Weighted energy linear quadratic regulator vibration control of piezoelectric composite plates

In this paper on finite element linear quadratic regulator (LQR) vibration control of smart piezoelectric composite plates, we propose the use of the total weighted energy method to select the weighting matrices. By constructing the optimal performance function as a relative measure of the total kinetic energy, strain energy and input energy of the system, only three design variables need to be considered to achieve a balance between the desired higher damping effect and lower input cost. Modal control analysis is used to interpret the effects of three energy weight factors on the damping ratios and modal voltages and it is shown that the modal damping effect will increase with the kinetic energy weight factor, approaching √2/2 as the strain energy weight factor increases and decrease with the input energy weight factor. Numerical results agree well with those from the modal control analysis. Since the control problem is simplified to three design variables only, the computational cost will be greatly reduced and a more accurate structural control analysis becomes more attractive for large systems.