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Dynamic Behavior
Apart from the amplifier, controller and sensor bandwidth, the maximum operating frequency of a tilt platform is also depending on its mechanical resonant frequency. To estimate the effective resonant frequency of the tilt mirror system (platform + mirror), the moment of inertia of the mirror substrate must be calculated first.Moment of inertia of a rotationally symmetric mirror
IM = m [(3R² + H²)/12 + (H/2 + T)²]
Moment of inertia of a rectangular mirror
IM = m [(L² + H²)/12 + (H/2 + T)²]
where,
m = Mirror mass [g]IM = Moment of inertia of the mirror [gmm²]
L = Mirror length perpendicular to the tilt axis [mm]
H = Mirror thickness [mm]
T = Distance pivot point to platform surface (see individual technical data) [mm]
R = Mirror radius [mm]
Using the resonant frequency of the unloaded platform (see individual technical data) and the moment of inertia of the mirror substrate, the system resonant frequency is calculated according to the following equation:
Resonant frequency of a tilt platform/ mirror system
f' = f0 * 1/ Ö(1 + IM /I0)
where,
f’ = Resonant frequency of platform with mirror [Hz]f0 = Resonant frequency of unloaded platform [Hz]
I0 = Moment of inertia of the platform (see individual technical data) [gmm²]
IM = Moment of inertia of the mirror [gmm²]
For more information on static and dynamic behavior of piezo actuators read corresponding pages in "Tutorial: Piezoelectrics in Positioning" section.
