Damping a pendulum's swing by string length adjustment - design and comparison of various control methods

A novel nonlinear control theory based feedback controller is proposed to damp the oscillations of the suspended load (pendulum) using the active modification of the length of the suspension string. This setting is a highly nonlinear one since the approximate linearization around the equilibrium working point is neither controllable, nor asymptotically stabilizable. The nonlinear design of the control law is therefore based on the conveniently selected control Lyapunov function. The resulting control law is then compared to the previously developed time-delay feedback control law, both in simulations and using the laboratory experimental realization of the suspended load system. Despite the fact that in the simulations the time-delay feedback control law suppresses the oscillations better than the nonlinear control law, in the experiments the performance of the time-delay feedback and of the nonlinear control law are rather similar. Moreover, the former keeps the pendulum string length oscillating, the latter stabilizes the nominal string length as well. Finally, the numerical optimization shows that the ideal damping would be provided by the impulsive-like control producing piece-wise constant string length dynamics.