Systems Integration and Control Midterm

The parallel plate form of a MEMS electrostatic actuator (Fig. 1) has the dynamics,

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md2y(t) + 􏰀b1 + b2y2(t)􏰁 dy(t) + k1y(t) + k3y3(t) = εAV 2(t) dt2 dt 2 (g0 − y(t))2

y(t) and its derivatives and V (t) are functions of time. m, b1, b3, k1, k3, ε, A, and g0 non-zero constants.

Linearize this equation of motion about the steady-state operating points V (t) = V ̄ , y(t) = y ̄.

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