Discrete-time controller synthesis of a piezoelectric cantilever beam with the consideration of finite precision

This paper describes a typical application of controlling the slope of a piezoelectric cantilever. An analytical model for the cantilever beam describing the dynamic relationship between tip slope and the applied voltage is introduced. With closed loop feedback control strategy, the trajectory tracking error of the cantilever deflection angle is evaluated. To control the slope of the cantilever precisely with discrete-time devices, a suitable processor with enough resolution is necessary. With the consideration of limited resolution, an estimation method of required wordlength for the digitalized controllers is also proposed. A discrete-time LQR controller realized with different resolutions was used to validate the proposed method.