Omar El-Khoury

Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.

Mitigation of the seismic response of multi-span bridges using MR dampers: Experimental study of a new SMC-based controller

Pounding between adjacent structures has been a concern in multi-span bridges in recent earthquakes. In this paper, a pounding mitigation strategy using magnetorheological dampers is proposed, and its performance is tested for a three-span bridge using a series of shake-table experiments. A new semi-active control algorithm called SMC-OPC is developed that is based on a clipped sliding mode control (SMC) with sliding surfaces designed using an optimal polynomial control (OPC) approach. The control design uses a stochastically linearized model of the nonlinear bridge with passive components of the magnetorheological dampers embedded to achieve a more representative system characterization. Optimal weighting matrices for the optimal polynomial control are found through a genetic algorithm. The proposed method along with uncontrolled, passive-off, and passive-on cases are tested on shake-tables for several scaled near-field Kobe ground motion records. Although no pounding is observed in all control cases for small earthquakes, significant pounding occurs in the uncontrolled and passive-off systems under large earthquakes. For these ground motions, the performance of the semi-active controller converges to that of the passive-on case but with noticeably reduced power consumption. The study shows that the use of magnetorheological dampers between adjacent spans is very effective in mitigating critical bridge responses especially under large earthquakes. In addition, the proposed SMC-OPC semi-active control strategy enables achieving balance among multiple performance objectives with significantly reduced power consumption as compared to passive-on case.

A constrained nonlinear stochastic optimal control for dynamic systems

ABSRTACT: An ideal controller assumes that the system is unconstrained and the control force in unbounded. However, in reality, control devices are restricted by their force capacity. Traditionally, the clipping strategy has been used extensively, where an ideal actuator is assumed in the control design, and then the inequality constraints are enforced through saturation. This approach may not provide optimal solutions since constraints are not considered in the control optimization. To overcome this limitation, this paper presents a constrained nonlinear stochastic optimal control algorithm for dynamic systems subjected to Gaussian white noise excitations. In this control algorithm, stochasticity and nonlinearity of a Hamiltonian dynamic system is considered based on stochastic averaging of energy envelope using Markovian approximation. An Ito equation of energy envelope is derived and represented by diffusion and drift components. For the control design, a prescribed cost function, the diffusion and drift components together with the force constraints are considered in solving the Hamilton Jacobian Bellman (HJB) equation. This proposed control approach is called here Constrained Stochastic Control (CSC). The performance of the CSC algorithm is demonstrated for a hysteretic column and the results are compared to simulation results for Clipped Stochastic Control (Cl-SC) and uncontrolled cases. Noticeable improvements in peak and root mean square values of displacement in the CSC case are observed over the Cl-SC algorithm.