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In this paper, the tip tracking control problem of a Timoshenko micro-cantilever beam is investigated. The beam is actuated by a piezoelectric layer laminated on one side of the beam. Dynamic equations of the beam and piezoelectric layer are found using the Hamilton principle. By employing the Galerkin projection method, state space representation of the system is derived. Then, a cascade control loop is used for tracking control of the beam’s tip. The cascade control structure consists of an inner loop stabilizer and an outer loop proportional-integral-derivative controller. The stabilizer has a linear feedback form whose states are obtained through a linear observer which is based on the beam tip displacement measurement. Stability analysis of the inner loop stabilizer is performed to study the effects of higher un-controlled modes on performance of the controlled system. Simulation results show the effectiveness of the proposed control method.

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In this paper flexural vibrations of an electrostatically actuated cantilever microbeam in an incompressible inviscid stationary fluid have been studied. By applying ''Three dimensional aerodynamic theory'' pressure jump across the microbeam has been investigated and the inertial effects of fluid on microbeam dynamics have been modeled as a mass added to microbeam mass. Magnitude of the added mass has been calculated for various aspect ratios of cantilever microbeams and compared with those of clamped-clamped microbeams. To investigate the dynamic characteristics, it has been considered that the microbeam has been deflected by a DC voltage, V DC and then the dynamic characteristics and forced response of the system have been considered about these conditions. Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been applied to solve the nonlinear static and dynamic governing equations, respectively. Water by neglecting viscidity effects, as an instant has been considered as a surrounding fluid and the frequency response of the microbeam has been compared with that of vacuum conditions. It has been shown that because of the added mass effects in watery environment, the natural frequencies of the microbeam decrease. Because of the higher dielectric coefficient and increasing electrical stiffness and decreasing total stiffness consequently, maximum amplitude of the microbeam vibrations increases in watery environment, compared with vacuum. Moreover, it has been shown that increasing the DC voltage, increases the electrical stiffness and maximum amplitude of the microbeam vibrations, consequently, It has been shown that in higher voltages (near pull-in voltage), the rate of variation of resonance frequency and maximum amplitude is stronger than lower voltages.

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