An Automated Design Technique for Nonlinear Structures and Controllers

Abstract: A design technique to simultaneously optimize the structure and controller to suppress vibration of nonlinear structures is presented. Newmark-beta explicit time integration is used to solve the nonlinear ordinary differential equations describing the closed-loop system. Computations in the integration only in-volve addition and multiplication of sparse matrices, and thus it is feasible to carry out the solution for a large number of time steps. The structure and controller parameters are optimized to drive the forced nonlinear system to its zero equilibrium solution using the minimum control force. Computations in the optimization are streamlined by computing the gradients of the design variables in closed form, or semianalytically, de-pending on the type of finite elements used in the model. No additional function evaluations or recursion are required to compute the gradient. A nonlinear truss is modeled using a geometrically exact structural the-ory to test the nonlinear design technique. The nonlinear behavior of the truss and the optimization of the nonlinear structure and design of linear and nonlinear controllers are discussed