Dynamics And Control Of The Active Control System With The State-dependent Actuation Time Delay

Actuation time delay is often related to state. Regarding it as a constant delay is not accurate. Generally the dynamics and control of active control system with the state-dependent time delay is a major problem. The research of the state-dependent delayed system’s dynamics is also a difficult problem internationally. Supported by the Nation-al Natural Science Foundation of China "Dynamics and control of the state-dependent delayed system" under Grant NO.11372282, this dissertation has been launched to study the dynamics and control of the active control system with the state-dependent actuation time delay. Firstly, the formula of the approximation actuation time delay in this dy-namical system (DDEs) is derived by solving an inequality. It displays that the actuation time delay is state-dependent. Secondly, the low dimensional approximation system of this delayed active control system is obtained by employing Galerkin projection scheme. Then, the stability and Hopf bifurcation of the approximation system are considered. At last, numerical simulations are executed to verify the correctness of the theoretical results and the validity of the derivation of the actuation time delay by employing the nonlinear dynamical software WinPP for the original time delay dynamics system.The results show stability can be realized by analyzing the choosing conditions of parameters and studying the delay-dependent quantities for the active control model with state-dependent delay. But the fixed time delay in the actuation should be in appropriate range, otherwise, the system will lose stability and produce periodic oscillation, inducing performance deterioration.