Optimal Adaptive Ultra-Local Model-Free Control Based-Extended State Observer for PMSM Driven Single-Axis Servo Mechanism System

This paper proposes an optimal adaptive ultra-local model-free control (OAULMFC) scheme for servo-mechanism actuated through a permanent-magnet synchronous motor drive. Owing to the uncertainties in real-time applications, the model-based controller cannot achieve good dynamic performance. Therefore, an OAULMFC based on ultra-local model is developed. The proposed control scheme requires estimating the total disturbance and the control input gains. Therefore, the composite control structure of the OAULMFC combines an ultra-local model-free controller (ULMFC), a robust adaptive extended state observer (ESO) and an optimal <inline-formula><tex-math notation="LaTeX">${{\mathcal{H}}_\infty }$</tex-math></inline-formula> controller. The ESO is developed to estimate the total disturbance whereas the optimal <inline-formula><tex-math notation="LaTeX">${{\mathcal{H}}_\infty }$</tex-math></inline-formula> controller is adopted as the auxiliary controller to provide the optimal control performance of the servo mechanism. For enhancing the estimation accuracy, an online direct heuristic dynamic programming (DHDP) strategy is utilized for adaptation the ESO parameters and control input gains of the ULMFC. Accordingly, an actor-critic neural-networks with DHDP is adopted to solve the Hamilton-Jacobi-Bellman (HJB) equation online. Concurrently, the actor neural-network provides the optimal control performance. Furthermore, the system stability and convergence conditions via Lyapunov theory is proved. The experimental results confirmed the robustness of the proposed OAULMFC in case of model perturbations and external disturbances compared with the conventional ULMFC.