Robust stabilization and disturbance attenuation for a class of underactuated mechanical systems

Abstract

The robust control problem for a class of underactuated mechanical systems called acrobots is addressed. The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unstable equilibrium position in the presence of parametric uncertainties and external disturbance. First, in the swing-up area, it is shown that the time derivative of energy is independent of the parameter uncertainties, but exogenous disturbance may destroy the characteristic of increase in mechanical energy. So, a swing-up controller with compensator is designed to suppress the influence of the disturbance. Then, in the attractive area, the control problem is formulated into a H ∞ control framework by introducing a proper error signal, and a sufficient condition of the existence of H ∞ state feedback control law based on linear matrix inequality (LMI) is proposed to guarantee the quadratic stability of the control system. Finally, the simulation results show that the proposed control approach can simultaneously handle a maximum ±10% parameter perturbation and a big disturbance simultaneously.