BLDC MOTOTR

Brushless dc (BLDC) motor is preferred as small horsepower control motors due to their high

efficiency, silent operation, compact form, reliability, and low maintenance. The problems are

encountered in these motor 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 have been combined to enable reliable,

cost-effective solution for a broad range of adjustable speed applications. The major appliances

include clothes washer’s room air conditioners, refrigerators, vacuum cleaners, freezers, etc.

Household appliance have traditionally relied on historical classic electric motor technologies such

as single phase AC induction, including split phase, capacitor-start, capacitor–run types, and

universal motor.

3.1 Principle of Brushless Linear DC (BLDC) Motor

Brushless DC electric motor (BLDC motors, BL motors) also known as electronically commutated

motors (ECMs, EC motors) are synchronous motor. Permanent magnet DC motors use mechanical

commutators and brushes to achieve the commutation. However, BLDC motors adopt Hall Effect

sensors in place of mechanical commutators 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. Hall Effect sensors detect the rotor position as the commutating signals.

Therefore, 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 studied. The speed of the

BLDC motor is controlled by means of a three-phase and half-bridge pulse-width modulation

(PWM) inverter. The dynamic characteristics of BLDC motors are similar to permanent magnet

DC motors.

3.2 Mathematical Modeling of BLDC Motor

Permanent magnet DC motors use mechanical commutators and brushes to achieve the

commutation. However, BLDC motors adopt Hall Effect sensors in place of mechanical

commutators and brushes [17]. 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.

Hall Effect sensors detect the rotor position as the commutating signals. Therefore, 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 studied. The speed of the BLDC motor is controlled

by means of a three-phase and half-bridge pulse-width modulation (PWM) inverter. The dynamic

characteristics of BLDC motors are similar to permanent magnet DC motors. The characteristic

equations of BLDC motors can be represented as

)(.)(

)(

)(.)(

)(.

)()()(

tDdt

tdJtT

tiKtT

tKv

tvtRidt

diLtv

i

bemf

emfapp

where 𝑣𝑎𝑝𝑝(t) is the applied voltage, ω(t) is the motor speed, L is the inductance of the stator, i(t)

is the current of the circuit, R is the resistance of the stator, 𝑣𝑒𝑚𝑓 (t) is the back electromotive

force, T is the torque of motor, D is the viscous coefficient, J is the moment of inertia, Kt is the

motor torque constant, and Kb is the back electromotive force constant.

Fig. 3.2(a) shows the block diagram of the BLDC motor. From the characteristic equations of the

BLDC motor, the transfer function of speed model is obtained. The parameters of the motor used

for simulation are as Follows

The Transfer Function of Linear BLDC Motor:

st

t

app KKsLDRJsLJ

K

sv

s

.)(.)(

)(2

17.394907.417

36.275577

)(

)(2

sssv

s

app

T

RLS

1

DJS

1

- 𝑇𝐿

appv 𝜔 t

K

bK

-

Fig.3.2 (a) The block diagram of BLDC motor

Fig.3.2 (b) The Simulation diagram of linear BLDC motor

Overall transfer function of BLDC Motor without PID controller is

)()(1

)(

)(

)(

sHsG

sG

sR

sC

Fig.3.2 (c) The Simulation Model of BLDC Motor without PID Controller

Result of Linear BLDC Motor system without PID Controller

Fig.3.2(d) The Step Response of BLDC Motor without PID Controller

Table 3.1

Parameters of the Motor

PARAMETERS Values and units

R 21.2 Ω

𝐾𝑏 0.1433 Vs 𝑟𝑎𝑑−1

D 1*10-4Kg-m s/ rad

L 0.052 H

Kt 0.1433 Kg-m/A

J 1*10-5Kgm 𝑠2/rad

Step Response Characteristics of BLDC Motor without PID Controller

Rise Time 0.0026

Settling Time 0.019

Overshoot 28.3691

Steady state Error 0.5334

3.3 PARTICLE SWARM OPTIMIZATION

PSO is an easy & smart artificial techniques and a evolutionary computation technique which is

developed by Kennedy & Eberhart [13] Particle Swarm optimization method is a computational

method that is used to optimize a problem by iteratively trying to improve a solution with regard

to a given measure of quality.PSO optimizes a problem by having a population of candidate

solutions, here particles , and moving these particles around in the search- space according to

simple mathematical formulae over the particle’s position and velocity. Each particle’s movement

is influenced by its local best known position and is also guided toward the best known positions

in the search-space, which are updated as better positions are found by other particles. This is

expected to move the swarm toward the best solutions.

It is used to explore the search space of a given problem to find the settings or parameters required

to optimize a particular objective. It is based on following two concepts: (i) The idea of swarm

intelligence based on the observation of swarming habits by certain kinds of animals (such as birds

and fish), (ii) The field of evolutionary computation .The assumption is basic of PSO [16]. For n-

variables optimization problem a flock of particles are put into the n-dimensional search space

with randomly chosen velocities and positions knowing their best values, so far (𝑃𝑏𝑒𝑠𝑡) and the

position in the n-dimensional space. The velocity of each particle, adjusted accordingly to its own

experience and the other particles flying experience.

3.3.1 PARAMETER SELECTION

Performance shows how a simple PSO variant performs in aggregate on several benchmark

problems when varying two PSO parameters. The choices of PSO parameters can have a large

impact on optimization performance. Selecting PSO parameters that yield good performance has

therefore been the subject of much research.

Basically, it can be imagined that the function which is to be minimized forms a hyper-surface of

dimensionality same as that of the parameters to be optimized (search variables). It is then obvious

that the 'ruggedness' of this hyper-surface depends on the particular problem. Now, how good the

search is depends on how extensive it is, which is decided by the parameters. Whereas a 'lesser

rugged' solution hyper-surface would need fewer particles and lesser iterations, a 'more rugged'

one would require a more thorough search- using more individuals and iterations. This is analogous

to another realistic situation of flocks searching for a good 'food' traversing a very difficult terrain

containing gardens all over, some better than others where a huge flock would be required in order

to reach the best (read global optimum) 'food' source, compared to another terrain where there are

very few gardens on an otherwise non-vegetated land, where it becomes easy to search for 'food'

and lesser number of individuals and iterations will suffice. The PSO parameters can also be tuned

by using another overlaying optimizer, a concept known as meta-optimization. Parameters have

also been tuned for various optimization scenarios. The particles in the swarm are the individual

elements in the swarm responsible for moving to there personal best values (pbest) and the swarms

best values (gbest) all the while continually searching their current position to monitor for better

values than what the individual has. The individuals’ position is the location given a specific

boundary for which to search in. Evaluation of the position is performed through a fitness function

that returns the optimal solution.

I) Number of particles The number of particles was assigned to 100 with the intent that this would

allow for a large number of individual elements to better explore and converge on the optimal PID

gains. Research by Robinson and Carliel suggest that the higher number of particles gives an

improved exploration for optimal values when compared to the number of particles at 20 or 30.

The compromise between the higher number is that the higher values takes longer to compute than

at 20 or 30 particles.

II) PID search space In order to find the optimal values for the proportional, integral, and derivate

elements, three ranges were established based upon the output from the WSDK ACF tuning. It

Provide an effective window to perform a search that would be similar to the PID values found

using the WSDK ACF tuning method. The search space also establishes the boundaries to which

the fitness function is to be evaluated.

III) Fitness function The pbest and gbest are initial assigned random values in the search space.

For each iteration, The pbest and gbest values are compared to the current location. If the current

location has better optimized values than the current pbest/gbest values, the fitness function returns

a numerical value that is used to evaluate a new velocity and the new values replace the old

pbest/gbest values.

IV) Number of trials The number of trials was set to 50 iterations for each particle. This number

was established to give each particle an opportunity to successfully find optimal PID values over

multiple trials. put more emphasis on the activities of pbest and gbest.

VI) C1 & C2 values The social factors of C1 and C2 determine the amount of emphases the particles

velocity is affected by pbest/gbest. C1 is set to 1 and C2 is set to 2 thus putting more emphases on

gbest.

VII) Velocity In order for the velocity (Vn) to be calculated, the fitness functions of pbest and gbest

needed to be evaluated. The rand(•) element in the equation provides the function a sense of natural

behavior found in nature.

𝑉𝑛𝑛𝑒𝑤 = 𝑤 ∗ 𝑉𝑛𝑜𝑙𝑑 + 𝐶1 ∗ 𝑟𝑎𝑛𝑑()(𝑝𝑏𝑒𝑠𝑡 − 𝑥𝑛) + 𝐶2 ∗ 𝑟𝑎𝑛𝑑()(𝑔𝑏𝑒𝑠𝑡 − 𝑥𝑛) (1)

VIII) Movement The movement of the particle is accomplished by adding the new velocity to the

current location.

Xn = Xn + t *Vnnew

3.3.2 Algorithm for PSO

A basic thing of the PSO algorithm works by having a population (called a swarm) of particles).

These particles are moved around in the search-space according to a simple formula. The

movements of the particles are guided by their own best known position in the search-space as

well as the entire swarm's best known position. When improved positions are being discovered

these will then come to guide the movements of the swarm. The process is repeated and by doing

so it is hoped, but not guaranteed, that a satisfactory solution will eventually be discovered.

Formally, let f: ℝn → ℝ is the cost function which must be minimized. The function takes a

candidate solution as argument in the form of a vector of real numbers and produces a real number

as output which indicates the objective function value of the given candidate solution. The gradient

of f is not known. The goal is to find a solution a for which f(a) ≤ f(b) for all b in the search-space,

which would mean a is the global minimum. Maximization can be performed by considering the

function h = -f instead.

Let S be the number of particles in the swarm, each having a position xi ∈ ℝn in the search-space

and a velocity vi ∈ ℝn. Let pi be the best known position of particle i and let g be the best known

position of the entire swarm. A basic PSO algorithm is then:

𝑋𝑖 =(𝑥𝑖1,𝑥𝑖2,𝑥𝑖3……………..𝑥𝑖𝑑)

in the d-dimensional space, the best previous positions of the 𝑖𝑡ℎ particle is represented as:

𝑃𝑏𝑒𝑠𝑡 = (𝑃𝑏𝑒𝑠𝑡 𝑖,1,𝑃𝑏𝑒𝑠𝑡 𝑖,2,𝑃𝑏𝑒𝑠𝑡 𝑖,3………………𝑃𝑏𝑒𝑠𝑡 𝑖,𝑑)

The index of the best particle among the group is 𝑔𝑏𝑒𝑠𝑡. Velocity of the 𝑖𝑡ℎ particle is represented

as:

𝑉𝑖 = (𝑉𝑖,1,𝑉𝑖,2𝑉𝑖,3………….𝑉𝑖,𝑑)

The updated velocity and the distance from 𝑃𝑏𝑒𝑠𝑡 𝑖,𝑑 to 𝑔𝑏𝑒𝑠𝑡 𝑖,𝑑 is given as [13]:

)*()*)(*()*. )(

,,2

)(

,1

)(

,

)1(

,

t

mimbesti

t

mmbesti

t

mi

t

mixgrandcxPrandcvwv

(2)

)1()()1(

,

t

m

t

m

t

mivxx (3)

i= 1, 2........, n

m= 1, 2,..........,d

n Number of particles in the group

d Dimension

t Pointer of iterations (generations)

𝑣𝑖,𝑚(𝑡)

Velocity of particle I at iteration t

w Inertia weight factor

𝑐1,𝑐2 Acceleration constant

rand() Random number between 0 and 1

𝑥𝑖,𝑑(𝑡)

Current position of particle i at iterations

𝑃𝑏𝑒𝑠𝑡𝑖 Best previous position of the ith particle

𝑔𝑏𝑒𝑠𝑡 Best particle among all the particles in the Population

3.2.3 Algorithmic Approach for specified Design

In BLDC motor case, we design the PID controller in PSO frame as given. We consider the three

dimensional search spaces like𝐾𝑝, 𝐾𝑖 & 𝐾𝑑. We take the fitness function based on time domain

characteristics. We take number of iterations based on expected parameters and time of

computation. The fitness function is defined as:

)(*))(exp()(*)exp(1()(rsssP

ttEMKW (4)

3.4 Implementation of PSO-PID for BLDC motor

In This dissertation a time domain criterion is used for evaluating the PID Controller. A set of good

control parameters P, I and D Can yield a good step response that will result in performance criteria

minimization in the time domain .These performance criteria in the time domain include the

overshoot, rise time, Settling time, and steady state error [13]. Therefore, the performance criterion

is defined as follows:

)(*))(exp()(*)exp(1()(rsssP

ttEMKW (5)

Where K is [P, I, D] and β is weightening factor. The performance criterion W(K) can satisfy the

designer requirement using the weightening factor β value. β can set to be larger than 0.5 to reduce

the overshoot and steady state error, also can set smaller 0.5 to reduce the rise time and settling

time. The optimum selection of β depends on the designer’s requirement and the characteristics of

the plant under control. In BLDC motor speed control system the lower β would lead to more

optimum responses. In this paper, due to trial, β is set to be 0.5 to optimum the step response of

speed control system.

The fitness function is reciprocal of the performance criterion, in the other words,

)(

1

KWf

A PSO-PID controller is used to find the optimal values of BLDC speed control system.

Block diagram of optimal PID control for the BLDC motor

Fig3.4(a) optimal PSO-PID control for BLDC Motor

In the proposed PSO method each particle contains three members P, I and D. It means that the

search space has three dimension and particles must ‘fly’ in a three dimensional space.

The flow chart of PSO-PID controller is shown in Figure shows implementation of particle swarm

optimization technique for PID controller tuning for a control system.

Start

Initial Population

Run the BLDC control system model for set of parameters

Calculate the𝑀𝑝, 𝐸𝑠𝑠, 𝑇𝑟, 𝑇𝑠 of model’s step response

Calculate the fitness function

Calculate the 𝑝𝑏𝑒𝑠𝑡 & 𝑔𝑏𝑒𝑠𝑡 of population

Fig.3.4 (b) Flowchart of PSO-PID control system

Particle Swarm has two primary operators: Velocity update and Position update. During each

generation each particle is accelerated toward the particles previous best position and the global

best position. At each iterations a new velocity value for each particle is calculated based on its

current velocity, the distance from its previous best position, and the distance from the global best

position. The new velocity value is then used to calculate the next position of the particle in the

search space. This process is then iterated a set number of times or until a minimum error is

achieved.

How does it work?

Uses a number of agents (particles) that constitute a swarm moving around in the search

space looking for the best solution

Each particle in search space adjusts its “flying” according to its own flying experience as

well as the flying experience of other particles

The particles fly through the problem space by following the current optimum particles.

A “swarm” is an apparently disorganized collection (population) of moving individuals

that tend to cluster together while each individual seems to be moving in a random

direction.

3.5 Advantages of PSO

(1) PSO is a swarm intelligence technique which is easy to implement & evolutionary

computation technique.

No

Yes

(2) There are few parameters in PSO which requires the adjustment.

(3) PSO is based on the artificial intelligence. It can be applied into both scientific research

uses.

(4) PSO has no more mathematical calculations. The search can be carried out by the

Speed of the particle.

(5) Faster convergence.

(6) Less parameter to tune.

(7) Easier searching in very large problem spaces.

3.6 PSO APPLICATIONS

The first practical application of PSO was in neural network by Kennedy and Eberhart 1995. In

many areas PSO method is used which includes control problems, telecommunications, power

system, data mining, designing, optimization, signal processing, biomedical, antenna, electronics

and electromagnetic, fuzzy and neurofuzzy, graphics and visualization.

In Antennas applications include the optimal control and design of phased arrays, broadband

antenna design and modeling, array failure correction, corrugated horn antennas, optimization

[27,28,29].

In Biomedical and pharmaceutical applications include human tremor analysis for the diagnosis of

Parkinson’s disease, inference of gene regulatory networks, human movement biomechanics

optimization, phylogenetic tree reconstruction, cancer classification[30] and survival prediction,

DNA motif detection, gene clustering, identification of transcription factor binding sites in DNA,

biomarker selection, protein structure prediction and docking, drug design, radiotherapy planning,

analysis of brain magneto encephalography data, RNA secondary structure determination,

electroencephalogram analysis, biometrics[31].

In Communication networks applications include Bluetooth networks, autotuning for universal

mobile telecommunication system networks, optimal equipment placement in mobile

communication, routing, radar networks, wavelength division multiplexed network, peer-to-peer

networks, TCP network control, bandwidth and channel allocation, WDM

Telecommunication networks, wireless networks, grouped and delayed broadcasting, bandwidth

reservation.

In control Application areas include automatic generation control tuning, design of controllers,

traffic flow control, adaptive inverse control, predictive control, PI and PID controllers [21], strip

flatness control, ultrasonic motor control, power plants and systems

control [26, 27], control of chaotic systems, process control, adaptive PMD compensation in WDM

networks, fractional order controllers, combustion control, inertia system control,

automatic landing control.