Shake table tests of stochastic optimal polynomial control of two span bridge equipped with MR dampers El-Khoury, Omar; Kim, Chunggil; Shafieezadeh, Abdollah; Hur, Jee-Eun; Heo, Gwang-Hee
This paper studies a nonlinear feedback controller based on Optimal Polynomial Control (OPC) in semi-actively controlled systems. OPC, for instance, is an extension to conventional linear quadratic regulator (LQR), where the cost function is of higher order and the control force is decomposed into linear and nonlinear terms. The main challenges of this state-space based control design method are nonlinearity of the system and the selection of covariance matrices. Traditionally, linearization is based on deterministic elastic strategies and that usually does not incorporate stochasticity or nonlinearity in the system. To overcome this limitation, a stochastic linearization of the passive system is considered which replaces the nonlinear portion of the system behavior with an equivalent linear model, where stochasticity of excitation and nonlinearity of the system are both preserved. Then, global optimization is conducted on the nonlinear system to determine the optimal covariance matrices. The OPC approach combined with stochastic linearization is referred to as Stochastic OPC (SOPC). For verification, the effectiveness of this control algorithm is analyzed, and tested via shake table experiments on a two span-bridge equipped with MR damper and subjected to pounding between spans and span to abutment.
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