Nonlinear control design for a class of underactuated systems

The major purpose of this paper is to apply backstepping design scheme for the balancing control of some pendulum-like plants, which are a class of underactuated systems. The key control objective of the inverted-pendulum-type underactuated systems is not only to maintain the pendulum at the upright position, but also to force the actuator to return its starting point. In order to investigate and realize the properties of pendulum-like systems, the linearized system around its equilibrium point is introduced and analyzed in advance. And then, the nonlinear backstepping controller is successfully developed for balancing target of the pendulum-like systems according to the information from the linear design. In addition, the partial feedback linearization is applied to reduce the complexity of pendulum-like systems in the design process. Finally, some simulation results are given to illustrate the excellent performance of nonlinear backstepping scheme applied to pendulum-like systems, including the cart-pole pendulum and the Furuta pendulum.