"Speed control of dc motor using Particle Swarm optimization technique by PSO Tunned

PID and FOPID"

Under the supervision of ByAKHILESH MISHRA ANUPAM AGARWAL (1201024501)

Organization of dissertation

INTRODUCTION MODELING OF DC MOTOR PID &FOPID PSO SIMULATION AND RESULTS CONCLUSION

INTRODUCTION

DC motor is a power actuator which converts electrical energy into mechanical energy.

DC motors are most suitable for wide range speed control.

DC motors have been widely used in many industrial applications such as electric vehicles, steel rolling mills, electric cranes etc.

A Separately excited DC motor model

Where Va is the armature voltage. (In volt) Eb is back emf the motor (In volt) Ia is the armature current (In ampere) Ra is the armature resistance (In ohm) La is the armature inductance (In henry) Tm is the mechanical torque developed (In Nm) Jm is moment of inertia (In kg/m²) Bm is friction coefficient of the motor (In Nm/ (rad/sec)) ω is angular velocity (In rad/sec)

5

Block diagram of separately excited DC motor model

Parameters of separately excited DC motor model:• Armature resistance (Ra) = 1.51Ω • Armature inductance (La) = 0.55e-3 H • Armature voltage (Va) = 200 V • Mechanical inertia (jm) = 1.10 e -6 Kg.m2 • Back emf constant (ke) = 0.027 V/rad/sec • Rated speed = 1500 r.p.m Armature resistance (Ra) = 1.51Ω • Armature inductance (La) = 0.55e-3 H • Armature voltage (Va) = 200 V • Mechanical inertia (jm) = 1.10 e -6 Kg.m2 • Back emf constant (ke) = 0.027 V/rad/sec • Rated speed = 1500 r.p.m • Motor torque constant (kt )= 0.027 N.m/A • Friction viscous gain(kf) =5.06 e-6 Nm/rad/sec• Motor torque constant (kt )= 0.027 N.m/A • Friction viscous gain(kf) =5.06 e-6 Nm/rad/sec

DC MOTOR STEP RESPONSE

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

5

10

15

20

25

30

35

40Comparative Step response of closed loop and open loop

Time (sec)

P.U

. spe

ed

PID & FOPID

• The PID controller is the most common general purpose controller in the today’s industries.

• It can be used as a single unit or it can be a part of a distributed computer control system.

• Over 30years ago, PID controllers were pneumatic-mechanical devices, whereas now a days they are implemented in software based techniques like ANN, Fuzzy Logic, Genetic Algorithm and most popular Optimization techniques.

• There are different approaches to tune the PID parameters like P, I and D. The Proportional (P) part is responsible for following the desired set-point while the Integral (I) and Derivative (D) part account for the accumulation of past errors and the rate of change of error in the process or plant, respectively.

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Ziegler-Nichols Tuning Method

• The PID tuning parameters as a function of the open loop model parameters K, T and θ from the Process reaction curve derived by Ziegler-Nichols .

• The method presented by Ziegler and Nichols is based on a registration of the open-loop step response of the system, which is characterized by two parameters.

• First determined, and the tangent at this point is drawn. The intersections between the tangent and the coordinate axes give the parameters T and θ.

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Cohen-Coon Tuning Method

• Cohen and Coon based the controller settings on the three parameters θ, T and K of the open loop step response.

• The main design criterion is rejection of load disturbances.

• The PID tuning parameters as a function of the open loop model parameters K, T and θ from equation as derived by Cohen-Coon.

Particle Swarm Optimization (PSO)

.James Kennedy an American Social Psychologist along with Russell C .Eberhart innovated a new evolutionary computational technique termed as Particle Swarm Optimization in 1995.

The approach is based on the swarm behavior such as birds finding food by flocking.

A basic variant of the PSO algorithm works by having population (called a swarm) of candidate solution (called particles)

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• The initial position of the particle is taken as the best position for the start and then the velocity of the particle is updated based on the experience of other particles of the swarming population.Parameter Values

No. of Particles 10

No. of Iterations 30

Velocity constant C1 0.5

Inertia(weighing ) .5 to .9

Velocity constant C2 1.5

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The Simulink model of various tuning method for speed control of DC motor using PID & FOPID controller

Speed versus Time plot with reference speed for PID tuned with Zeigler Nicholas & Cohen Coon

Step Response

Time (sec)

Am

pli

tud

e

0 1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

1.2

1.4

System: ZNicolasI/O: Step to Z-NicolasRise Time (sec): 0.976

From: Step To: Out(1)

System: Cohen-CoonI/O: Step to Cohen-CoonRise Time (sec): 0.547

ZNicolas

Cohen-Coon

Step response of system tuned with FOPID Method-Step Response (fopid)

Time (sec)

Ampl

itude

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

0.2

0.4

0.6

0.8

1

1.2

1.4From: Step To: Subsystem3

FOPID

Step response of system tuned with PID & FOPID by Z-Nicolas

Step Response

Time (sec)

Am

pli

tud

e

0 1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

1.2

1.4 System: Model (9)I/O: Step to Z-NicolasPeak amplitude: 1.12Overshoot (%): 12At time (sec): 2.1

System: Model (9)I/O: Step to Z-NicolasTime (sec): 3.11Amplitude: 1.03

System: Model (9)I/O: Step to Z-NicolasFinal Value: 1

From: Step To: Z-Nicolas

System: Model (9)I/O: Step to Z-NicolasRise Time (sec): 0.976

STEP RESPONSE OF FOPID &PID TUNNED bY PSO

Step Response(Comparative response of FOPID and PID Tunned by PSO)

Time (sec)

Am

pli

tud

e

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

Table Comparative analysis of various tuning methods

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Conclusion

Performance comparison of different controllers has been reviewed and it is found that Particle Swarm optimization is best among the all methods which are used for tuning the parameter of PID controller for which settling time and rise is found to be less.

The conventional controllers however are not recommended for higher order and complex systems as they can cause the system to become unstable. Hence, a heuristic approach is required for choice of the controller parameters which can be provided with the help of Bio inspired methods such as Particle swarm Optimization, where we can define variables in a subjective way.

BIBLIOGRAPHYAkhilesh K. Mishra, Anirudha Narain, “Speed Control of

Dc Motor Using Particle Swarm Optimization”, International Journal of Engineering Research and Technology Vol. 1 (02), 2012, ISSN 2278 - 0181A. A. El-Samahy, “Speed control of DC motor using adaptive variable structure control,” IEEE 31st Annual Power Electronics Specialists Conference, 2000, pp. 1118- 1123.

Gopal K. Dubey, “Fundamentals of Electrical Drives”, Narosa Publishing House Pvt. Ltd., 2001, chap. 6.

J. Kennedy, “The Particle Swarm: Social Adaptation of Knowledge”, Proceeding of the IEEE International Conference on Evolutionary Computation, ICEC1997, Indianapolis, pp. 303-308, 1997.

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