LQR and PID Algorithms for Vibration Control of Piezoelectric Composite Plates
In this paper, a formulation of a sandwich plate integrating an elastic central layer (isotropic or composite) between two piezoelectric sub-layers (actuators and/or sensors), which can be taken as a smart (intelligent) structure and allowing active control vibrations is presented. A 9-node finite element quadratic plate element with 5 degrees of freedom per node is used which takes into account the effect of transverse shear with an additional degree of freedom for each node of the piezoelectric sub-layer.
At First, the static control of the deflection by taking the two piezoelectric sub-layers as actuators with two configurations of the total and partial recovery of the surface is undertaken. Thus, the influence of patches position, for the second configuration, on the attenuation of vibrations is analyzed.
In a Second step, the active vibration control using two types of LQR and PID controllers with different control parameters is tested and compared for the two recovery configurations (total and partial) of the piezoelectric elements. It is demonstrated throughout the present results that the performances of the partial recovery are almost as good as those of the total recovery despite a ratio of the surfaces piezoelectric patches which is 1/3. It is also noticed that the PID controller is more efficient than the LQR controller. But, if using the PSO (Particle Swarm Optimization) algorithm, the LQR's parameters are optimized and give almost the same performances as those of the PID controller.