Fixed-time Cooperative Model-free Sliding Mode Control for Fractional-order Multi-motor Systems

Speed inconsistency in multi-motor systems may lead to mechanical structure damage, low cooperative precision, and even cause equipment breakdown. Traditional control methods may induce pronounced consensus error fluctuations and prolonged convergence time under complex conditions such as system parameter mismatch, sudden load changes, and inaccurate mechanism models. To address these challenges, we propose a fixed-time cooperative model-free sliding mode control (FCM-SMC) method based on a fractional-order ultra-local model (FOULM). Specifically, the proposed approach integrates fractional-order dynamics into the system model to better capture the non-integer order characteristics of multi-motor systems. Then, to estimate the unknown terms of FOULM, a novel fixed-time disturbance observer (FTDO) is designed. Additionally, grounded in the framework of FOULM, the FCM-SMC protocol is designed to ensure that the consensus error of the multi-motor systems converges within a fixed time. Taking motor #1 as an example, compared with existing methods, the error metrics (ME, MAE, and RMSE) of the proposed method are reduced by up to 64.8%, 70.2%, and 69.7%, respectively.