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In this paper, trajectory tracking control of suspended microchannel resonators (SMRs) is studied. A finite element procedure based on modified strain gradient theory will be used to model the SMR. Finite element methods usually lead to a model with a relatively high number of degrees of freedom. Thus, first, we will utilize the second order Krylov subspace method based on multi-moment matching to obtain a second order bilinear reduced system. Then, an output feedback controller and an optimal controller which take much less computation time and effort will be designed for the reduced system. The SMR is a micro-resonator which oscillates in a special frequency in practical cases, and thus tracking the desired paths is considered here as the control objective. Simulation results show the excellent performance of the proposed controllers.

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