Swing-up Control of a Translational Inverted Pendulum Having Restricted Travel

Swing-up and stabilizing control of an inverted pendulum is one of the most common experiments used for illustrating nonlinear control techniques. Since an actual inverted pendulum has limited pivotal travel, the controllers have to be designed to satisfy this constraint. However, it is difficult to design controllers for underactuated systems with state constraints, like inverted pendulums. Consequently, there have been very few studies into this problem. In this paper, we propose a control law which can swing up and balance a translational inverted pendulum through limited pivot travel. Bearing in mind that the energy of the pendulum can be controlled according to the sign condition of pivot acceleration, we develop a method for swinging up the pendulum which involves controlling acceleration of the pivot as well as limiting its travel. The proposed balancing control law is a linear one designed by applying block control methods to the linearized model about an unstable equilibrium point, which can stabilize the whole system as keeping the amplitude of the pivot small. The results of our simulations and experiments demonstrate the effectiveness of the proposed control law.