Mohammed MahdiComputer Engineering

DepartmentPhiladelphia University

moh_19592002@yahoo.co.uk

Monzer KrishanElectrical Engineering

DepartmentAl-Balqa Applied

University krishan97@hotmail.com

Ali. Al-khwaldeh Computer Engineering

DepartmentPhiladelphia University

akhwaldeh@philadelphia.edu.jo

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