Optimal decision strategies for active control of nonlinear structural response

The objective of this research is to study the feasibility of using Optimal Decision Strategies (ODS) for the active control of multi-degree-of-freedom flexible (non-rigid) structures exhibiting nonlinear response. ODS is a pointwise optimal control algorithm which involves the repeated on-line solution of a constrained minimization problem in the space spanned by the control force vector. The objective at each discrete time point is to instantaneously bring the system state derivative as close as possible, in the weighted {dollar}Lsb2{dollar} norm sense, to a reference state derivative which is generated on-line. A priori knowledge of the nonlinear stiffness and damping of the structure is not needed.; The research entails both analytical and numerical investigations. The analytical investigations begin with the assumption of full state feedback and an independent control input at every degree of freedom (DOF). A reference trajectory, of equal dimension to the state vector and computed from the measured state and a reference model, is proposed as a basis for control. The issue of stability in the neighborhood of an isolated stable equlibrium point is addressed.; When there are fewer control inputs than structural DOF, tracking of the reference trajectory is possible only in a subspace of dimension equal to the number of control inputs. It is demonstrated that excellent control performance is achieved by specifying the structure's flexibility matrix in the weighting matrix of the {dollar}Lsb2{dollar} norm. A major contribution of the research is the extension of ODS to the case of fewer state measurements and fewer control inputs than structural DOF by use of a reduced-order reference model.; Numerical simulations of ODS applied to a five-story steel frame with inelastic semi-rigid connections are used to assess controller performance. The simulations demonstrate clearly that ODS is an effective controller, especially when formulated with limited state measurements in conjunction with a reduced-order reference model. The simulations further demonstrate the controller's robustness in the presence of time delays and its ability to account for actuator saturation rationally.