Abstract    In this paper the problems of state estimation, tracking control and shape control in a micro-cantilever beam with nonlinear electrostatic actuation are investigated. The system’s partial differential equation of motion is converted into a set of ordinary differential equations by projection method. Observabillity of the system is proven and a state estimation system is designed using extended Kalman filter (EKF) algorithm. A tracking control system is designed to make a specific point of the beam follow a reference signal. The effect of mode selection to include in model on controller performance is also investigated. Based on the tracking controller a shape control algorithm is designed to form the shape of beam into a desired shape. The proposed algorithms are validated by numerical simulation and resulted in a promising performance.

Keywords    micro-cantilever, electrostatic actuation, state estimation, tracking control, shape control.

چکیده    در اين مقاله مسأله تخمين متغيرهاي حالت، کنترل رهگيري و کنترل شکل يک ميکروتير يکسردرگير با تحريک غيرخطي الکترواستاتيکي مورد بررسي قرار گرفته است. براي اين منظور معادلات ديفرانسيل پاره‌اي سيستم با استفاده از روش گالرکين به يک ست از معادلات ديفرانسيل معمولي تبديل شده است. پس از اثبات مشاهده‌پذيري سيستم يک الگوريتم تخمين متغيرهاي حالت براي آن بر اساس روش کالمن فيلتر توسعه يافته طراحي شده و از متغيرهاي تخمين زده شده، در سيستم کنترل مورد بحث استفاده شده است. سيستم کنترل به منظور کنترل مسير حرکت نقاط مورد نظر از تير طراحي شده و اثر مودهاي منتخب براي کنترل بر روي اين کنترل کننده مورد بررسي قرار گرفت. در پايان با استفاده از کنترل‌کننده مسير طراحي شده، يک الگوريتم کنترل شکل براي تير پيشنهاد گرديد. مجموعه اين الگوريتم‌ها با استفاده از شبيه‌سازي عددي صحه‌گذاري شده و نتايج مورد بحث قرار گرفته‌اند.

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