This paper demonstrates the effectiveness of a Modified Linear Integral Resonant Controller (MIRC) based on its original LTI cousin, known just as the ‘IRC’, for suppressing Jump-Phenomenon and hysteresis found in Micro-Cantilevers. 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 inconsistencies when comparing closed-loop Method of Multiple Scales to traditional numerical integration. A suitably designed Modified Integral Resonant Controller is implemented in closed-loop. Both analytical and numerical results agree with each other and show significant damping performance. Efficacy of the proposed control scheme is validated via frequency response plots, phase portraits and quiver plots.
Bibliographical noteCredit author statement
James MacLean: developed the theory and performed the simulations. Sumeet S. Aphale: supervised the overall research, helped with theoretical development, presentation of results and document formatting.