MIMO ultra-local model-based adaptive enhanced model-free control using extremum-seeking for coupled mechatronic systems

Multiple degree-of-freedom (DOF) mechatronic systems, such as robots and robotic arms, play a crucial role in modern life and production. However, due to strong coupling, uncertain dynamics, and external disturbance, accurately modeling these systems is challenging, making traditional model-based control methods impractical. To address this, this paper proposes an extremum-seeking-based adaptive enhanced model-free control for multi-input multi-output (MIMO) mechatronic systems to realize robust trajectory tracking. Unlike previous model-free control methods that decouple and reorganize the MIMO system into several single-input single-output ultra-local models, this paper develops a MIMO ultra-local model with a non-diagonal gain matrix $\alpha$ to approximate the system dynamics within an ultra-short time window. Time-delay estimation (TDE), Proportional–Derivative (PD) control law and accuracy compensation compose an TDE-based enhanced intelligent PD control that ensures the closed-loop stability. Furthermore, an extremum-seeking (ES) technique is designed to optimize the gain matrix $\alpha$ to enhance control performance. The main contributions of this paper are the development of a model-free control framework based on the MIMO ultra-local model and the successful application of ES to optimize the non-diagonal gain matrix $\alpha$. Stability analysis of the closed-loop system is conducted using Lyapunov theorem. Finally, numerical simulations on a 2-DOF robotic manipulator and co-simulation results on a 3-DOF PUMA 560 robotic manipulator validate the effectiveness and superiority of the proposed methods.