Real-Time Stabilization of a Single Inverted Pendulum Using a Power Series Based Controller

Abstract

The single inverted pendulum (SIP) system is a classic example of a nonlinear under-actuated system. Despite its simple structure, it is among the most difficult systems to control and is considered as one of the most popular benchmarks of nonlinear control theory. In the past fifty years many nonlinear methods have been proposed for the swing-up and stabilization of a self-erecting inverted pendulum, however, most of these techniques are too complex and impractical for real-time implementation. In this paper, the successful real-time implementation of a nonlinear controller for the stabilization of the pendulum is discussed. The controller is based on the power series approximation to the Hamilton Jacobi Bellman (HJB) equation. It performs similarly to the traditional linear quadratic regulator (LQR), but has some important advantages. First, the method can stabilize the pendulum for a wider range of initial starting angle. Additionally, it can also be used with state dependent weighting matrices, Q and R, whereas the LQR problem can only handle constant values for these matrices.