DETERMINATION OF PARAMETERS FOR CART AND MOTOR: SQUARE WAVE INPUT
Square Wave Input:
For
Due to static friction inherant in the cart and motor system
it is difficult to obtain an accurate Bode plot when pure
sinusoidal inputs are used. When the voltage to the motor
is near zero the system tends to stick and not move at all.
To overcome this problem we will use a square wave
input instead of a sine wave input. We now examine the
response we expect to get using a square wave input.
A square wave of frequency
can be expressed as the sum of sine waves as follows:
Since our transfer function for the cart and motor is
linear, the output due to a square wave is the sum of the
outputs due to each of the sinusoudal terms which make up the
square wave.
From our earlier analysis we know the magnitude of the
output oscillations due to an input of
is:
For
this becomes
For a square wave input expressed as the sum of a
series of sinusoidal inputs the magnitude of the
output becomes:
We thus expect the output due to a square wave input to be
about 1.233 times the output due to a sine wave input when (
)
Expressed in decibels this becomes:
The output due to a square wave input is about 1.82 DB greater
than it would be for a sine wave input when (
)
(Proof)
