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plc pid -25.9

Summation Block: e = Cdesired – Cactual (1)

Controller: V= Ke (2)

cp

Current Amplifier: Vm = V(3)

c

2

K

?? Km

m

????

---------? Servomotor: - ?+ ? ?= -------Vm (4)

?? JR ?

dt JR?

??

d

(5)?= --- ?actual

dt

?actual (6)

Ball Screw: x = -------------

TPI

Encoder:

Cactual = PPR(?actual )(7)

Figure 25.9 A Servomotor Feedback Controller

The system equations can be combined algebraically to give a single equation for the entire system as shown in Figure 25.10 .The resulting equation (12) is a second order non-homogeneous differential equation that can be solved to model the performance of the system.

2

?

d 2 Km ?d Km

??

(21.4), (21.5) ?? + ? ??= -------V(21.8)

---------? --

- ?actual JR ?? ?actual m

?? JR?

dt dt ?

??

(21.2), (21.3) V= Ke (21.9)

mp

(21.1), (21.9) V= K()(21.10)

m pCdesired – Cactual

2

?

d 2 Km ?d Km

??

(21.8), (21.10) ???actual + ? ??= -------K(

-- ---------? --- ?actual JR?pCdesired – Cactual )(21.11)

?? JR ?? ?

dt dt

??

2

?

d 2 Km ?d Km

??

(21.7), (21.11) ???actual + ? ??= -------K(

-- ---------? --- ?actual JR?pCdesired – PPR?actual )

?? JR ?? ?

dt dt

??

2 (21.12)

d 2 Km ?dK(PPR)Kp?KK

?

?? ??? ???

--------? --- m pm

-- ?actual + -JR ?? ?actual + ---------------------------- ?actual = --------------Cdesired

?? JR ??

dt dt ? JR ?

??

plc pid -25.10

Figure 25.10 A Combined System Model

A proportional control system can be implemented with the ladder logic shown in Figure 25.11 and Figure 25.12.

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