A Linear Integral Resonant Controller for Suppressing Jump-Phenomena in MEMS

This paper demonstrates the effectiveness of a modified Linear Integral Resonant Controller based on its original LTI cousin, known just as the ‘IRC’, for suppressing Jump-Phenomena found in MEMS and other Duffing-Type systems wherein the primary nonlinearity is that of the cubic nonlinearity. A Method of Multiple Scales frequency response is derived, explored and compared with a Runge-Kutta based numerical integration method in order to understand any shortcomings in approximate analytical methods for the analysis of closed-loop nonlinear systems with the inclusion of a stability analysis. It is found that there exist some mild behavioural inconsistencies when comparing closed-loop Method of Multiple Scales to traditional numerical integration. Finally, it is shown that with sensibly chosen controller gains, a MEMS with Jump-Phenomena can be made to behave similarly to a linear second order resonant system opening up the possibilities of Laplace Domain and Linear State-Space techniques once more.