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Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems. Abstract: - - PowerPoint PPT Presentation
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Mohammed MahdiComputer Engineering
DepartmentPhiladelphia University
Monzer KrishanElectrical Engineering
DepartmentAl-Balqa Applied
University [email protected]
Ali. Al-khwaldeh Computer Engineering
DepartmentPhiladelphia University
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
PEB PEM PES ZE NES NEM NEB
ZU NUS NUM NUB NUB NUB NUB NCEB
PUS ZU NUS NUM NUM NUM NUB NCEM
PUM PUS ZU NUS NUS NUM NUB NCES
PUB PUM PUS ZU NUS NUM NUB ZCE
PUB PUM PUS PUS ZU NUS NUM PCES
PUB PUM PUM PUM PUS ZU NUS PCEM
PUB PUB PUB PUB PUM PUS ZU PCEB
(1)
(2)
Where and are the maximum elements in and respectively, while & are the maximum measured error and change-in-error.
With regard to the output (control action) scaling factor GU, it is simply
set to
maxm
Nm e
VGe
maxm
Mm ce
WGce
VN 0 WM 0 E CE
| |maxem | |maxcem
mm GceorGe ..max
1
(3)
For the next instructions:-
(4)
A stopping iteration criterion is taken based on minimizing a Performance Index of the form:
(5)
m
mN
m GeGUandGce
SP
VGe
1,0.1,
max,
m
Mm
Nm ce
WGce
SP
VGe
mm GceorGeGU
..max
1
T
m dteIP0
25.0.
n-node
hidden layer
.
.
.
.
.
.
.
cem
2-node
input layer
Wij i= 1, 2
j=1... n
tansh
tansh
u
1-node
output layer
Wj1
me
100100
100)(
2
sssG
0 0.5
1 1.5
2
2.5 3
3.5
4 4.5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
y ( t )
SP
Controlled response with P.I = 13.54
uncontrolled
time sec.
100100
100)(
2
sssG
Fig. (2) Controlled & uncontrolled responsesof the underlying unstable system
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14 16 18 20
y ( t )
SP P.I = 15.94 , y s.s = 1.013
time sec.
G ss s
( )
100
100 1002
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
0 2 4 6 8 10 12 14 16 18 20
y ( t ) P.I = 51.3
time sec.
Fig.(5) Effect of steady-state disturbanceimposed on the controlled response
Fig. (6) Generalization feature to track stair case input signal
0)0(.,
sin
4sin
1
22
12
211
xwithxy
uxxx
uxxx
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5 3 3.5 4
y ( t )
SP
uncontrolled P.I= 1218.3
time sec.
Fig. (8): Uncontrolled unity feedback response of the underlying non-linear system
-0 .5
0
0.5
1
1.5
2
2.5
0 2 4 6 8 1 0 1 2 14 16 18 2 0
y ( t )
input ( t )
P.I = 0.00007
time sec.
Fig. (9): Controlled response of the underlying non-linear system
Fig. (10) Generalization to track ramp input
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