Actuator/controller design for a novel reduced model of piezoelectric beam equations
These Wolfram Demonstration Projects are produced for the "AMS - PME Undergraduate Student Poster Session" of the Joint Mathematics Meeting'23 presentation in Boston, USA, held on Friday, January 6, 2023.
Co-authors: Rafi Emran, Ahmet Kaan Aydin
Project members: Jacob Walterman, Ahmet Kaan Aydin
This material is based upon work supported by the National Science Foundation under Cooperative Agreement No. 1849213. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
The partial differential equations model governing the mechanical vibrations and total charge on a piezoelectric smart beam will be discussed, with an emphasis on the actuator/sensor design for control and stabilization of the system through two state feedback sensors/controllers. The solutions of the closed-loop system is shown to decay exponentially in its natural energy space. However, its Finite Difference approximations do not retain the exponential stability uniformly as the mesh parameter tends to zero. This discrepancy is eliminated by the Fourier Direct Filtering Technique. The process of determining the optimal feedback gains and damping rate will be discussed.
Wolfram Demonstrations Projects, which are currently under revision at Wolfram, help simulate the models in real time for given control parameters. These demonstrations heuristically show the (or the lack of) exponential stability of the closed-loop system where sensor measurements are fed back to the actuator.