Cable-stayed Parametrically Excited Instability Of Active And Semi-active Control

Active and semi-active controls for the parametrically excited instability of an inclined cable under support-motion excitations are studied in this thesis. Firstly, using the established multi-degree-of-freedom (MDOF) parametrically-excited vibration equation of an inclined cable under support-motion excitations and according to the direct numerical method which was developed based on the Floquet theory, Fourier series and generalized eigenvalue analysis, etc., for the parametrically excited instability of a MDOF system, unstable regions of the cable are obtained through the numerical computation, and modal compositions of the unstable regions are analyzed.Secondly, an optimal active control law and its implementing conditions for the cable are determined based on the dynamical programming principle and LQ control method. By a large number of numerical computations, abundant and new results of the active control (including single-modal and multi-modal control) for the cable's parametrically excited instability are obtained, and the influences of control weighting parameters on the control effectiveness are investigated in detail. Results show that the effectiveness of the optimal active control is remarkable, and there exists an optimal control weighting parameter. Meanwhile, both the effectiveness of the active control for the cable's instability under simultaneous motion excitations of the deck and the tower, and effects of acting positions of the control force on the control effectiveness are studied. As the acting position approaches the middle span of the cable, the control effectiveness improves. Moreover, a new method of two-point optimal active control is proposed. Numerical results show that its effectiveness is better than that of single-point optimal active control. Also, a nonlinear polynomial optimal active control strategy is determined in terms of the dynamical programming principle. A cubic nonlinear optimal control force and its new implementing conditions are obtained. Numerical computations indicate that the result of nonlinear optimal control for the instability dependent on the controlled mode of the cable is close to that of linear optimal control.Furthermore, according to the aforementioned optimal control law for the parametrically excited instability of the inclined cable, and the Bingham model of a Magnetorheological (MR) damper, a semi-active optimal control force of the MR damper and its new implementing conditions are determined. By means of numerical simulation, the unstable regions of the semi-active controlled cable are obtained. The influences of important control factors such as the control force bound, control time-delay, system observation error, etc., as well as geometrical and physical...