Proxim RangeLAN2 7920 Manual de usuario descargar pdf (Pagina 45)

Now if we apply a drive signal to the plant that is proportional to E, then we can say that

our feedback mechanism invokes proportional error control in our system. The equation

of motion for such motion is given by:

(5)

meqeq

TJF

θθ

&&&

where

θ =

and

d θ

θ =

is the motor torque,

eqlm

JJJ

, lJ is the inertia of the load reflected through the

gears and

is the inertia of the motors,

is friction and

is angle. We can also say

that:

(6)

TKI

where

is the motor current and

is a constant. Equating (4) and (5) gives:

(7)

KIJF

θθ

&&&

If we invoke proportional control, we can assume that we will apply a current that is

proportional to the error:

∝

or we can say using equation (3) that

()

θθ

=−

where

is a constant. Therefore:

(8) θθθθ

&&&

FJk

+=− )(

Here we have absorbed the constants

into

and rewritten

for

and

for

to simplify. Now if we assume that

, then our equation of motion is:

(9) 0=++ θθθ

kFJ

&&&

If we assume a solution

and let kk

= then (8) reduces to:

(10)

JqFqk

++=

Solving for q gives:

(11)

FFJk

−±−

We see that if:

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Proxim RangeLAN2 7920 Manual de usuario Pagina 45

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