Advanced control engineering (S.R. Burns, 2001)

e

ce

NB

NM

NS

Z

PS

PM

PB

NB

–5

–4

–3

–3

–2

–1

0

NM

–4

–3

–3

–2

–1

0

1

NS

–3

–3

–2

–1

0

1

2

Z

–3

–2

–1

0

1

2

3

PS

–2

–1

0

1

2

3

3

PM

–1

0

1

2

3

3

4

PB

0

1

2

3

3

4

5

$

#

$

$ #

1

Connections

Activation

function

wj 1

∑

fj

x1

yj

$

s

s

(a) Hard-Limiting (Unit Step)

(b) Linear (Ramp)

f(s)

f(s)

1.0

1.0

(c) Hyperbolic Tangent

(d) Sigmoid

b

b = bias

b

x1

b

y1

b

x2

b

y2

x3

b

Input

Hidden

Output

layer

layer

layer

# $ #

$

$

$

$

$

$

$

$

$

$

$

#

#

#

$

$

$

$

$

$

$

$ $

$

$

$

$

$

#

$

$

#

$

$ #

$

$

$

$

#

$

$ #

$

$

yj

Output layer

j = 1

( = 2)

y0 = 1

w10

w13

w11

w12

y1

y3

y2

j = 1

j = 2

j = 3

Hidden layer w10

w12

w30

( = 1)

w20

x0

= 1

w31

w11

w22

w21

w32

x0 = 1

x0 = 1

x1

x2