In this paper, the influence of PM[Formula: see text] on children’s respiratory diseases is taken as the main research focus. Based on the real monitoring data of children’s respiratory diseases in Anhui province, the traditional model is modified substantially, leading to the establishment of two mathematical models. First of all, considering that the PM[Formula: see text] changes over time, a nonautonomous air pollution-related disease model is constructed to study its permanence and extinction. Furthermore, regarding lag days of PM[Formula: see text] exposure, an air pollution-related disease model with the lag effect is installed and its local and global stabilities and Hopf bifurcation are investigated. Meanwhile, the above two models are numerically simulated, respectively. Our study demonstrates that the threshold conditions of permanence and extinction are obtained by the nonautonomous air pollution-related disease model, and the optimal parameters are obtained through the annual revision of the data by integrating the mathematical model, such that the number of children with respiratory diseases in the future can be checked and predicted. Also our study finds that the lag days of PM[Formula: see text] exposure have little effect on children with respiratory diseases in the air pollution-related disease model with a lag effect, but the PM[Formula: see text] has a tremendous influence on the number of patients. Once the lag days are combined with the effect of the PM[Formula: see text], it can have a significant impact on the patients’ number, e.g. an emergence of periodic oscillations, with an approximate period of 11 days in Anhui Province, due to the Hopf bifurcation.

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The dynamics model used for inertially or strapdown inertially stabilized platforms is based on the rotor and motor load, and it either does not consider the stator or it implicitly assumes a fixed stator. It has been determined that vibrations occur in the system when a controller is used in strapdown inertially stabilized platforms with a light base support. As the system is also affected by multi-source disturbances, which are the main factors that affect the control accuracy. For the above two problems, this paper originally establishes a multi-body dynamics model including the controller. The composite controller not only suppresses the vibration successfully, but also greatly improves the disturbance compensation and tracking performance of the strapdown inertially stabilized platforms. Specifically, a modified feedback controller is used to suppress the vibrations analyzed according to the dynamics model. The friction feedforward and residual disturbance observer facilitates the design of compound disturbance compensation on the basis of composite hierarchical anti-disturbance control. To emphasize the advantages of strapdown inertially stabilized platforms, the feedforward controller employs feedforward angular velocity and acceleration. The results of the numerical analysis and experiments indicate that vibrations are successfully suppressed and tracking accuracy and disturbance isolation ability are improved.