Grey prediction approach for designing grey sliding mode controller

In this work, the grey prediction is integrated into the SMC to develop a grey sliding mode controller (GSMC). But unlike the traditional SMC, which obeys the variable structure control principle by adopting a switching control term, the proposed GSMC uses a unified continuously varying term instead. As a result, not only the chattering phenomenon of the system is completely eliminated, but also the response and robustness are all improved as well. In most of these studies, the systems are limited to second-order. Thus, a decoupled method is introduced to generalize this approach to high-order systems. This demonstrates that the decoupled GSMC is applicable to the high-order systems, such as the permanent magnet synchronous motor drive system.