In permanent magnet synchronous motor (PMSM) control, the jitter problem affects the system performance, so a novel reaching law is proposed to construct a non-singular fast terminal sliding mode controller (NFTSMC) to reduce the jitter. To enhance the immunity of the system, a disturbance observer is designed to observe and compensate for the disturbance to the sliding mode controller. In addition, considering that the controller parameters are difficult to adjust, and the traditional zebra optimization algorithm (ZOA) is prone to converge prematurely and fall into local optimum when solving the optimal solution, the improved zebra optimization algorithm (IZOA) is proposed, and the ability of the IZOA in practical applications is verified by using international standard test functions. To verify the performance of IZOA, firstly, the adjustment time of IZOA is reduced by 71.67% compared with ZOA through the step response, and secondly, the tracking error of IZOA is reduced by 51.52% compared with ZOA through the sinusoidal signal following. To verify the performance of the designed controller based on disturbance observer, the designed controller reduces the speed overshoot from 2.5% to 0.63% compared with the traditional NFTSMC in the speed mutation experiment, which is a performance improvement of 70.8%, and the designed controller outperforms the traditional NFTSMC in the load mutation experiment, which is a performance improvement of 60.0% in the case of sudden load addition, and a performance improvement of 90.0% in the case of load release, which verifies that the designed controller outperforms the traditional NFTSMC.

Personalized gait curves are generated to enhance patient adaptability to gait trajectories used for passive training in the early stage of rehabilitation for hemiplegic patients. The article utilizes the random forest algorithm to construct a gait parameter model, which maps the relationship between parameters such as height, weight, age, gender, and gait speed, achieving prediction of key points on the gait curve. To enhance prediction accuracy, an attention mechanism is introduced into the algorithm to focus more on the main features. Meanwhile, to ensure high similarity between the reconstructed gait curve and the normal one, probabilistic motion primitives (ProMP) are used to learn the probability distribution of normal gait data and construct a gait trajectory model. Finally, using the specified step speed as input, select a reference gait trajectory from the learned trajectory, and reconstruct the curve of the reference trajectory using the gait key points predicted by the parameter model to obtain the final curve. Simulation results demonstrate that the method proposed in this paper achieves 98% and 96% curve correlations when generating personalized lower limb gait curves for different patients, respectively, indicating its suitability for such tasks.