Model-Based Design of an Optimal Lqg Regulator for a Piezoelectric Actuated Smart Structure Using a High-Precision Laser Interferometry Measurement System

Abstract

Smart structure control systems commonly use piezoceramic sensors or accelerometers as vibration measurement devices. These measurement devices often produce noisy and/or low-precision signals, which makes it difficult to measure small-amplitude vibrations. Laser interferometry devices pose as an alternative high-precision position measurement method, capable of nanometer-scale resolution. The aim of this research is to utilize a model-based design approach to develop and implement a real-time Linear Quadratic Gaussian (LQG) regulator for a piezoelectric actuated smart structure using a high-precision laser interferometry measurement system to suppress the excitation of vibratory modes. The analytical model of the smart structure is derived using the extended Hamilton Principle and Euler-Bernoulli beam theory, and the equations of motion for the system are constructed using the assumed-modes method. The analytical model is organized in state-space form, in which the effects of a low-pass filter and sampling of the digital control system are also accounted for. The analytical model is subsequently validated against a finite-element model in Abaqus, a lumped parameter model in Simscape Multibody, and experimental modal analysis using the physical system. A discrete-time proportional-derivative (PD) controller is designed in a heuristic fashion to serve as a baseline performance criterion for the LQG regulator. The Kalman Filter observer and Linear Quadratic Regulator (LQR) components of the LQG regulator are also derived from the state-space model. It is found that the behavior of the analytical model closely matches that of the physical system, and the performance of the LQG regulator exceeds that of the PD controller. The LQG regulator demonstrated quality estimation of the state variables of the system and further constitutes an exceptional closed-loop control system for active vibration control and disturbance rejection of the smart structure