For the Micro Electro Mechanical System for surface scanning shown below, driven by an electrostatic attraction force, the following equation drives the membrane:

This device’s operational mechanism, which can measure distances smaller than a pico-meter (10-12 m), is
illustrated in the following figure:

The displacement x of the following figure is measured from the equilibrium position of the membrane:

SOLVE: Linearize the system around an equilibrium point(x̅,v). Find the transfer function G(s) = X(s)/V(s) that is valid about the equilibrium. Show that G(s) becomes unstable for x̅ > x_0 / 3.

  
 
 

f(v,x) = 2 & Av 2(x - x) f(v,x) = 2 & Av 2(x - x)