Self-excited periodic motion in underactuated mechanical systems using two-fuzzy inference system

Dynamic systems with self-excited periodic motion have a wide range of applications in mechanical systems. For instance, a class of non-minimum phase underactuated and nonprehensile systems require self-oscillations instead of tracking an external reference signal. To solve this problem, we proposed a two fuzzy inference system, which is based on fuzzy logic theory, in order to generate a periodic output. The idea is to enforce the conditions that ensure the orbital asymptotic stability of the periodic solution of the closed-loop system. In this study, we considered Euler-Lagrange systems, with emphasis in underactuated systems. The describing function method was used to design the fuzzy controller and set the desired frequency and amplitude of the periodic output. Moreover, in accordance with Loeb's criteria, we established sufficient conditions for orbital stability. Finally, we tested and validated our proposal, via simulation and experiments on two laboratory platforms: a single-link pendulum and an underactuated non-minimum-phase rotational inverted pendulum.