Robust Koopman-MPC Approach With High-Order Disturbance Observer for Control of Pneumatic Soft Bending Actuators Under External Loads

Controlling the bending angle of the pneumatic soft bending actuator (PSBA) under external loads presents a significant challenge. Previous studies have indicated that the Koopman-based model predictive control (MPC) strategy, combined with active disturbance rejection technologies, shows promise but also has limitations due to coarse Koopman modeling and its ability to suppress only constant disturbances. This article proposes a robust Koopman-MPC approach with a high-order disturbance observer (HDOB) to address these limitations. The proposed approach involves improved Koopman modeling, time-varying disturbance estimation, and robust control design. First, we introduce an experimental method to determine the proper sampling frequency for Koopman modeling. Also, time-delay states and inputs are incorporated into the lifting functions based on typical nonlinearities of PSBA. Both of them collectively improve the accuracy of Koopman modeling. Next, the HDOB is first developed to estimate and predict the time-varying disturbances caused by external loads and modeling errors. Furthermore, a robust MPC is derived based on the improved Koopman model and HDOB to control the PSBA. Extensive experimental results demonstrate that our approach outperforms classical antidisturbance controllers, particularly in tracking time-varying trajectories under relatively large loads, and validate the effectiveness of all proposed improvements.