Aiming at the problems of strong coupling, multivariate, nonlinearity, and time delay in the simulated moving bed chromatographic separation system, a fuzzy decoupling control method for simulated moving bed component purity based on the self-tuning PID parameters of BP neural network with an improved sand cat swarm optimization algorithm is proposed. First, fuzzy decoupling is used to eliminate the coupling between the purity control loops of components A and B. Then, combined with the improved sand cat swarm optimization algorithm and BP neural network, the adaptive adjustment of PID parameters is realized, thereby effectively controlling the purity of components A and B. In the improved sand cat swarm optimization algorithm, the Cubic chaotic map is introduced to initialize the sand cat population to improve the uniformity of population distribution; the variable spiral search strategy is added in the prey search phase to enable the sand cat swarm to have more search paths to adjust its position; simultaneously, the alert mechanism of the sparrow search algorithm is integrated to accelerate the convergence speed of the algorithm. The effectiveness of the improved sand cat swarm optimization algorithm is verified by 12 CEC2022 test functions. The simulation results show that the proposed method can not only effectively eliminate the coupling effect between the purity control loops of components A and B, but also demonstrates excellent performance in various real-world application scenarios. Compared to traditional PID control methods, the proposed approach reduced the settling time by 75.40% and 77.57%, and decreased the overshoot by 91.84% and 81.96% under flow rate fluctuation conditions. This method possesses strong anti-interference ability and good robustness, and improves the control performance of the entire system.