Transition Control of a Double Inverted Pendulum Using an LW-RCP

This study investigates the transition control problem for a double inverted pendulum system, which has one stable and three unstable equilibrium points. We propose a method for implementing transition control using a lab-built double inverted pendulum and extend swing-up control to achieve this. The proposed method uses a two-degree-of-freedom control structure that combines feedforward and feedback controls. To obtain the feedforward trajectories offline, we construct an optimal control problem with two-point boundary values that has constraints on the dynamic equations, boundary values at the equilibrium points, and input and output constraints. We use energy as the cost of the optimal control problem and employ a direct collocation method to transform the continuous-time optimal control problem with constraints into a nonlinear optimization problem. During real-time control, we use a time-varying LQ controller as a feedback controller to compensate for the uncertainty of feedforward control and accurately follow the feedforward trajectories. We implement the proposed transition control based on high-level thinking using the lab-built light-weight rapid control prototyping (LW-RCP) system to shorten the design time and provide useful information in the design and experiment processes. Finally, we perform an actual transition control experiment and validate the performance of the proposed method using the experimental results.