% Lumped model of the electrostatic actuator
% Spring restrained parallel-plate capacitor - static equlibirum
% G. K. Ananthasuresh for MEAM 550
clear all
clg
clc
axis normal

% Input
k = 3.1696; % Spring constant
g0 = 1.6E-6; % Initial gap
A = 250*50E-12; % Area of the plate
V_PI = sqrt( 8*k*g0^3 / 27 / 8.854e-12 / A ); % Pullin voltage

i = 0;

for V = 0.01:0.01:V_PI+0.01,
i = i + 1;
C3 = 1;
C2 = -2*g0;
C1 = g0^2;
C0 = -8.854E-12*V^2*A/2/k;
C = [C3 C2 C1 C0];
soln = roots(C)*1E6;

px(i) = V;
py(i,1) = soln(1);
py(i,2) = soln(2);
py(i,3) = soln(3);
end

plot(px,py(:,3),'-b','LineWidth',2);
hold on
plot(px,py(:,2),'-g','LineWidth',2);
hold on
plot(px,py(:,1),'-r','LineWidth',2);

legend('Stable','Unstable','Infeasible');
xlabel('Voltage (V)');
ylabel('Displacement (um)');
grid




