Analysis and computer simulation of optimal active vibration control
Dhotre, Nitin Ratnakar
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Methodologies for the analysis and computer simulations of active optimal vibration control of complex elastic structures are considered. The structures, generally represented by a large number of degrees of freedom (DOF), are to be controlled by a comparatively small number of actuators.Various techniques presently available to solve the optimal control problems are briefly discussed. A Parametric optimization technique that is versatile enough to solve almost any type of optimization problems is found to give poor accuracy and is time consuming. More promising is the optimality equations approach, which is based on Pontryagin’s principle. Several new numerical procedures are developed using this approach. Most of the problems in this thesis are analysed in the modal space. Even complex structures can be approximated accurately in the modal space by using only few modes. Different techniques have been first applied to the cases where the number of modes to control was the same as the number of actuators (determined optimal control problems), then to cases in which the number of modes to control is larger than the number of actuators (overdetermined optimal control problems). The determined optimal control problems can be solved by applying the Independent Modal Space Control (IMSC) approach. Such an approach is implemented in the Beam Analogy (BA) method that solves the problem numerically by applying the Finite Element Method (FEM). The BA, which uses the ANSYS program, is numerically very efficient. The effects of particular optimization parameters involved in BA are discussed in detail. Unsuccessful attempts have been made to modify this method in order to make it applicable for solving overdetermined or underactuated problems. Instead, a new methodology is proposed that uses modified optimality equations. The modifications are due to the extra constraints present in the overdetermined problems. These constraints are handled by time dependent Lagrange multipliers. The modified optimality equations are solved by using symbolic differential operators. The corresponding procedure uses the MAPLE programming, which solves overdetermined problems effectively despite of the high order of differential equations involved.The new methodology is also applied to the closed loop control problems, in which constant optimal gains are determined without using Riccati’s equations.
DegreeMaster of Engineering (M.Eng.)
CommitteeFotouhi, Reza; Chen, X. B. (Daniel); Burton, Richard T.; Boulfiza, Mohamed
Copyright DateAugust 2005
Finite Element Method