Design and Parameter Estimation of a Double Inverted Pendulum for Model-based Swing-up Control

Mathematical models and parameters with high accuracy are required for the swing-up control of a double inverted pendulum. This study proposes a mechanical structure of a double inverted pendulum having excellent matching characteristics with a mathematical model. The implementation of a parameter estimation method based on nonlinear optimization, which is essential for swing-up control, is also proposed. The proposed structure of a double inverted pendulum eliminates backlash using the direct drive of a BLDC motor, minimizes the unmodeled frictional force through bearing cleaning and oiling, minimizes unnecessary load torque using the double support of a timing pulley shaft and power transmission through a coupling, and constrains the pendulum rotation to one degree-of-freedom by adopting a dual-bearing joint. In addition, both 3D printing and CNC milling are appropriately used to satisfy the requirements for each mechanical part. The swing motion of the manufactured double inverted pendulum is measured using the lab-built light-weight rapid control prototyping 02 (LW-RCP02). The proposed parameter estimation method based on nonlinear optimization is implemented to match the response trajectory of the actual double inverted pendulum with that of a Simulink model implemented as an S-function. Finally, the effectiveness of the proposed double inverted pendulum design and parameter estimation method is confirmed by showing that the mathematical model that, based on the parameters estimated using the proposed method, accurately describes the response characteristics of the double inverted pendulum. © ICROS 2022.