1. A
Presentation
on
Automatic Voltage Regulation Using FOPID
Controller Tuned by Particle Swarm
Optimization Technique
SUPERVISOR
(Mr. AKHILESH KUMAR MISHRA)
Assistant Professor
Presented By
Tushar Verma
(1201024508)
2. CONTENTS
1. Objective
2. Introduction
3. Automatic Voltage Regulation
4. PID Controller
5. FOPID Controller
6. Classical tuning methods of PID & FOPID Controller
7. Optimal Tuning of FOPID Tuning using PSO
8. Simulation Result
9. Conclusion
3. 1. OBJECTIVE
• The aim of my work is to develop a controller based
on Particle Swarm Optimization Technique to
simulate an Automatic Voltage Regulator (AVR) for
a synchronous generator in order to achieve better
stability of the system and fulfil the requirements of
good excitation control.
4. 2. INTRODUCTION
• In this work bio-inspired optimization technique in
controllers and their advantages over conventional
methods is discussed using MATLAB/Simulink.
• Also the advantage of FOPID controller over
Conventional PID controller is discussed using
MATLAB/Simulink.
• The main aim is to apply PSO technique to design
and tune parameters of FOPID controller to get an
output with better dynamic and static performance.
5. 3. AUTOMATIC VOLTAGE
REGULATION
• The Automatic Voltage Regulator (AVR) is widely
used in industrial application to obtain the stability
and good regulation of different electrical apparatus.
• The automatic voltage regulator or AVR, as the name
implies, is a device intended to regulate voltage
automatically: that is to take a varying voltage level
and turn it into a constant voltage level.
6. Contd…
• A simple AVR consists of:-
1. Amplifier,
2. Exciter,
3. Generator and
4. Sensor.
9. 4. PID CONTROLLER
• PID (proportional-integral-derivative) control
is one of the earlier control strategies.
Fig: Block Diagram of PID Controller
10. Contd…
• PID controller has all the necessary dynamics:
• Fast reaction on change of the controller input (D
mode),
• Increase in control signal to lead error towards zero (I
mode) and
• Suitable action inside control error area to eliminate
oscillations (P mode).
• The o/p of PID controller is given as:
11. Contd…
• Table : Effect of each controllers Kp, Ti and Td on a
closed-loop system
12. 5. FOPID Controller
• Fractional-order calculus is an area of mathematics
that deals with derivatives and integrals from non-
integer orders.
• In fact, in principle, they provide more flexibility in
the controller design, with respect to the standard PID
controllers, because they have five parameters to
select (instead of three).
• The concept of FOPID controllers was proposed by
Podlubny in 1997 (Podlubny et al., 1997; Podlubny,
1999a).
13. Contd…
• It is Clear, by selecting λ = 1 and μ = 1, a classical PID
controller can be recovered. Using λ = 1, μ = 0, and λ = 0, μ =
1, respectively corresponds to the conventional PI & PD
controllers.
• All these classical types of PID controllers are special
cases of the FOPID controller.
•
14. Contd…
• The mathematical representation of such a controller
is as follows:
• ADVANTAGES OF F-O CONTROLLER
1. If the parameter of a controlled system changes, a fractional
order controller is less sensitive than a classical PID controller.
2. FOC has two extra variables to tune. This provides extra
degrees of freedom to the dynamic properties of fractional order
system.
19. Contd…
• 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.
20. Contd…
FOPID Tuning
• Ziegler-Nichols Type Tuning Rules
• First set of tuning rules
• The first set of tuning rule is given as
• P=-0.0048+0.2664L+0.4982T+0.0232L2-0.0720T2-0.0348TL
27. Contd…
2. Origin
• 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.
28. Contd…
• Each particle adjusts its travelling speed dynamically
corresponding to the flying experience of itself and its
colleagues.
• Each particle keeps track:
• its best solution, personal best, pbest
• the best value of any particle, global best, gbest
29. Contd…
• Each particle modifies its position according to
• Its current position
• Its current velocity
• The distance between
its current position and
pbest
• The distance between its
current position and pbest
32. Contd…
Particle update rule
p = p + v
With
v = v + c1 * rand * (pBest – p) + c2 * rand * (gBest – p)
where
• p: particle’s position
• v: path direction
• c1: weight of local information
• c2: weight of global information
• pBest: best position of the particle
• gBest: best position of the swarm
• rand: random variable
33. Contd…
1. Create a ‘population’ of agents (particles) uniformly
distributed over X
2. Evaluate each particle’s position according to the
objective function
3. If a particle’s current position is better than its
previous best position, update it
4. Determine the best particle (according to the
particle’s previous best positions)
34. Contd…
5. Update particles’ velocities
6. Move particles to their new positions:
7. Go to step 2 until stopping criteria are satisfied
47. Contd…
• the figure shows the step response of AVR which is
tuned by Cohen Coon open loop tuning method.
48. Contd…
• The figure shows the Simulink model of AVR using
FOPID controller which is tuned by the conventional
tuning method i.e. Ziegler Nichols open loop tuning
method for the first set of tuning rules
49. Contd…
• The figure shows the step response of AVR using
fractional order PID controller which is tuned by the
ZN tuning method for the first set of tuning rules
50. Contd…
• The figure shows the Simulink model of AVR using
FOPID controller which is tuned by the bio inspired
optimization method i.e. Particle Swarm Optimization
Technique.
51. Contd…
• The figure shows the step response of AVR using
fractional order PID controller which is tuned by the
Particle Swarm Optimization Technique based on bio
inspired method
52. Contd…
• The figure show the comparative model of AVR using PID
controller tuned by ZN & CC open loop tuning method and
Fractional Order PID controller tuned by ZN & Particle
Swarm Optimization method respectively.
53. Contd…
• The figure shows the comparative step response of AVR
obtained by the PID controller tuned by ZN & CC open loop
tuning method and FOPID controller tuned by conventional
tuning method i.e. ZN tuning method for the first set of tuning
rule
54. Contd…
• Now the following table shows the comparative
analysis of PID controller tuned by ZN & CC and
FOPID controller tuned by ZN & PSO for AVR.
From the table 8.1 it is clear that the settling time of
the response for AVR obtained by FOPID controller
tuned by Particle Swarm optimization is better than
all the responses obtain by different methods
performed and it desirable condition.
56. 9. Conclusion
• Hence a controller is developed based on Particle
Swarm Optimization Technique to simulate an
Automatic Voltage Regulator (AVR) for a
synchronous generator in order to achieve better
stability of the system and fulfil the requirements of
good excitation control.
