Adaptive gain sliding mode observer based on recursive least square for ultra-local model estimation in model-free predictive control of brushless DC motor drives

Introduction. Accurate current estimation is essential for high-performance brushless DC (BLDC) motor drives, especially in finite control set model predictive control (FCSMPC), where prediction accuracy directly affects control quality. Problem. Sliding mode observers (SMOs) are widely adopted for this purpose due to their robustness against modeling uncertainties. However, the performance of conventional SMO strongly depends on proper gain tuning, which is typically fixed and may lead to degraded performance under parameter variations and changing operating conditions. Goal. To develop an adaptive SMO gain strategy that automatically adjusts the observer gain online using recursive least squares (RLS) approach to improve robustness and estimation accuracy of the ultra local model without manual tuning. Methodology. The proposed method proposes the SMO gain adaptation as an online regression problem, where the RLS algorithm is used to recursively update the observer gain at each sampling instant. The adaptive SMO is integrated into an FCSMPC scheme. Its performance is evaluated through simulations under nominal conditions and parameter mismatches and compared with static-gain and PI-based adaptive SMO approaches using dynamic and steady-state performance metrics. Results. Simulation results demonstrate that the proposed RLS-based adaptive gain SMO achieves faster convergence, reduced chattering, and improved robustness against parameter variations. Scientific novelty. The main contribution of this work is the use of RLS to adapt the SMO gain rather than directly estimating system parameters, providing a stable and statistically grounded gain adaptation mechanism. Practical value. The method reduces the integral of time-weighted absolute error (ITAE) of the sliding variable by 5.8 % compared to the static-gain approach and provides faster settling time and lower steady-state error in speed response. The settling time is reduced by 33 % and decreasing steady-state error by 58 % compared to the conventional static-gain approach. In addition, the adaptive mechanism enhances robustness under parameter mismatch and load disturbance conditions. References 34, tables 3, figures 6.