A new solution to the swing up control problem for the Acrobot

Studies the swing up control for the Acrobot, i.e., to move the Acrobot from its stable downward position to its unstable inverted position and balance it about the vertical. A control scheme which combines of the partial linearization control (related to the first link) for the swing up phase introduced in Spong (1995) and robust control for the capture and balance phase is proposed. The key idea is to treat the speed of the second link when the Acrobot rotates across the vertical as an uncertainty, and to design a robust controller to cope with such uncertainty by using the LMI solution to the quadratic stabilization problem. Hence, the basin of attraction of the robust controller is bigger than that of the LQR controller which is designed based on the linearized model of the Acrobot around the unstable equilibrium. The simulation results have verified the effectiveness of the proposed control scheme.