Design of PMSM Controller with Continuous Function Reaching Law and Integral Sliding Surface

An innovative improved reaching law (IRL) is introduced to overcome the inherent limitations found in the traditional sliding mode control (TSMC) that is based on the exponential reaching law (ERL). The ERL has been found wanting in its inability to concurrently achieve rapid convergence to the sliding surface and a reduction in chattering. The IRL addresses these issues by integrating a continuous function with an integral sliding surface, merging the advantageous aspects of both exponential and power reaching laws. This new approach abandons the conventional switching function in favor of a hyperbolic tangent function to create a unique continuous function reaching law. Through rigorous theoretical analysis, it has been shown that the IRL not only accelerates the reaching speed from the initial state to the sliding surface but also maintains certain switching characteristics while drastically minimizing chattering. With the IRL as its cornerstone, an improved sliding mode controller (ISMC) is developed specifically for permanent magnet synchronous motors (PMSMs). To guarantee stability, a comprehensive Lyapunov stability analysis is performed. Both simulation and experimental results validate the practicality and efficiency of the ISMC. When contrasted with the TSMC, the ISMC exhibits a quicker response time and more precise tracking of the required reference position sinusoidal signal, all while successfully reducing chattering to a significant degree.