Stabilization of the Acrobot via Multiple sliding surface Control

This paper considers the stabilization problem of the Acrobot, a widely studied benchmark nonlinear under-actuated mechanical system. For such systems the design of control Law becomes a challenging task owing to complex internal dynamics and lack of feedback linearizibility. These result in need of closed form solutions for highly nonlinear equations or hybrid/switching controllers. A novel nonlinear controller design, using recently introduced Multiple Sliding Surface Control technique is presented as the solution. Proposed controller doesn’t require analytical calculation of certain derivatives requiring closed form solutions of highly nonlinear equations. The proposed design procedure is shown to be simpler and more intuitive than existing designs. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and verified using numerical simulations. Key-Words: Acrobot, Under Actuated Mechanical Systems, Multiple Sliding Surface Control, backstepping, singular perturbation model