Hybrid Control of a Pendubot System Using Nonlinear H∞ and LQR

Abstract

In this paper, a hybrid control approach is synthesized for stabilizing an under-actuated mechanical system, the Pendubot. This kind of system is divided into two modes, the swing-up mode, and the balancing mode. First, dynamic modeling is established by the Euler-Lagrange method. Next, the robust nonlinear H∞ is designed for the swing-up mode, which handles with the nonlinear model. To weaken the under-actuation characteristic, the control law is developed for the active link with its coupling with the passive link. The LQR is designed for the balancing mode where LQR handles with the linearized model about the unstable top equilibrium position. A simulation is achieved under the MATLAB/Simulink environment. It shows robustness against the external inputs and the fast convergence to the equilibrium position.