0195136047.pdf

16.2 FEEDBACK CONTROL SYSTEMS 785

The transfer functionMof the closed-loop system is then given by

M=

C

R

=

G

1 +HG

=

direct transfer function

1 +loop transfer function

(16.2.3)

The block diagrams of complex feedback control systems usually contain several feedback
loops, which might have to be simplified in order to evaluate an overall transfer function for the
system. A few of the block diagram reduction manipulations are given in Table 16.2.1; no attempt
is made to cover all possibilities.

TABLE 16.2.1Some Block Diagram Reduction Manipulations

Original Block Diagram Manipulation Modified Block Diagram

Cascaded elements

Addition or subtraction

(eliminating auxiliary

forward path)

Shifting of pick-off

point ahead of block

Shifting of pick-off

point behind block

Shifting of summing

point ahead of block

Shifting of summing

point behind block

Removing H from

feedback path

Eliminating

feedback path

RCG 1 G 2

G 1

G 2

RC+

+−

R G 1 G 2 C

R G 1 +− G 2 C

REG

C

+

−

REG

C

+

−

G

H

RC+

−

1/H H G

R + C

−

G

G

R E

C

+

−

G

1 /G

RE

C

+

−

G

1 /G

RC

G

H

RC+

−

RCG

G

1 + GH

RC

RCG

G

G

RC