A finite element analysis approach with integrated PID control for simultaneous precision positioning and vibration suppression of smart structures

Abstract

This paper focuses on the development of an ANSYS finite element analysis (FEA) environment with integrated PID control scheme for simultaneous precision positioning and vibration suppression of smart composite structures with piezoelectric flat patches acting as actuators. This environment includes three modules: structural modeling, PID controller design, and dynamic analysis of smart structures. Two types of PID controllers are investigated, namely, PID vibration suppression (PID-VS) controller and PID simultaneous precision positioning and vibration suppression (PIDSPPVS) controller. The PID-VS controller is suitable to perform only vibration suppression with no positioning capability. The PID-SPPVS controller is equipped with SPPVS capabilities. The characteristics of individual control gains and their behavior with respect to each other for the two PID controllers are also studied. The gain selection for the PID-VS controller is based on obtaining the best VS while the gain selection for the PID-SPPVS controller is based on achieving the best positioning accuracy and VS simultaneously. In this study, a horizontal cantilevered graphite/epoxy composite beam with one surface-mounted ACX piezoelectric flat patch located at the beam root is first modeled. Next, the FE modal analysis is performed to determine the natural frequencies and hence the time step interval needed for the FE transient analysis. During the transient analysis, the mid-point of the beam tip is subjected to different types of external excitations such as sine loadings with different frequencies as well as random forces to evaluate the two PID controller performances. It is demonstrated that the FEA model with integrated PID-SPPVS controller is able to reach the desired position in a much shorter time in comparison to the PID-VS controller. Vibration amplitude reduction capabilities for the both PID controllers are very similar, although the PID-VS controller performs slightly better. This study also implies that the integrated FEA environment, consisting of the structural modeling of active composite structures with piezoelectric flat patches, modal and transient analyses, controller design, and simulation, provides a powerful tool for the design, analysis, and control of smart structures with SPPVS capabilities.