An automated design technique for nonlinear structures and controllers

A design technique to simultaneously optimize the structure and controller to suppress vibration of nonlinear structures is presented. Newmark-beta ex plicit time integration is used to solve the nonlinear ordinary differentia l equations describing the closed-loop system. Computations in the integrat ion only involve addition and multiplication of sparse matrices, and thus i t is feasible to carry out the solution for a large number of time steps. T he structure and controller parameters are optimized to drive the forced no nlinear system to its zero equilibrium solution using the minimum control f orce. Computations in the optimization are streamlined by computing the gra dients of the design variables in closed form, or semianalytically dependin g 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 theory to test the nonlinear design technique. The nonlinear behavior of the truss and the opt imization of the nonlinear structure and design of linear and nonlinear con trollers are discussed.