Adaptive Neural Network Unified Control for General MIMO Underactuated Mechatronic Systems With Disturbances via Modified Normal Forms

Meng Zhai, Tong Yang, Ming Li, Xuerui Jiao, Yongchun Fang, Ning Sun

Abstract: The control problem of underactuated mechatronic systems is one of the key representatives of complex nonlinear dynamical systems. Starting from the dynamical structures of underactuated systems is usually one of the most direct and effective ways to design controllers. However, controllers developed for specific dynamic models are often difficult to be directly generalized to other underactuated systems. Moreover, due to the lack of control inputs, designing robust controllers for unmatched disturbances (acting on unactuated states) remains a challenging problem. Therefore, based on the Euler-Lagrange dynamics of multi-input-multi-output (MIMO) underactuated systems, this paper gives four coordinate transformations according to different configurations of the inertia matrix, which extends the Olfati transformation to some extent and finally unifies underactuated systems into normal forms. A sliding manifold and an adaptive neural network sliding mode controller are developed with the derived normal forms, which improves transient performance and avoids the chattering problem in traditional sliding mode controllers by combining an estimation error-driven adaptive law, a high-order sliding-mode differentiator, and the super-twisting algorithm. More importantly, the stability is guaranteed by Lyapunov techniques even in the presence of both persistent matched disturbances and asymptotically vanishing unmatched disturbances. Furthermore, the proposed control strategy is applied to overhead cranes and tower cranes, whose superior control performance is verified by hardware experiments. Note to Practitioners—Underactuated mechatronic systems, with fewer independent actuators than degrees of freedom, are common in real-world automation applications, such as cranes, aerial vehicles, and flexible joint robots. However, designing robust and generalizable controllers for such systems remains a significant engineering challenge due to their nonlinear dynamics, structural diversity, and sensitivity to matched and unmatched disturbances. This paper proposes a unified control framework, which is specifically designed to meet the needs of engineers and practitioners working with complex underactuated mechatronic systems. This paper presents a systematic approach to normalizing the dynamics of different underactuated mechatronic systems. Based on the unified model, a robust control strategy is proposed with good applicability. The proposed control strategy improves positioning accuracy and control smoothness, particularly in effectively handling unmatched disturbances (such as sudden impact disturbances on the suspended payload). The effectiveness of the proposed strategy is validated through experiments on two representative underactuated mechatronic systems (tower cranes and overhead cranes), demonstrating its broad potential for automation tasks.

External IDs:doi:10.1109/tase.2025.3593468