Vibration control of EMU car body based on secondary vertical actuators and piezoelectric actuators

To reduce the rigid and elastic vibration of car body of high-speed electric multiple units (EMU), the active vibration control method was proposed based on secondary vertical actuators and car body piezoelectric actuators. Based on a certain type of high-speed EMU, an active reducing method of vibration was designed in which vertical actuators were installed in thesecondary suspension, piezoelectric actuators were arranged in the under-frame of the car body, and an H_∞ robust optimal controller was used to coordinate the vehicle control. A mechanics model of rigid-flexible coupled vibration reduction based on vehicle dynamics parameters was established. The placement positions of the piezoelectric actuators and sensors were optimized by using the H₂ and H_∞ norms. The H_∞ feedback controller was designed by robust optimal control method. The effect of vibration damper and active control method on vehicle dynamic performance was simulated by MATLAB. The dynamic performance differences between passive suspension vehicle, secondary vertical actuators vehicle and active control vehicle were compared. Analysis results show that when the piezoelectric actuators and the piezoelectric sensors are arranged at the distances of 7.15, 12.25, and 17.35 mfrom the left end of the car body, the normalized H₂ and H_∞ norms of the first and second-order elastic modes of the car body are the largest, and can be used as the placement positions of piezoelectric actuators and sensors. The robust optimal control method based on the secondary vertical actuators and car body piezoelectric actuators can effectively suppress vibration of the car body, and the acceleration power spectrums of the first order vertical bending vibration frequency on the car body centre and above the bogie reduce by 5% and 10% of passive suspension vehicle, respectively. With higher velocity, the vibration acceleration suppression effect is more obvious. When vehicle's speed is 200 and 350 km·h^-1, its mean square root of vibration acceleration decreases by 10% and 18%, respectively. Compared with the passive suspension, the magnitudes of output force power spectrums of the secondary vertical actuators are 106 N²·Hz^-1 at the bounce and pitch vibration frequencies of the car body. Thus, the secondary vertical actuators can greatly suppress the rigid vibration of the car body. The voltage power spectrums of the piezoelectric actuators reach a peak of 4 000 V²·Hz^-1 at the first order vertical bending vibration frequency of the car body, which greatly suppresses the elastic vibration of the car body.