Файл: Advanced control engineering (S.R. Burns, 2001).pdf

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Forward Path

Summing

point

Take-off

R(s)

+

E(s)

point

C(s)

G(s)

–

B(s)

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First Minor Loop

Cascade

R(s) +

+

+

C(s)

–

G1

G2

G3

–

–

H3

H4

H5

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Cascade

Second Minor Loop

R(s)

+

+

C(s)

G2G3

G1

1 + G3H3

–

–

R(s) +

G1G2G3

C(s)

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Transformation

Equation

Block diagram

Equivalent block diagram

1. Combining

X

Y

X

Y

blocks in

Y =(G1G2)X

G1

G2

G1G2

cascade

2. Combining

blocks in

X

Y

+

+

parallel; or

Y = G1X –G2X

G1–G2

eliminating a

X

G1

+

Y

forward loop

+

–

3. Removing a

G2

X

.

G1

+

Y

block from

Y = G

X +G X

G2

G2

a forward

1

– 2

+

–

path

4. Eliminating

Y = G (X + G Y )

X +

Y

X

G1

Y

a feedback

1

– 2

G1

.

1

+

loop

–

– G1G2

+

5. Removing a

X

1 +

Y

block from

Y = G1(X

+

G

2

G1G2

a feedback

– G2Y)

G2

–

loop

+

6. Rearranging

W

+

+

W

+

+

+

summing

+

+

+

Z

+

+

Z = W – X –Y

Y

Z

points

X

–

–

–

–

Y

X

7. Moving a

X

+

Z

X +

G

Z

summing

G

+

Z = GX +Y

+

point ahead

–

–

1

of a block

–

Y

Y

G

8. Moving a

X +

Z

X

G

+

summing

G

+

Z

point

+

+

Z = G(X –Y)

–

beyond

Y

–

Y

G

a block

9. Moving a

X

Y

X

G

take-off

Y = GX

G

Y

point ahead

Y

of a block

Y

G

10. Moving a

X

Y

X

G

. Y

G

take-off

Y = GX

point beyond

X

X

1

a block

G