A robust controller design for a piezoelectric bimorph nonlinear actuator is considered in this paper. The nonlinear dynamics of the actuator are first linearized using the stochastic equivalent linearization method and reformulated into a standard almost disturbance decoupling problem. Then a robust controller, which is explicitly parameterized by two tuning parameters, is carried out using a so-called asymptotic timescale and eigenstructure assignment approach. The parameterized controller can be tuned by adjusting the parameters to achieve disturbance decoupling and other design goals for the problem that we consider. Simulation results of time-domain responses show that the design is very successful in terms of steady-state tracking error and settling time as well as other performances. Index Terms-Actuators, disturbance decoupling, H H H1 1 1 control, piezoelectric devices, robust control, suboptimal control. I. INTRODUCTION TO THE PROBLEM P IEZOELECTRICITY is a fundamental process in electromechanical energy conversion. It relates electric polarization to mechanical stress/strain in piezoelectric materials. Under the direct piezoelectric effect, an electric charge can be observed when the materials are deformed. The converse or the reciprocal piezoelectric effect is when the application of an electric field can cause mechanical stress/strain in the piezo materials. There are numerous piezoelectric materials available today with PZT (lead zirconate titanate), PLZT (lanthanum modified lead zirconate titanate), and PVDF (piezoelectric polymeric polyvinylidene fluoride) to name a few (see [11]). Piezoelectric structures are widely used in applications that require electrical to mechanical energy conversion coupled with size limitations, precision, and speed of operation. Typical examples are micro-sensors, micro-positioners, speakers, medical diagnostics, shutters and impact print hammers. In most applications, bimorph or stack piezoelectric structures are used because of the relatively high stress/strain to input electric field ratio (see [11]). The present work is motivated by the possibility of applying piezoelectric micro-actuators in magnetic recording. The exponential growth of area densities seen in magnetic disk
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