Self-excited oscillations in an inverted cart–pendulum based on the two-relay approach

Solving the orbital stabilization of a class of underactuated systems near its open-loop unstable equilibrium point is a challenging task but useful in repetitive tasks. This paper addresses the control problem of an inverted cart–pendulum's motion driven by a two-relay controller. This controller is tuned to set the desired amplitude and frequency using the locus of the perturbed relay system, which is a frequency-domain method. We solved the periodic motion of the pendulum occurring in its open-loop unstable equilibrium point. The experimental results showed that the proposed two-relay controller forced the pendulum into a periodic motion around the upright position.