With the growing trend of higher running speed and lighter body weight in the high-speed train, the influences of fluctuating crosswind on running stability and safety are becoming more and more not negligible, especially under the combined action of unsteady aerodynamic loads and random orbital excitation. In order to investigate this problem, a vehicle dynamic model of with 42 degree of freedom is built, in which the major body, two bogies and eight wheels are involved. The unsteady aerodynamic loads under stochastically fluctuating crosswind are obtained based on Cooper theory and the harmonic superposition method, and the random excitation of the track is also taken into consideration. For the vertical vibration originated from the fluctuating crosswind and the random track spectrum, the skyhook damping and the magneto-rheological fuzzy semi-active control strategies are individually applied to suppress the vibrating amplitude and improve the running stability. It is indicated that the vertical vibration under the coupling influence of the unsteady aerodynamic loads and the random orbital excitation are significantly increased, and the vibrating amplitude can be effectively suppressed by both the two different control approaches. It is also shown that the index of running stability in the case of the fuzzy control is evidently better than the skyhook damping.

Rolling mill system may lose its stability due to the change of lubrication conditions. Based on the rolling mill vertical–torsional–horizontal coupled dynamic model with nonlinear friction considered, the system stability domain is analyzed by Hopf bifurcation algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. In order to restrain the instability oscillation induced by the system Hopf bifurcation, a linear and nonlinear feedback controller is constructed, in which the uncoiling speed of the uncoiler is selected as the control variable, and variations of tensions at entry and exit as well as system vibration responses are chosen as feedback variables. On this basis, the linear control of the controller is studied using the Hopf bifurcation algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. The results show that the system stability domain can be expanded by reducing the linear gain coefficient. Through choosing an appropriate nonlinear gain coefficient, the occurring of the system subcritical bifurcation can be suppressed. And system vibration amplitudes reduce as the increase of the nonlinear gain coefficient. Therefore, introducing the linear and nonlinear feedback controller into the system can improve system dynamic characteristics significantly. The production efficiency and the product quality can be guaranteed as well.