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:

Note: (Proof) | |||

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:

DB | = | ||

= | |||

= |

The output due to a square wave input is about 1.82 DB greater than it would be for a sine wave input when ( )

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