A non-ideally excited pendulum controlled by SDRE technique

In this work, the perturbation theory is applied to the analysis of an electromechanical pendulum system. The frequency response behavior of the system is studied, and the existence of unstable poles is detected using the Routh-Hurwitz criterion. Numerical simulations show the existence of nonlinear behaviors such as hysteresis and the Sommerfeld effect in the resonance region. To damp the electromechanical system oscillations due to the nonlinear characteristics of the system the State Dependent Riccati Equation (SDRE) technique is used. The SDRE control strategy is applied considering two control signals, a feedback control that force the state trajectory of the system to a previously defined periodic orbit, and a nonlinear feedforward control that keeps the system motion synchronized to the periodic orbit. Additionally, the robustness of the control technique is tested for parametric uncertainties.