Optimized PID controller for BLDC motor using Nature ... · Keywords— Brushless direct current...

Optimized PID controller for BLDC motor using

Nature-inspired Algorithms

Manoj Kumar Merugumalla

Department of Electrical Engineering

Andhra University

Visakhapatnam, India

[email protected]

Prema Kumar Navuri

Department of Electrical Engineering

Andhra University

Visakhapatnam, India

[email protected]

Abstract— The class of population algorithms for solving

various problems of global optimization is often called as

methods inspired by nature. Methods in this class are based on

the modelling of intelligent behaviour of organized members of

the population. The nature of this collective intelligence is

found among the social insects, such as ants, bees and among

some species of fish and birds. Population based algorithms

have number of advantages over classical methods for solving

complex optimization problems. This paper presents the

comparison of population algorithms with classical methods of

tuning PID control parameters for the control of speed of

brushless direct current (BLDC) motor .The position of BLDC

rotor here is determined by measuring the changes in the Back

emf. Sensorless control method reduces the cost of motor as it

does not need sensors to detect position of rotor. The BLDC is

modelled in MATLAB/SIMULINK and trapezoidal back emf

waveforms are modelled as a function of rotor position using

matlab code. The proposed population algorithms are effective

in tuning control parameters thereby reducing the time

domain parameters like steady state error, settling time, rise

time and peak overshoot. The population algorithms such as

Particle swarm optimization (PSO) algorithm and bat

algorithm (BA) based on effective objective function-Integral

absolute error (IAE) are proposed for the optimal tuning of

controller parameters. The results obtained from these

algorithms are compared with the classical methods.

Keywords— Brushless direct current motor, sensorless

control, particle swarm optimization, bat algorithm, PID

controller.

I. INTRODUCTION

BLDC motor came into existence in 1960s. The motor has

several advantages such as high efficiency, flat speed-torque

characteristics and high speed range, when compared against

Brushed DC motor. BLDC motors are electronically

commutative motors in contrast to the mechanically

commutated brushed dc motor. The rotor position can be

determined either by Hall effect sensors or by measuring

the changes in the bemf at each of the armature coils as the

motor rotates which is sensorless control method[1]-[3]. The

position of rotor is determined by measuring the changes in

the trapezoidal bemf. PID controller is mostly used for the

speed control of many motors, but tuning of control

parameters is a difficult task. Nature-inspired algorithms

have advantages over classical methods of tuning controller

parameters. To demonstrate the effectiveness of nature-

inspired algorithms over classical methods, the particle

swarm optimization, bat algorithm, Ziegler-Nichols method

and Tyreus-Luyben method are proposed and compared in

this paper. Nature inspired algorithms are applicable to any

virtual problem that can be treated as an optimization task. It

requires some data to represent solutions and a performance

index to evaluate solutions. In Particle swarm optimization

algorithm the particles play the role of agents and are

distributed in parameter space of optimization problem [5].

The particles move in parameter space and change their

direction and speed of motion based on certain rules. At each

iteration the value of target function is calculated according

to the current particle position. Particle also knows the

position of neighbor particles and information about its best

position based on previous values. According to this

information, the rule for changing particle position and speed

in the parameter space is determined. Bat-inspired algorithm

is another method in the class of population algorithm. Bat

have unique echolocation which is used to fly in darkness

and to detect prey [5]. During search process bat generates

signal with frequency and volume.

The objective in the optimal PID-design is to

reduce the overshoots and settling time in system oscillations

with minimum error. Classical methods and nature-inspired

algorithms has been used for optimization of PID controller

parameters. Objective function needs to be formulated for

optimal PID-design.

II. BLDC MOTOR DRIVE SYSTEM

A. BLDC motor

Unlike brushed dc motor, field of brushless dc

motor is on rotor and armature is on stator, armature on

stator has an advantage of conducting heat away from

winding. The BLDC is supplied by the inverter. BLDC

motor accomplishes electronic commutation using feedback

from rotor position to determine the current switching. The

rotor position can be determined either by using a Hall

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com

415

effect sensor or by measuring changes in back emf at each

of the armature coils as motor rotates. However sensors

cannot be used in applications where rotor is in a closed

housing. Therefore BLDC sensorless driver monitor BEMF

signal instead of the position detected by Hall sensors to

commutate the signal [4].The schematic diagram of BLDC

motor drive control is shown in figure.1

Fig.1 BLDC motor drive control scheme

The equations that describe the model is as follows:

(1)

(2)

(3)

where Eb and Rb –voltage and resistance of source ,

Rc-resistance in capacitor, isk- converter input current ,

vc- voltage across capacitor, is- source circuit current,

ic- current through capacitor

Voltage equations at the motor side are:

(4)

(5)

(6)

Where Vsa, Vsb, Vsc are the inverter output voltages that

supply the 3-Ф winding. Va, Vb, Vc are the voltages across

the motor armature winding,Vn – voltage at the neutral

point.

The stator winding voltages in terms of the winding

parameters are expressed as in shorter version

(7)

and the electromotive forces of three- phase windings are:

, where, (E=Ke.ωm) (8)

Equation that links the supply and motor sides

(9)

The Torque balance equation of drive system is expressed

as:

TJ +TD+ TS+TL=Te (10)

Torque due to Inertia, (11)

Where, J – Moment of inertia,

Torque due to viscous friction, (12)

Where, B – Friction coefficient,

The Electromagnetic torque of 3-phase motor is

(13)

The electrical position of the rotor is

) (14)

B. Hysteresis current controller

In the PWM current controller instantaneous

current control is not possible, it acts only once in a cycle.

The current may exceed the maximum limit in between two

consecutive switching. Therefore in PWM controller the

current is controlled on an average basis but not on

instantaneous basis. The Hysteresis current controller

overcomes such a drawback. It controls the current within a

narrow band of excursion from its desired value. The

operation of the hysteresis current controller for the drive is

employed using Embedded Matlab Code. The simulink

model of Hysteresis current controller with reference

currents and actual currents as input is shown in figure 3.

Fig.3 Simulink model of Hysteresis Current Controller


416

C. Reference current generator

The reference currents in all the three phases are

implemented in SIMULINK using the Embedded Matlab

code. The simulink model of reference current generator is

shown in figure 4.

Fig:.4 Simulink model of Reference current generator

D. PID Controller

The proportional – integral – derivative (PID)

controller occupied the major portion of the control systems

due to its simple structure and ease of operation. In PID

controller, the proportional, integral and derivative modes

have to be tuned and all the three gains combine together for

the control of the drive system [6]-[9]. The controller

parameters are to be tuned properly to provide reliable

performance. The block diagram of PID controller with

proposed tuning methods are shown in figure 2. R(S) is the

reference input signal, U(S) is the controlled output, Y(S) is

the system output and E(S) is the error, which is the

difference between reference and the actual value. The aim

of tuning the controller parameters is to reduce rise time,

settling time with zero overshoot and without steady state

error.

Fig.5 Optimal PID controller

III. CLASSICAL METHODS

A. Ziegler-Nichols method

Ziegler-Nichols method is popular and the most widely used

method for tuning of PID controllers. This method is also

known as online method. [11][12].

Steps involved Z-N tuning method:

Step 1: Deactivate integral and derivative control, i.e. set

τi=0, τd=0.

Step 2: Raise the gain kc until the process begin to oscillate..

Step 3: Note the values as ultimate gain (ku) and ultimate

period (τu)

Step 4: Evaluate control parameters

The step response of closed loop system with ZN-PID and

without ZN-PID (with Kp=1) is shown in figure 6,

electromagnetic torque is shown in figure 7.

Fig.6 Step response of closed loop system with ZN-PID and without ZN-

PID (with Kp=1)

Fig.7 Electromagnetic Torque with ZN-PID

B. Tyreus-Luyben method

The Tyreus-Luyben tuning method developed by

Tyreus and Luyben in 1997 which is based on oscillations

as in the Ziegler-Nichols method, but with modified

formulas for the controller parameters to obtain better

stability in the control loop compared with the Ziegler-

Nichols method. The Tyreus-Luyben procedure is quite

similar to the Ziegler–Nichols method but the final

controller settings are different. Also this method only


417

proposes settings for PID controllers. The step response of

the system with TL-PID and without TL-PID (with Kp=1) is

shown in figure 8 and electromagnetic torque waveform is

shown in figure 9.

Fig.8 Step response of closed loop system with TL-PID and without TL-

PID (with Kp=1)

Fig.9 Electromagnetic Torque with TL-PID

IV. NATURE -INSPIRED ALGORITHMS

A. Particle swarm optimization algorithm

The class of population algorithms such as Particle

swarm optimization, bat algorithms for solving global

optimization problems are often called as Nature-inspired

algorithms. They offer practical advantages to the difficult

optimization problems. These algorithms can be applied to

any virtual problem that can be formulated as an

optimization task. It requires a data to represent solutions, a

performance index to evaluate those solutions and some

operators to generate new solutions. In contrast to the

classical methods nature-inspired algorithms can adapt

solutions to the changing circumstances and gives robust

response to changing circumstances. Particle Swarm

Optimization (PSO) algorithm is a population based

stochastic optimization technique developed for solving

optimization problems. A swarm in PSO consists of a

number of particles. Each particle represents a potential

solution to the optimization task [13]-[14. A fairly useful

performance index is the integral of absolute error (IAE),

and it is expressed in the equation as

IAE= (15)

Where ω(t)ref is reference speed and ω(t)act is actual speed.

IAE integrates the absolute error over time. Therefore, the

design problem can be formulated as the optimization

problem and the objective function is expressed as

(16)

Subjected to constraints

PSO algorithm implementation steps are as follows:

Step 1: Read the system data and initial solution generation

randomly.

(17)

(18)

Step 2: Calculation of fitness value (objective function).

Step 3: Calculate objective function value of each particle in

the population and after comparing , pbest for the current

iteration is recorded:

(19)

Where, k is the number of iterations,

Step 4: Calculation of global best i.e. the best objective

function associated with the pbest among all particles is

compared with that in the previous iteration and the lower

value is selected as the current overall global best.

(20)

Step 5: Update the velocity, by using below equation

(21)

C1 and C2 are the acceleration coefficients usually in range

[1, 2]. A large inertia weight (w) provides a global search

while a small inertia weight provides a local search.

Step 6: Checking velocity constraints occurring in the limits

from the following conditions,

Step 7: update the position of each particle at the next

iteration (k+1) is modified as follows:

(22)

Step 8: After reaching the maximum iteration then go to

step 9 for global best otherwise, go to step 2.


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Step 9: The individual which generates the latest global best

is the optimal PID parameters at minimum objective

function.

The flow chart for the particle swarm optimization

technique for the tuning of PID control parameters is

shown in figure 10.The step response of the closed loop

system with particle swarm optimization tuning of PID

controller is shown in figure 11 and electromagnetic torque

with PSO tuning of PID controller is shown in figure 12.

Fig.10 Implementation flowchart of particle swarm optimization algorithm

Parameter description of PSO algorithm:

Population size P : 20

Number of particles npar : 3

Maximum number of iterations Itermax : 50

Cognitive parameters C1, C2 : 2, 2

Max. Inertia weight factor Wmax : 0.9

Min. Inertia weight factor Wmin : 0.4

Fig.11 Step response of closed loop system with PSO-PID

Fig.12 Electromagnetic Torque with PSO-PID

B. Bat Algorithm

Bat algorithm is another population based

algorithm which exploits echolocation behavior of bats to

find their prey Bats are the second largest order of

mammals. They migrate to hundreds of kilometers. Bat

echolocation is a perceptual system where ultrasonic sounds

are emitted to produce echoes.bat algorithm was proposed

by Xin-She-Xang for for solving engineering optimization

problems [15-16].

Steps for implementation of Bat algorithm:

Step 1: initialize the algorithm parameters such as

dimension of the problem, population size and number of

maximum iterations (Itermax).

Step 2: generation of PID gains randomly

pop

d

pop

d

poppop

pop

d

pop

d

poppop

dd

dd

xxxx

xxxx

xxxx

xxxx

X

121

11

1

1

2

1

1

22

1

2

2

2

1

11

1

1

2

1

1

(23)

Where, d is the number of decision variables, which

represents PID gains,

Step 3: calculate fitness evaluation using eq.15 and record

the best solution.

Step 4: Starting evolution procedure and frequency for each

Bat is assigned randomly

fi = fmin + (fmax – fmin) β (24)

Where β [0, 1] is a vector drawn randomly from a uniform

distribution. Initially each bat is assigned a frequency

randomly which is drawn uniformly from minimum and

maximum values.


419

Step 5: generation of bat positions randomly

(24)

(25)

Step 6: evaluation of Fitness (Objective function)

Calculate fitness value for each initial solution using Eq. 16

Step 7: Selection of best solution among initial bats.

Step 8: Stop if the number of maximum iterations is

reached. Otherwise, Step 4 to Step 7 is repeated.

The problem specific implementation flow chart of bat

algorithm has been given in figure 13.

.

Fig.13 Implementation flow chart of Bat Algorithm

Parameter description of Bat algorithm:

Population of bat pop : 20

Dimensional search space of bats N : 6

Loudnes A : 0.5

Pulse rate R : 0.5

Minimum frequency fmin : 0. 00

Maximum frequency fmax : 2. 00

Max.no of iterations Itermax : 50

The step response of the closed loop system with BA-PID is

shown in figure 14 and electromagnetic torque response is

shown in figure 15.

Fig.14 Step response of closed loop system with BA-PID

Fig.15 Electromagnetic Torque response with BA-PID

The comparison of step responses of classical tuning

methods are shown in figure 16, small oscillations can be

observed in classical methods of tuning. Step responses of

nature-inspired algorithms are shown in figure 17 without

oscillation and overshoot. The actual speed of the motor

tracks the reference speed with minimum disturbance and

quickly settled at reference speed without delay with the

population algorithms. These algorithms effectively tune the

control parameters under sudden load changes and abnormal

conditions. The step responses of all methods are shown in

figure 18. The electromagnetic torque responses are shown

in their respective sections. The step response of the PSO-

PID at rated speed of 700 rpm is shown in figure 19. The

step response of PSO-PID with step change in reference

speed and when subjected to a load torque at 0.5 seconds is

shown in figure 20.

Fig.16 Step response of closed loop system with TL-PID, ZN-PID


420

Fig.17 Step response of closed loop system with BA-PID, PSO-PID

Fig.18 Step response of proposed tuning methods

Fig.19 step response of PSO-PID at rated speed of motor

Fig.20 step response of PSO-PID with step change in reference speed and

subjected to load torque at 0.5 seconds

Table.1 Performance Parameters of ZN-PID, TL-PID, PSO-

PID, BA-PID

Controller

Parameter

ZN-PID TL-PID BA-PID PSO-PID

Kp 2.25 1.704 0.3484 1.4891

Ki 4.444x103 1721.76 4.883 3.9750

Kd 0.056x10-3 1.217x10-4 0.0002 0.0007

Peak time(tp) 0.0035 0.0033 0.0131 0.0067

Rise time (tr) 0.0035 0.0032 0.0091 0.0028

Settling time(ts) 0.0041 0.0045 0.0133 0.0066

Delay time(td) 0.0016 0.0015 0.0017 0.0016

Max.peak

overshoot(Mp)

0 0.29 0 0

Steady state

error(ess)

0.85 0.81 0.20 0.03

The motor drive used for simulation process has following

specifications:

Motor rating : 0.5 HP

Number of Poles : 4

Inductance : 0.0272H

Back emf constant : 0.5128V/rad/sec

Torque constant : 0.49 N-m/A

Moment of inertia : 0.0002 kg-m/s2

Rateds speed : 700 rpm

DC voltage : 160V

Frequency : 2kHz

CONCLUSION

In this paper the nature-inspired algorithms are

proposed to search the PID controller parameters for the

speed control of BLDC motor and compared with the

classical methods. The overall control system has been

modeled and simulated in MATLAB/SIMULINK. Several

time domain parameter performance measures such as rise

time, peak time, delay time, settling time, peak overshoot

and steady-state error of nature inspired algorithms are

compared with classical methods. The results obtained from

the simulations clearly demonstrate the improved

performance with the nature inspired algorithms particularly

particle swarm optimization algorithm when the system

subjected to sudden loads and with the sudden change in

reference speed. Since nature-inspired algorithms exhibits

robustness and good performance, these are ideal for the

speed control of brushless direct current motor.


421

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