A dual model-free control of non-minimum phase systems for generation of stable limit cycles

This paper presents a method allowing recent model-free control technique to deal with non-minimum phase systems for stable limit cycles generation. A first controller is designed in order to track parametrized reference trajectories on a subset of the coordinates. In order to stabilize the closed loop system, a second controller is designed using one parameter of reference trajectories as input. The overall system is therefore able to track the desired trajectories while stabilizing the internal dynamics of the system. The proposed method is illustrated through two examples of non-minimum phase systems. Numerical simulations are presented showing the effectiveness of the proposed method as well as its robustness toward external disturbances.