyzi, M. Ebadpour, Student Member IEEE, S. A. KH. Mozaffari Niapour, Member IEEE, Arshya Feizi, and R. Mousavi Aghdam, Student Member IEEE Department of Electrical and Computer Engineering University of Tabriz Tabriz, Iran E-mail: [email protected], [email protected], [email protected] Abstract—For closed-loop current control of brushless dc (BLDC) motors, instantaneous phase currents are measured using appropriate current sensors. Such sensors are often bulky, heavy, and expensive, making them appealing for elimination. Likewise, the use of two or more separated sensors can cause undesirable imbalances in the phase currents as well as pulsating torque due to mismatched in the current sensor sensitivities. To overcome these problems, a new single current strategy for high performance BLDC motor drives is proposed. It is based on estimation and regulation of phase currents, using two single sensors for dc-link voltage and current. In this method, the phase currents are reconstructed in a two-stage process including estimation and regulation. Estimation is based on dynamic motor model, while regulation relies on the inverter switches states and the measured dc-link current. Besides, to access better dynamic response characteristic of the motor speed, Particle Swarm Optimization (PSO) has been used to regulate the PID parameters of speed controller. The effectiveness of proposed system has been validated by comparative studies and simulation results. Index Terms--Brushless DC (BLDC) motor, single current strategy, high performance drives, particle swarm optimization (PSO).

I.

INTRODUCTION

BLDC motor offers many advantages including high efficiency, low maintenance, greater longevity, reduced weight and more compact construction. The BLDC motors have been widely used for various industrial application based on inherent advantages. They are the most suitable motors in application field with requiring fast dynamic response of speed, because they have high efficiency and can be easily controlled in a wide speed range. Most BLDC drives include a current control loop, which maintains the load current at some required level by switching the constant dc-link voltage across the motor windings. Conventional control of the current loop requires that the feedback current be provided by direct measurement of the winding currents, which implies that each motor phase must have a separate current sensor. However, the current sensors and the associated accessories increase the complexity, the cost and size of the motor drives and reduce the reliability of the system. Therefore, reduction of the number of sensors is desirable in motor drives. The conventional method of current control in a three phase inverter is to compare current demand with actual winding current, where the winding current is obtained by direct measurements on the motor windings. This method of current measurement relies upon total uniformity of current sensors, to achieve a balanced output. The problem of     



current sensor imbalance can lead to unacceptable torque ripple at low speeds. By using a single sensor located on the dc-link, there is inherent balance. Therefore most appealing current sampling method for BLDC motor is using only one current sensor. The easiest method is using a DC link current sensor. There are some single current controls strategies have been studied on BLDC motor drives [1]-[6]. Single-current-sensor sliding mode driving strategy for four-switch three-phase brushless DC motor proposed in [2]. It introduced two kinds of methods based on phase plane portrait and Taylor-series expansion to determine the sliding mode plane convergence domain. In [3] a simple novel digital pulse width modulation control to develop a low cost controller for domestic applications has been implemented for a trapezoidal BLDC motor drive system with single current sensor. A modified DC link current sensor proposed in [4]. It adds an inductance in the upper DC bus to stabilize the current flowing through the sensor during a Pulse Width Modulation (PWM) period. Although it is helpful to evaluate the phase current with no need of any PWM strategy information, the existence of inductance tends to prevent the desired current regulation in phases. So this method is not suitable for current loop. Another current sensor proposed in [5] also works well at any instant despite what PWM strategy is used. The key theory of this method is collecting both the freewheeling current through the antiparallel freewheeling diode and the dc-link current. Therefore, it will not lose any current information during a PWM period. But, in this case the freewheeling current in the closing phase is still a torque source and produces torque ripple in commutation region. Another method proposed in [6], is suitable for PWM strategies. However, this improved method still has some disadvantage, since discrete freewheeling diodes have to be used to circulate motor reactive currents following the openings of the inverter switches, and the effect of the antiparallel freewheeling diode integrated into a power switch must be eliminated by another discrete diode connected in series with the switches. Therefore, this method increases the size of inverter. In this paper, a new single current strategy for high performance BLDC motor drives is proposed. This single current scheme is obtaining three phase currents from only a single dc-link voltage and current sensors. It has been applied to reduce the cost and increase the reliability for various voltage-fed PWM and hysteresis inverter. In this proposed method, the phases current are reconstructed in a two-stage

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process: estimation and regulation. Estimation is based on dynamic motor model, while regulation relies on the inverter switches states and measured dc-link current sensor. Besides, for accessing better dynamic response characteristic for BLDC motor speed, Particle Swarm Optimization (PSO) has been used to regulate the PID parameter of speed controller. The effectiveness of proposed system has been validated by comparative studies and simulation results. The proposed system has been simulated by MATLAB software, and a comparative study among the proposed and conventional methods has been done to validate the advantages of proposed method. II.

 S1

S4

S3

S6

S5

(1)

where va, vb, vc are the phase voltages, ia, ib, ic are the phase currents, ea, eb, ec are the phase back-EMF waveforms, R is the phase resistance, L is the self inductance of each phase and M is the mutual inductance between any two phases. So the electromagnetic torque can be obtained as:

BLDC MOTOR OPERATION PRINCIPLE

Permanent magnet DC motors use mechanical commutator and brushes to achieve the commutation. However, BLDC motors adopt Hall Effect sensors in place of mechanical commutator and brushes. The stators of BLDC motors are the coils, and the rotors are the permanent magnets. The stators develop the magnetic fields to make the rotor rotating. HallEffect sensors detect the rotor position as the commutating signals. Therefore, the BLDC motors use permanent magnets instead of coils in the armature and so do not need brushes. In this paper, a three-phase and two-pole BLDC motor is used. For the three phases BLDC motor the back-EMF and phase current waveforms with 120° conduction mode are shown in Fig. 1.

ª R 0 0º ªia º «0 R 0» «i » »« b » « «¬0 0 R »¼ «¬ic »¼ 0 º ªia º ªea º ªL  M 0 »d « » « » «  « 0 L  M 0 » «ib »  «eb » dt «¬ 0 0 L  M »¼ «¬ic »¼ «¬ec »¼

ªv a º « » « vb » «¬vc »¼

Te

(ea ia  eb ib  ec ic ) / Z r

(2)

where Zr is the mechanical speed of the rotor and Te is the electromagnetic torque. The equation of motion is: d Z r (Te  TL  BZ r ) / J (3) dt B is the damping constant, J is the moment of inertia of the drive and TL is the load torque. The electrical frequency related to the mechanical speed for a motor with P numbers of poles is: Z e ( P / 2)Z r (4) III.

THE PROPOSED SINGLE CURRENT SENSOR TECHNIQUE

The single current Control strategy described in this paper uses single dc-link voltage and current sensors. For this purpose, a suitable method to estimate the phase currents and voltages is proposed and the performance of the resulting drive is assessed. A. Phase Voltages Estimation For phase current estimation, it is necessary to estimate the phase voltage. As illustrated in Fig. 1 the motor is fed by an inverter, which according to the switch states is able to generate six possible voltage space vectors as illustrated in Fig. 2. They are marked with a subscript from 1 to 6 and are labeled with the switch states (S1, S2,  , and S6). Since in the BLDC motor drives the upper and lower switches in a phase leg may both be simultaneously off, irrespective of the state of associated freewheeling diodes in two-phase conduction mode, six digits are required for the inverter operation, one digit for each phase. Therefore, there is a total six non-zero voltage vector for BLDC motor drive as shown in Table I. The stator voltage space vectors calculator computes the space vector v s of the voltage applied to the motor by:

S2



vs

v d  jv q  (S 5  S 2 )e

Fig. 1. Configuration of BLDC motor drive system, back-EMF pattern and reference current generation

The analysis of a BLDC motor is represented in [7] as the following equations:

2S j( ) ­ 1 V dc ®(S 1  S 4 )  (S 3  S 6 )e 3 3 ¯ j(

2S ) 3

½ ¾ ¿

(5)

where Vdc is the inverter dc-link voltage, and (S1, S3, and S5) and (S4, S6, and S2) are the states of the upper and lower switches of the inverter, respectively (S=1 means switch closed and S=0 means switch open).

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V1 3 V d / V dc

TABLE I q-d Voltage Components V2 V3 V4

3/2

3 V q / V dc

1/ 2

0

1

 3/2

1/ 2

 3/2 1 / 2

V5

V6

0

3/2

1

D. Current Regulation For each one of the six active vectors one of the motor phase currents is the same as the one flowing and measured on the dc-link. Table II illustrates according to the switch states the relationship between the dc-link current and the phase currents. From Table II it is clear that by knowing the inverter switch position the real current for one of the phases can be obtained. Comparison of this value with the predicted value (10) serves to obtain an error which is used to compensate the other two predicted phase currents. The compensation process is simple and consists on dividing the current deviation into two equal parts and adding these equal parts to the other two phases [9, 10].

1 / 2

TABLE II Relationship between dc-Link and Phase Currents

30o

Fig. 2. Inverter voltage space vectors

B. Phase Current Reconstruction The phase currents are reconstructed in a two-stage process. In the first stage, the stator currents are estimated, but in the second stage, the predicted values are regulated. Estimation is based on the dynamic motor model, whereas regulation relies on the inverter switches states and the measured dc-link current [8]. C. Current Estimation The prediction stage relies on the dynamics of the stator currents. For each one of the six active voltage vectors the BLDC motor can be modeled by the following equations:

Rs i q , d  L

diq ,d

(6)  E q ,d dt where Eq,d are calculated from the motor back-EMF constant (ke), electrical rotor speed ( Ze ) and electrical rotor position

v q ,d

( Te ) as follows: Eq Ed

k e q (Te )Ze

(7)

k ed (Te )Ze

(8)

k ed and k eq are stationary reference (d-q axes) frame backEMF constant usually pre-stored look-up table. Solving (6) for current i as follows: 1 iq , d (9) ³ (vq ,d  Eq ,d  Rs iq ,d )dt L If (6) solved by mean of a discretization process we get:

>

@

Ts v q , d ( k )  E q , d ( k )  Rs iq , d ( k ) (10) L where Ts is the sampling time, and k and k+1 represented the past and current iq ,d values. iq ,d (k  1)

iq ,d ( k ) 

Voltage Vector

(S1, S4)

(S3, S6)

(S5, S2)

V1

(1,0)

(0,0)

(0,1)

V2

(1,0)

(1,0)

(0,1)

V3

(0,1)

(1,0)

(0,0)

ib

idc

V4

(0,1)

(0,0)

(1,0)

ia

idc

V5

(0,0)

(0,1)

(1,0)

ic

idc

V6

(1,0)

(0,1)

(0,0)

ib

idc

IV.

Phase Current

ia

idc

ic

idc

PID CONTROLLER DESIGN AND PROBLEM FORMULATION

The PID controller is used to improve the dynamic response and reduce the steady-state error. The transfer function of a PID controller is described as: ki  kd s (11) s where kp , ki and kd are the proportional, integral and derivative gains, respectively. The system response can be evaluated by the overshoot (Mp), rise time (tr), settling times (ts), and steady-state error (Ess). To improve the system performance by considering these parameters, an objective function is defined. The objective function will be minimized by an appropriate regulation of PID parameters (Kp , Ki , Kd). By minimizing the objective function, desired transient response to load disturbance is achieved [11]. Objective function can be defined as: Gc ( s )

kp 

f ( K ) (1  e  E )( M p  E ss )  e  E (t s  t r )

(12)

K is [kp , ki , kd] and  is the weight factor. Decreasing rise time and settling time can be caused by smaller weight factor than 0.7 and enhancing this parameter upper than 0.7, lead to reduction in overshoot and steady state error. The lower and upper limits of control variables (Ki , Kp , Kd) are chosen 0 and 10 values, respectively. Because of the system nonlinear behavior, the objective function should be minimized by intelligent algorithms. Nowadays, PSO algorithm is one of the fast and accurate methods in comparison with other intelligent algorithm. So in this paper it is utilized to achieve optimal PID controller parameters by MATLAB software. The PSO results for

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iteration= 20 and weight factor= 0.5 are shown in the Table I. TABLE I Best PID controller with =0.5 value gained by PSO algorithm BLDCM 

Iteration

kp

ki

kd

0.5

20

1.36

1

0.1

Mp

Ess (%)

tr(sec)

ts(sec)

Min Cost

0

0.17

0.0065

0.0224

0.0103

V.

PROPOSED CONTROL SYSTEM DESCRIPTION

The common control algorithm for BLDC motor is current control scheme. Hysteresis band control is one of the simplest closed-loop control schemes. In hysteresis band control, the value of the controlled variable is forced to stay within certain limits (hysteresis band) around a reference value. The drawbacks of the hysteresis band control technique are the high and uncontrolled switching frequencies when a narrow hysteresis band is used and large ripples when the hysteresis band is wider [12]. The uncertain switching frequency makes filtering of acoustic and electromagnetic noise difficult. In general, this technique has high current control capability. One of the best strategies of current control for a high performance BLDC motor drive is accomplished by hysteresis current control with current shaping as shown in Fig. 3. In order to reduce torque ripple and maintain the electromagnetic torque constant, it requires appropriate current references. These current references are generated according to the predetermined back-EMF waveforms [13]. Although, it is based on the measurement of phase currents, the proposed for accessing real phase currents use only a single dc-link voltage and current sensors. Fig. 3 shows a schematic of the proposed control strategy. The operation of the system is as follows. Since the motor is of the brushless DC type, the waveforms of armature currents are the brushless DC type, the waveforms of armature currents are quasi-square. The speed of the motor is compared with its reference value, and the speed error is processed in the PID speed controller, tuned by PSO. The output of this controller is considered as the reference torque, then reconstructed values of stator currents are compared with reference currents and the error current is obtained. Finally, all the three hysteresis controllers independently send the required command to the power switches in order to adjust each of the phase currents. Furthermore, the restriction is expelled on the PID speed controller output depending on the permissible maximum winding currents. This expelled restriction causes a good compatibility with practical systems. Reconstructed values of stator currents are compared with reference currents and the error current is obtained. VI.

REVIEW OF CONVENTIONAL CURRENT CONTROL METHODS

A. PWM Current Control In PWM current control the motor is turned on and off at a high rate. The chopping frequency is fixed but the length of the duty cycle depends on the control error. The fact that the frequency is fixed, makes filtering of acoustic and electromagnetic noise easier. PWM current control is divided

into unipolar PWM method and bipolar PWM method. The general driving method, unipolar PWM of 120o conduction makes fewer switching loss and current ripple, but lower dynamic response of current. As a result, it cannot be applied to application field like as servomotor demanding precision position control. On the contrary, bipolar PWM method makes higher dynamic response of current, but this method more switching loss and current ripple than unipolar PWM method. The three PWM strategies generally used in BLDC motor drives are double-sided basic PWM, single-sided PWM and double-sided complementary PWM [4]. It should be noted that some PWM techniques cause circulating current in the floating phase. This results in torque error with higher torque ripple and thus reduction of efficiency. It also makes a dc-link current sensor unfavorable [13]. Although a bipolar PWM modulation technique such as H_PWM_L_PWM does not generate the circulating current in the floating phase [14], it increase switching loss in the power circuit and winding loss due to high ripple current in the motor windings. Although a bipolar PWM modulation technique such as H_PWM_L_PWM does not generate the circulating current in the floating phase [14], it increase switching loss in the power circuit and winding loss due to high ripple current in the motor windings. On the other hand, although the unipolar PWM modulation technique such as PWM_ON, ON_PWM, and PWM_ON_PWM gives low switching loss, the ripple current still exists and this makes a torque ripple [15].

B. Variable DC-Link Voltage Control Using a variable DC voltage source to control the applied voltage consequently to control the motor phase currents, can have some advantages over the PWM control scheme. A linear power stage is cheaper than a pulsed power stage (PWM) but the losses can be high at low voltage and high current. However, at high speed, a linear power stage can be the best alternative when switching losses and commutation delay of a pulsed power stage significant [16]. The variable dc-link voltage control technique is the only technique that does not cause high frequency disturbances, at least if it is assumed that the variable voltage sources is ideal. Its performance was similar to the PWM method but it produced much smoother torque due to the absence of high frequency switching. In the frequency domain, the variable dc-link voltage control technique contains only harmonics caused by the current commutation. Its performance was similar to the PWM method but it produced much smoother torque due to the absence of high frequency switching. In the frequency domain, the variable dclink voltage control technique contains only harmonics caused by the current commutation VII. SIMULATION RESULTS AND COMPARATIVE STUDIES To evaluate the performance of the proposed system, simulation models have been established using MATLAB/SIMULINK. The sampling interval is 50sec, the magnitude of the current hysteresis band and switching frequency in conventional PWM control scheme are 0.2A and 20 kHz, respectively. The simulation parameters of BLDC motor are as follows:

IEEE CCECE 2011 - 000422

¦

¦

T3

¦

T5

T2

T6

¦

e

m

P 2

dm dt

Fig. 3. Overall block diagram of proposed strategies

Rs

0.4: ,

T eN

10 N .m , j

Ls

13mH ,

nN

p

1500rpm ,

2

0.004kg.m , and k e

2,

0.4V/(rad/sec) .

The BLDC motor phase currents, for each mentioned strategies are depicted in Fig. 4. Phase C urrents (A)

5

0

-5 0.25

0.255

0.26

0.265

0.27

0.275

0.28

0.285

0.29

0.295

0.3

Time (s ec)

(a)

4.5

0

-5 0.25

0.255

0.26

0.265

0.27

0.275

0.28

0.285

0.29

0.295

0.3

Time (s ec)

Electromagnetic Torque (N.m)

Phase C urrents (A)

5

As clearly seen from the Fig. 4(c), reconstructed phase currents are well agreed with real currents. Besides, the square waveforms of phase currents using proposed method (Fig. 4(c)) verify the well control capability of BLDC motor in comparative to two conventional methods. As shown in Fig. 4(c), the current spikes in commutation region and current ripple in conduction region are eliminated effectively. It can be deduced that proposed system has a better current performance in comparison with two conventional methods. The BLDC motor electromagnetic torques is shown in Fig. 5. Since, there is a linear relationship between the phase current and electromagnetic torque in BLDC motor, hence the current ripple in proposed strategy is reduced; therefore the torque ripple has been reduced. 4 3.5 3 2.5 2 0.25

0.255

0.26

0.265

0.27

0.275

0.28

0.285

0.29

0.295

0.3

0.28

0.285

0.29

0.295

0.3

0.285

0.29

0.295

0.3

Time (sec)

(a) Electromagnetic Torque (N.m)

5

0

-5 5

4 3.5 3 2.5 2 0.25

0.255

0.26

0.265

0.27

0.275

Time (sec)

(b) 0

-5 0.25

3.8

0.255

0.26

0.265

0.27 0.275 0.28 Time (sec)

0.285

0.29

0.295

0.3

(c) Fig. 4. Motor phase currents a) PWM control b) Variable DC link voltage control scheme c) proposed method: measured (upper trace) and reconstructed (lower trace).

Fig. 4(c) shows simulation result of real (upper) and reconstructed (lower) phase currents for proposed method.

E lectromagnetic torque (N.m)

R econstructed phase currents (A)

Measured phase currents (A)

(b)

3.6 3.4 3.2 3 2.8 0.25

0.255

0.26

0.265

0.27

0.275

0.28

(c) Fig. 5. The electromagnetic torques a) PWM control b) Variable DC link voltage control scheme c) proposed method.

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As shown in Fig. 5(c), the percentage of torque ripple in proposed strategy is about 3 while, in PWM control and variable DC link voltage control scheme are 24 and 20, respectively. The PSO has been used to regulate the PID parameter of speed controller. As it can be seen from the Fig. 6(c), the speed response characteristic has been completely satisfied to have no overshoot, small rise and settling time. The obtained high performance speed response for BLDC motor is differentiated by circle region in Fig. 6(c).

reduce the steady-state speed error. The Simulation results showed a good agreement between corresponding values in reconstructed and real phase currents and also a higher performance on speed response in comparison two conventional methods. REFERENCES [1]

[2]

Speed (rpm)

1500

[3]

1000

500

0

[4] 0

0.01

0.02

0.03

0.04

0.05 0.06 Time (s ec)

0.07

0.08

0.09

0.1

[5]

(a)

Speed (N.m)

1500

[6] 1000

500

[7] 0

0

0.05

0.1

0.15 Time (s ec)

0.2

0.25

0.3

[8]

(b)

Speed (rpm)

1500

1000

[9]

500

[10]

0.021s ec 0

0

0.01

0.02

0.03

0.04

0.05 0.06 Time (s ec)

0.07

0.08

0.09

0.1

(c) Fig. 6. The speeds of rotor a) PWM control b) Variable DC link voltage control scheme c) proposed method.

[11]

[12]

VIII. CONCLUSION A new approach by using two single sensors for dc-link voltage and current sensors is proposed to reconstruct threephase inverter currents. Due to inherent advantages, the proposed control scheme is particularly suitable for highperformance application such as variable and positional application. Therefore, to reduce the torque ripple and also high current control capability of BLDC motor, hysteresis current control with current shaping is used. In addition, the proposed method is more attractive for BLDC motor applications since it requires minimization of cost, volume, and weight. It will also benefit from reduction on the number of current sensors. The last but not the least, the PSO tuned PID controller is used to improve the dynamic response and

[13]

[14]

[15]

[16]

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