Transcript Simulation of Neurofuzzy Controller Design for - CEE-SECR

Mohammed Mahdi
Computer Engineering
Department
Philadelphia University
[email protected]
Monzer Krishan
Electrical Engineering
Department
Al-Balqa Applied University
[email protected]
Ali. Al-khwaldeh
Computer Engineering
Department
Philadelphia University
[email protected]
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Abstract: Rule-based fuzzy control, in which the plant model is replaced by a number of
control rules, provides an alternative approach and has been developed
significantly. On the other hand, the potential benefits of neural networks
extend beyond the high computation rates provided by the massive parallelism
to provide a greater degree of robustness. integrating these two approaches
brings what is so-called neurofuzzy system which gives rise to gain the merits
of both approaches.
Structural and functional mapping from a fuzzy logic-based algorithm to the
neural network-based approach has been considered with a thorough design
procedures for SISO control systems. Simulation technique will be implemented
through out this research using C++ programming language to verify the
proposed controller capabilities.
Keywords: - Functional Neurofuzzy Controller (FNFC), Multi-Layer Perceprtron
Neural Networks (MLP NN)
Simulation has many advantages, and even some disadvantages.
These are listed by Pegden, Shannon, and Sadowski [1]. The
advantages are:-
1.New policies, operating procedures, decision rules, information
flows, organizational procedures, and so on can be explored
without disrupting ongoing operations of the real system.
2. New hardware designs, physical layouts, transportation
systems, and so on, can be tested without committing resources
of their acquisition.
3. Hypotheses about how or why certain phenomena occur can be
tested for feasibility.
4. Time can be compressed or expanded allowing for a
speed up or slow down of the phenomena under
investigation.
5. Insight can be obtained about the interaction of variables.
6. Insight can be obtained about the importance of variables
on the performance of the system.
7. A simulation study can help in understanding how the
system operates rather than how individuals think the
system operates.
8. "What if" questions can be answered? This is particularly
useful in the design of new systems.
While the disadvantages are:1- Simulation results may be difficult to interpret.
2- Simulation modeling and analysis can be time
consuming and expensive
A classical 49-fuzzy rule as in table (1) below, with triangular fuzzifier of
7-fuzzy sets for each controller input error and its rate of change and center
of gravity defuuzifier a fuzzy logic controller of Mamdani style is
designed.
Table (1): 49-fuzzy production rule
NCEB
NEB
NUB
NEM
NUB
NES
NUB
ZE
NUB
PES
NUM
PEM
NUS
PEB
ZU
NCEM
NUB
NUM
NUM
NUM
NUS
ZU
PUS
NCES
NUB
NUM
NUS
NUS
ZU
PUS
PUM
ZCE
NUB
NUM
NUS
ZU
PUS
PUM
PUB
PCES
NUM
NUS
ZU
PUS
PUS
PUM
PUB
PCEM
NUS
ZU
PUS
PUM
PUM
PUM
PUB
PCEB
ZU
PUS
PUM
PUB
PUB
PUB
PUB
Gem 
VN
em max
Gcem 
WM
cem max
(1)
(2)
Where VN  0 and WM  0are the maximum elements in E and CE
| em |max & | cem |max
respectively, while
are the maximum measured error
and change-in-error.
With regard to the output (control action) scaling factor GU, it is simply
1
set to
maxGem .or.Gcem 
Gem 
VN
, Gcem  1.0, and
SP
GU 
1
Gem
(3)
For the next instructions:-
Gem 
VN
WM
, Gcem 
SP
cem max
GU 
1
maxGem .or.Gcem 
(4)
A stopping iteration criterion is taken based on minimizing a Performance
Index of the form:
T
P.I  0.5 e 2 m dt
0
(5)
Wij i= 1, 2
tansh
j=1... n
em
.
W j1
u
.
ce m
.
2-node
input layer
.
.
tansh
.
n-node
.
hidden layer
1-node
output layer
100
G(s)  2
s  100 s  100
4.5
4
y(t)
G (s) 
3.5
100
s 100 s  100
2
3
2.5
Controlled response with
2
P.I = 13.54
uncontrolled
1.5
SP
1
0.5
time sec.
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Fig. (2) Controlled & uncontrolled responses
of the underlying unstable system
0.18
0.2
1.2
y(t)
1
SP
P.I = 15.94 , y s.s = 1.013
0.8
0.6
0.4
G ( s) 
100
s 2  100 s  100
0.2
time sec.
0
0
2
4
6
8
10
12
14
16
18
16
18
20
Fig.(5) Effect of steady-state disturbance
imposed on the controlled response
3.5
y(t)
P.I = 51.3
3
2.5
2
1.5
1
0.5
time sec.
0
0
2
4
6
8
10
12
14
20
-0.5
-1
Fig. (6) Generalization feature to track stair case input signal
x1  sin x1  x 2  4u 

2
x 2  x1  sin x 2  u 
y  x1 , with.x(0)  0
3
y(t)
2.5
2
uncontrolled P.I= 1218.3
1.5
SP
1
0.5
time sec.
0
0
0.5
1
1.5
2
2.5
3
Fig. (8): Uncontrolled unity feedback response of the
underlying non-linear system
3.5
4
Fig. (9): Controlled response of the underlying non-linear system
2.5
y(t)
2
1.5
P.I = 0.00007
1
input ( t )
0.5
time sec.
0
0
2
4
6
8
10
12
14
-0.5
Fig. (10) Generalization to track ramp input
16
18
20
Conclusion:- The merits of linking both fuzzy logic and neural network
approaches are obvious, confirmed through the
comprehensive
knowledge
extraction,
robustness,
adaptivity and generalization characteristics offered by the
neurofuzzy system.
- Simulation gives a very good insight view to the underlying
system before implementation which yields to less cost and
efforts.
- Simulation results in this research showed the good
capability of the proposed controller when used to control
unstable and non-linear systems.
Thank You