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6.2. 6740-XX Notch FUter Module

6.2.1 Background Theorv

All mechanical systems are subject to vibrations via extemal excitation forces. The degrees of

freedom of a vibrating mechanical system are defined by the number of independent coordinates

required to identify its displacement during vibration. If we have a Cartesian coordinate system

witii

y, and z axis, then for a freely vibrating body, we can have six degrees of

freedom.

This

includes translational and rotational vibration in each of the three axis. Each of these possible

vibrations is referred to as a mode of vibration. Each mode of vibration has a natural frequency

associated with it that is independent of all the other modes.

For our discussion with respect to the scanner, we will concenfrate on the rotational axial mode

vibration.

The natural frequency Fr of this mode is a fimction of the mirror load inertia and

rotor inertia as well as the torsional spring constant of the rotor shaft which couples the two

inertias. The undamped natural resonant frequency of this mechanical system is described by the

equation below:

COR

= k'^[(J,+J2)/J,J2]''', Fr=(OR/27t

where k = rotor torsional spring constant

Jl = mirror load inertia

= rotor inertia

Note that in a real mechanical scanner system damping due to bearing friction, air friction on the

rotor and mirror load, etc. do indeed exist. However, CTI scanners exhibit very low bearing

friction, and the above equation will approximate the resonant frequency quite closely. The

damping constant inversely influences the natural resonant

frequency

slightly. In other words, as

the damping constant increases, the natural resonant

frequency

decreases.

This torsional resonant frequency can exhibit a high Q, which is defined in one sense as the

sharpness and amplitude of the resonant frequency peak. If this resonance occurs in a closed

loop servo system where the gain vs

frequency

has fallen off enough that the (negative) position

feedback phase shift approaches

180°,

and the amplitude peaking at resonance is enough that the

position feedback gain rises near unity, servo loop instability and oscillations will result. This is

the reason for using a notch filter in the forward path of the servo loop, after the summing

amplifier. The notch filter is tuned to remove the

frequency

component ofthe ertor drive signal

sent to the scanner confrol coil which is at the same frequency as the scanner torsional

resonance. This keeps the scanner from being excited at its resonant

frequency.

The rejection of

this driving

frequency

aids the stability ofthe servo by not exciting this natural resonant mode,

and allows the closed loop bandwidth ofthe system to be higher. Higher closed loop bandwidth

allows decreased step response times.

However, this does not mean that the scanner torsional resonance dissappears. Ideally, it is only

that the servo amplifier no longer

"kicks"

the scanner at this frequency.

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