Linear quadratic regulator with genetic algorithm for flexible structures vibration control

There has been tremendous growth in the study of active vibration suppression of flexible structures in aerospace and robotics applications. The mathematical modeling of flexible structure is usually complex; for the control of flexible structure one needs to design an algorithm which is related to mathematical model. This thesis is addressed to the comprehensive analysis for generic structure control that has not been adequately dealt with in the literature. The comprehensive account is given by way of a generic example with the solution of LQR problem using genetic algorithm for this structure. First, the dynamic analysis of a cantilever beam hinged with linear spring at the tip is studied analytically and numerically as a baseline. Then, a cantilever beam bonded with piezoelectric sensor and actuator is considered for the study of the vibration control. For this purpose, a flexible Euler–Bernoulli beam is analyzed using Hamiltonian mechanics. The free vibration problems of the beam structures are solved using analytical and finite element method. The analytical method can only be used for certain class of geometries particularly simple ones and the finite element method can be applied for more general cases. In addition the analytical method can be used for validation purposes. The first three major natural modes and frequencies for all these two methods have been verified by present study. In addition the results of these studies are compared to available and acceptable data for validation and assessment. For dynamic problem, the state-space approach can be used to design the effective controller for convenience, accuracy and computational efficiency. In the workout examples, the first two modes are used to control. The effective vibration control is designed by resorting to two methods one is PID and the other is LQR. The PID, which is the most direct method, will be used as a reference in finding the better methods. The LQR is then utilized to obtain the better or eventually the best solution. The LQR is formulated by full–order state observer. These methods are elaborated and it was found that satisfactory answer can be obtained by using two modes of the beam. The work has demonstrated the effectiveness of LQR method judged from computation time and accuracy. In addition, to improve the LQR trial and error procedure, genetic algorithm has been used to obtain the LQR weighting matrices. The method has been elaborated and the results obtained show better improvement than earlier trial and error method