An optimization method for time-delayed feedback control of partially observable linear building structures subjected to seismic excitation is proposed. A time-delayed control problem of partially observable linear building structure under horizontal ground acceleration excitation is formulated and converted into that of completely observable linear structure by using separation principle. The time-delayed control forces are approximately expressed in terms of control forces without time delay. The control system is then governed by It? stochastic differential equations for the conditional means of system states and then transformed into those for the conditional means of modal energies by using the stochastic averaging method for quasi-Hamiltonian systems. The control law is assumed to be modal velocity feedback control with time delay and the unknown control gains are determined by the modal performance indices. A three-storey building structure is taken as example to illustrate the proposal method and the numerical results are confirmed by using Monte Carlo simulation.
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method.First,the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay.Then the averaged It stochastic differential equations for the system are derived using the stochastic averaging method.Finally,the response of the system is obtained by solving the Fokker-Plank-Kolmogorov (FPK) equation associated with the averaged It equations.A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus-trate the proposed method.The analytical results are confirmed by digital simulation.We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
A strategy for time-delayed feedback controloptimization of quasi linear systems with random excitationis proposed. First, the stochastic averaging method isused to reduce the dimension of the state space and to derivethe stationary response of the system. Secondly, the controllaw is assumed to be velocity feedback control with timedelay and the unknown control gains are determined by theperformance indices. The response of the controlled systemis predicted through solving the Fokker-Plank-Kolmogorovequation associated with the averaged It equation. Finally,numerical examples are used to illustrate the proposed controlmethod, and the numerical results are confirmed byMonte Carlo simulation.
Xueping Li Demin Wei Weiqiu Zhu School of Civil Engineering and Transportation, South China University of Technology, 510640 Guangzhou, China Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, 310027 Hangzhou, China
The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.
LIU ZhongHua1 & ZHU WeiQiu2 1 Department of Civil Engineering, Xiamen University, Xiamen 361005, China
Many physical systems can be modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems can be applied to yield reasonable approximate response sta-tistics.In the present paper,the basic idea and procedure of the stochastic averaging method for quasi Hamiltonian systems are briefly introduced.The applications of the stochastic averaging method in studying the dynamics of active Brownian particles,the reaction rate theory,the dynamics of breathing and denaturation of DNA,and the Fermi resonance and its effect on the mean transition time are reviewed.
