On the adequacy of linearized methods for control of nonlinear bridge oscillations

In this paper, control of nonlinear oscillations of a single-span flexible bridge with light damping is examined to improve bridge safety and reliability. The control forces are applied through a king-post truss tendon mechanism. The nonlinear terms in the equation of motion are geometric in nature and result from inclusion of midplane stretching of the bridge deck in the problem formulation. A quadratic cost function is considered, and an optimal control law is derived which accounts for the nonlinear behavior. The control which is obtained is an infinite series of polynomials in the states and readily allows the importance of the nonlinear terms in the control law to be assessed. It is found that for typical bridge parameters, higher order terms in the control can be neglected with little or no performance degradation. Further, it is shown that a control strategy which eliminates the nonlinear response of the structure is not necessarily optimal.