Pointing angle control of electrostatic micro mirrors with modified sliding mode control algorithm for precision control

A method for controlling a MEMS having a pivotable micro mirror above a substrate, a first and second capacitors disposed between the mirror and the substrate so that as the mirror pivots, an effective air gap of the capacitors changes, the method comprising the steps of:

• defining a deflection angle for the mirror as a set point,
• comparing an actual position of the mirror with a desired position by measuring the difference in capacitances in the capacitors,
• controlling the position of the mirror using sliding mode control to adjust the mirror so that it achieves a desired reflection angle according to the following relationship:
• e(t)=s(t)−u(t)−λ(du(t)/dt)
• where e(t) is the error signal, s(t) is the desired deflection angle, u(t) is the angle readout, and λ is a selected value that varies depending on the position of the mirror.

A MEMS micro mirror comprising:

• a mirror, a substrate below the mirror,
• a gimbal structure for movably supporting said mirror about said first and a second axes;
• a position detector that determines the position the mirror,
• a controller implementing a first order differential sliding mode control to move the mirror to a desired position, wherein the differential gain varies depending on the position of the mirror,
• wherein the position detector determines the position of the mirror by variations in capacitance between the mirror and the substrate and,
• wherein the mirror is controlled using sliding mode control to adjust the mirror so that it achieves the desired deflection angle according to the following relationship e(t)=s(t)−u(t)−λ(du(t)/dt).

A MEMS device including a movable component comprising:

• a position detector that determines the position of the movable component,
• a controller that implements a sliding mode control process to move the movable component to a desired position wherein the sliding mode control is implemented according to the following relationship:
• e(t)=s(t)−u(t)−λ(du(t)/dt)
• where e(t) is the error signal, s(t) is the desired deflection angle, u(t) is the angle readout, and λ is a selected value that varies according to the distance the set position of the mirror and the actual position of the mirror.