Design of an iterative learning control with a selective learning strategy for swinging up a pendulum

Swinging up a pendulum on a cart is a well-known demonstration example for trajectory tracking in a nonlinear system. The standard realtime feedback control approach fails if the plant output is not available in real time, e.g. due to large or variable measurement delays. However, the task can be solved in multiple trials by applying feedforward inputs that are improved from trial to trial by Iterative Learning Control (ILC). Our examination demonstrates that an ILC can be used for trajectory tracking close to the singularities and the unstable equilibrium of a non-linear system. Specifically, we present an ILC algorithm for pendulum swing-up by angle trajectory tracking. The controller design is based on a modified plant inversion approach that restricts the learning process to trajectory segments with small tracking errors and sufficient input sensitivity. We show that these restrictions lead to improved learning progress in contrast to conventional learning from the complete trajectory. Controller performance is evaluated in an experimental testbed. The ILC starts from a zero-input trajectory and learns to swing up the pendulum within six iterations. Robustness is analyzed experimentally, and the performance is compared to literature results. The convergence is at least two orders of magnitude faster than the one achieved by other methods that avoid feedback and do not rely on a suitable initial input trajectory.