Summary
This paper addresses pole placement of a nonlinear system and experiment carried out using hammer test to demonstrate how the poles can be moved in the Laplace domain. Receptance method is developed for nonlinear systems that is extended formulation of the linear receptance method. The mathematical model considered in this manuscript to study the nonlinear equation is a duffing oscillator with cubic stiffness. First, mathematical equation of pole placement of a nonlinear system and the eigenvalue sensitivities to parametric perturbations are derived. Then eigenvalue sensitivities are minimized to enhance the performance robustness of dynamical system control. This approach is applicable to all the nonlinear systems that experience variations caused by manufacturing and material tolerances, damages, and environmental fluctuations. The nonlinear system's poles and eigenvalue sensitivities are assigned through linear feedback control and the Sherman-Morrison formula under varying levels of excitation and minimization of the calculated feedback gains. Given the amplitude-dependent response of the nonlinear system, an iterative method is employed to determine the optimal feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions (FRFs) using the rational fraction polynomial method, making it unnecessary to measure the ????,????,???? matrices.
