Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

this paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. the behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. a control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. the state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. general polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. this methodology is applied to systems with quadratic and cubic non-linearities. strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. numerical results emphasize the importance of considering time delay in the project of active structural control systems.