LQR and LQG-Kalman active control comparison of smart structures with finite element reduced-order modeling and a Monte Carlo simulation - El Khaldi, Loukmane; Sanbi, Mustapha; Saadani, Rachid; Rahmoune, Miloud (Frontiers in Mechanical Engineering, 2022)
The present contribution presents a comparison between two types of controls, namely, optimal Linear Quadratic Regulator LQR and Kalman-LQG controller using Model Order Reduction Process. Due to numerical constraints, models of the structures have been reduced so that the design of the controllers and/or the estimators could be performed. The proposed method results significant reduction in computational costs for dynamic analysis without compromising on accuracy. Transforming the full order state space resulting from finite element space to lower model reduces simulation time with a few degrees of freedom and helps to implement easily the control without changes in the structures dynamics. The estimator Kalman is used here in order to estimate the modal states of the system which 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. Monte Carlo simulation (MCS) was used to improve the number and locations 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.