0195136047.pdf

16.2 FEEDBACK CONTROL SYSTEMS 795

Amplifier

Tachometer generator

Output rate

− Potentiometer Servomotor

−Et

Js^2 + Fs

REK^1 C

p Ka Km

Ea Td

sKo

Figure 16.2.12Block diagram of servomechanism with output-rate damping.

M(s)=

C(s)

R(s)

=

K

Js^2 +(F+Qo)s

1 +

K

Js^2 +(F+Qo)s

=

K

Js^2 +(F+Qo)s+K

(16.2.31)

whereK=KpKaKmis known as the loop proportional gain factor, as stated earlier.
The manner in which output-rate damping effects in controlling the transient response are
most easily demonstrated is by assuming a step input applied to the system. The output-rate signal
appears in opposition to the proportional signal, thereby removing the tendency for an excessively
oscillatory response. With error-rate damping and output-rate damping, the damping ratio can be
seen to be

ξ=

F+Q

2

√

KJ

(16.2.32)

whereQ=QeorQo, in which a term is added to the numerator, while the natural frequency is
unchanged (as given byωn=

√
K/J). The damping ratio can then be adjusted independently
throughQeorQo, whileKcan be used to meet accuracy requirements.

INTEGRAL-ERROR(ORRESET)CONTROL

A control system is said to possess integral-error control when the generation of the output in
some way depends upon the integral of the actuating signal. By designing the servoamplifier such
that it makes available an output voltage that contains an integral term and a proportional term,
integral-error control can be obtained. By modifying the transfer function of the servoamplifier in
the block diagram, the complete block diagram of the servomechanism with integral-error control
is shown in Figure 16.2.14, whereKiis the proportionality factor of the integral-error component.
The direct transmission function is then given by

G(s)=

KpKm(Ki+sKa)

Js^3 +Fs^2

(16.2.33)

and the corresponding closed-loop transfer function becomes

−

Js^2 + (F + Qo)s

RE CK KaKm

p

Figure 16.2.13Simplified block diagram of Figure 16.2.12.