Robust Control and Thermal Analysis of a Reduced Model of Kirchhoff Composite Plate with Random Distribution of Thermopiezoelectric Sensors and Actuators

Abstract

This paper presents an implementation of a robust control LQG-Kalman model applied to composite Kirchhoff plate dynamics. A reduced model of a finite element method and control procedure is considered in the modeling of a structure because of the important number of piezoelectric patches used in control. Replacing the full model with a short model reduces the computational and time costs, especially when the number of degrees of freedom is significant. In robust control, the measurement of all states is not necessary and the observability and estimability criteria can be exploited, while conventional LQR control assumes that the data accessibility of all states is available. For this reason, robust control is proposed to control the random external disturbances and is compared to LQR control to illustrate its practicability and efficiency. The sensors and actuators in the thermo-piezoelectric material are randomly distributed on both sides of the plate to establish the control procedure. A Monte Carlo simulation is used in the selection of the degrees of freedom of sensors presenting high electrical outputs. Numerical simulations are performed to demonstrate the effectiveness of the proposed control procedure in a reduced model and under mechanical and thermal disturbances in comparison with the LQR control.

Keywords

• Kirchhoff plate
• FEM
• reduced model
• active control
• LQR
• LQG