Steering the deflection of a piezoelectric bender

Motion planning and open-loop (steering) control synthesis for a cantilever beam with a uniformly distributed piezoelectric actuator on the whole surface, called a piezoelectric bender is considered. With a flatness based control design method an exact formula is derived for the control voltage which must be applied in order to achieve a prescribed deflection in a specified finite time. This control is given as an infinite power series the convergence of which is ensured by an appropriate choice of the desired trajectory of the "flat" or "basic output".