International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) - 2016
SENSORLESS SPEED CONTROL OF
BRUSHLESS DC MOTOR USING FUZZY
CONTROLLER
J. SRINIVAS RAO
Dr. G. Ravi Kumar
Dr. O. Chandra sekhar
Research Scholar at KLUniversity
& Assoc. Professor in EEE Dept.,
Anurag Engineering College, Kodad,
janigasrinivasrao@gmail.com
Professor & HOD in EEE Dept.,
Bapatla Engineering College,
Bapatla.
Goli.ravikumar@gmail.com
Professor & HOD in EEE Dept.,
KL University,
Guntur.
Abstract— This paper proposes a fuzzy controlled integrated
speed – Sensorless approach for the speed control of Brushless
DC Motor (BLDCM). This speed sensorless approach employs a
load observer to estimate the disturbed load torque, and thus
develops a speed sensorless algorithm. For the load observer, the
inputs are mechanical rotor inertia constant and the friction
coefficient, which are estimated using the recursive least-square
rule. Thus this approach is insensitive to motor parameter
variations and integrated drift problem. The proposed algorithm
is simple when compared to extended Kalman filter in estimating
the speed. A comparison is made among fuzzy controller,
modified model reference adaptive control and PI controller. It is
found that the fuzzy controller has superior performance over
other two controllers. The proposed scheme is simulated using
MATLAB/SIMULINK.
Keywords— BLDCM, Fuzzy Controller.
I. INTRODUCTION
Recent investigations of AC motor controls have
been based on two motor drive frame works – Vector control
and Direct torque control. The former, using axes
transformation from the three phase electric terminal axis and
some control algorithms, controls the motor in a simple
environment, and involves more complex computing
algorithms compared to the later. The later, without the inner
current loop, controls the motor using switching table at the
desired torque and flux, but exhibits a ripple speed response,
even though its drive framework is simpler than that of
former. This study adapts the vector control motor drive to
develop a new speed sensorless vector control for a Brushless
DC Motor (BLDC).
The BLDCM is same as the permanent magnet
synchronous motor. However, the former name refers to the
driving method, and later refers to structure. The BLDCM has
been extensively used in industry because it has high power
density, large torque and high efficiency. One of its
shortcomings is the need for sensors to support position or
speed feedback control, such as an encoder or resolver. These
I Thank Anurag Engineering College for supporting to present this paper
under TEQIP-II.
978-1-4673-9939-5/16/$31.00 ©2016 IEEE
sensors add to the cost and weight of motor drive and reduce
the reliability of the system. Research on speed – sensorless
control of BLDCM, based on estimating the position or speed
of rotor by making measurements at the input terminals has
been conducted to solve these problems. Studies in this field
can be grouped into three categories:
1) Back EMF based approaches [1], [2]
2) State observer based approach [3] – [5]
3) Estimator based approach [6], [7]
First two methods are sensitive to both the timevariant motor parameters and the integrator drift problem that
arises in measuring process. Estimator based approach, which
is used an estimator such as the extended Kalman filter to
estimate the speed, require complex computing algorithms and
suffer from the initial-value problem. Additionally they can
only be applied if a high performance PC or DSP is available.
The torque observer [8] was employed as feed
forward compensator for the position controller. The torque
observer was derived from mechanical dynamic equation with
estimated parameters namely the mechanical rotor inertia
constant and friction co-efficient. Based on this approach the
paper proposes a new speed sensorless approach, which has
simpler computing algorithm and is uninfluenced by the time
variant motor parameters or the integrator drift problem.
The performance of speed-sensorless approach is
governed by the type of controller. For better performance,
MMRAS, an adaptive control algorithm is used for the speed
controller. The performance of speed controller influences the
speed sensorless approach. Therefore modified model
reference adaptive system (MMRAS) [11], an adaptive
controller algorithm is used in speed control of BLDCM to
improve the performance of the speed sensorless approach [9].
In this paper fuzzy controller is being employed in place of
MMRAS.
II. SPEED-SENSORLESS TECHNIQUE
Synchronously rotating reference frame (d-q axis) of the
vector control drive is adapted here to analyze the BLDCM.
The state equation is given by
 − Ra
ida   L
P  =  a
iqa  − ωre

Fig. 1. Sensorless technique with load observer

ωre 
ida 
Vda  1
V  −
 qa  La
1
  +
− Ra  iqa  La
La 
0
e  (1)
 qa 
Where
P is d/dt; Ra is armature winding resistance
La is armature winding inductance
Vda ,Vqa are the d-axis and q-axis armature voltages
Ida and Iqa are d-axis and q-axis armature currents.
The mechanical dynamic equation is
(Te – TL) = J*Pωrm + ωrm*B
(2)
Where
T = Developed torque, TL = Load torque
J = Mechanical rotor inertia constant
B = Friction coefficient.
Both J and B are parameters of mechanical dynamic
equation; they may vary with environmental conditions and
uncertainties. The RLS rule is applied to estimate the
parameters, Ĵ and B̂ and thus enhance the robustness of the
system.
Equation (2) is written as
T −T
B
Pωrm = e L − ωrm *
J
J
ω
ω
T
−
Let Y = P rm , φ = [- rm e TL
(3)
],θ
T
B
=
J
1.
J 
The MMRAS algorithm is modified version of model
reference adaptive system (MRAS). Basically MRAS uses a
reference model to generate the desired output and compares
with the actual output of the closed loop system to yield error
signal and minimizes this error by adjusting the parameter Ө
= [Ө1 Ө2]. According MIT rule, the parameter Ө adjustment
algorithm is
dθ
∂J
∂e
= −γ
= −γe
dt
∂θ
∂θ
Where
The loss function J( θ ) is defined as J( θ ) = (1/2)e2,
free parameter to be tuned.
1
dθ1


= −γ ' e 2
uc
dt
P
aP
b
+
+


(
)
= Pp (t − 1)ϕ (t ) λI + ϕ T (t )Pp (t − 1)ϕ (t )
θ (t ) = θ (t − 1) + K (t )(Y (t ) − ϕ (t )θ (t − 1))
(I − K (t )ϕ (t ))Pp (t − 1)
Pp (t ) =
λ
T
−1
(8)
γ
is the
For updating the controller parameters, the fallowing
equations are obtained.
(4)
Then the rules of RLS yield
K (t ) = Pp (t )ϕ (t )
III. MMRAS SPEED CONTROLLER
(5)
(6)
(7)
Where λ is the forgetting factor. The estimated parameters
Ĵ and B̂ are used in the following torque observer.
By using the inputs Ĵ , B̂ and ω rm , the torque
observer generates the estimated load torque ( ), which is
substituted into mechanical dynamic equation (3) to be solved
for mechanical angle rate ( ω̂rm ). The second row of equation
(1), the q – axis differential equation and eq. (2) are combined
to derive the block diagram of speed control loop [12], [13]
and the same is shown in fig. 1.
1
dθ 2


= γ ' e 2
c
dt
 P + aP + b 
(9)
(10)
Where γ ' = γc , a, b and c are constants (a=Ra/La + B/J),
b=Ra*B/(La*J),c=p*φfa / /(La*J), p is number of pair of poles ,
Uc is the command signal.
The block diagram of the MMRAS controller is presented in
fig. 2.
Fig. 2. Block diagram of the MMRAS.
Fig. 6. Plot of membership function for current
The MMRAS is designed to force the plant output to the
desired output, enhancing the effect of speed control and
improving the performance of speed-sensorless technique.
Fig. 3. Block diagram of sensorless speed control of BLDCM.
IV. SIMULATION RESULTS
III. PROPOSED FUZZY LOGIC CONTROLLER
A fuzzy controller is suitable for complex and
nonlinear systems. An effort is made to implement the fuzzy
controller. In the proposed controller there are two inputs,
which are speed error and change in speed error and one
output, which is current.
There are seven membership functions both in input
and output, in that five are triangular and two are trapezoidal
membership functions. These linguistic variables of
membership functions are denoted by negative large (NL),
negative medium (NM), negative small (NS), zero (ZE),
positive small (PS), positive medium (PM), positive large
(PL).
The following figures show the membership
functions for speed error, change in speed error and current.
The simulation is performed in MATLAB
environment. Fig. 3. represents the simulation block diagram
of sensorless speed control of BLDCM. First, the parameters J
and B are estimated using RLS rule, estimated parameters, J
and B are used in torque observer to establish the sensorless
algorithm.
In the second step, sensorless algorithm is being
implemented with PI, MMRAS and fuzzy speed controller.
The simulated results are presented in Fig. 7. Fig. 8. and
Fig. 9. respectively. Table I shows the average root mean
square error (RMSE) of the sensorless BLDCM Simulation
with various controllers. The results reveal that new sensorless
algorithm with fuzzy controller is effective.
Fig. 7. Simulated speed response of system with PI controller
400
350
300
speed(rpm)
250
Fig. 4. Plot of membership function for speed error
200
150
100
50
0
0
0.5
1
1.5
2
2.5
Tme(sec)
3
3.5
4
4.5
5
Fig. 8. Simulated speed response of system with MMRAS
Fig. 5. Plot of membership function for change in speed error
350
300
speed(rpm)
250
200
150
100
50
0
0
0 .5
1
1 .5
2
2 .5
T im e (s e c )
3
3 .5
4
4 .5
5
[3]
Fig. 9. Simulated speed response of system with Fuzzy controller
[4]
[5]
[6]
[7]
Table1. Average RMSE of the sensorless BLDCM with PI, MMRAS
algorithm and fuzzy algorithm for under various load conditions
Average RMSE
Speed
365
Controller
type
When
load is
3 N-M
Step
change
in load
Max peak of
error when
there is
change in
load
PI
3.1
5
15
MMRAS
1.75
2.5
8
Fuzzy
Controller
0.8
1.8
5
.
[2]
[10]
[11]
[12]
[13]
[14]
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