LQR and LQG-Kalman active control comparison of smart structures with finite element reduced-order modeling and a Monte Carlo simulation

Abstract

The present contribution presents a comparison between two types of controls, namely, the optimal linear quadratic regulator (LQR) and the Kalman-LQG controller using the model order reduction process. Due to numerical constraints, the models of structures have been reduced so that the design of controllers and/or estimators could be performed. The proposed method results in a significant reduction in computational costs for dynamic analysis without compromising on accuracy. Transforming the full order state-space resulting from finite element space to a lower model reduces the simulation time with a few degrees of freedom and helps to implement easily the control without changes in the dynamics of the structure. The estimator Kalman is used here in order to estimate the modal states of the system that are used in modal analysis. In this context, a one-side cantilever Timoshenko beam is chosen with perfectly bonded piezoelectric layers of actuators and sensors to apply this comparison. The Monte Carlo simulation was used to improve the number and location selection of piezoelectric sensors on the chosen beam model. Neglecting environmental effects, numerical results relating to this comparison without and with model order reduction are established. Simulation results are presented to illustrate the effectiveness of the proposed vibration control algorithm for the studied beam.