The invention provides a method for designing a 
rolling mill vertical vibration suppression controller based on self-adaptive fuzzy 
backstepping, which comprises the following steps of: firstly, establishing a four-degree-of-freedom mechanical-hydraulic 
coupling nonlinear model of 
rolling mill vertical vibration according to a dynamic principle of a 
rolling mill vibration 
system; setting the 
vertical vibration displacement of the working roll of the rolling mill to be close to zero as a control target according to the condition that the vertical vibration of the rolling mill causes the workingroll to jump up and down; and finally, in combination with a 
nonlinear model of rolling mill vertical vibration, selecting a proper 
Lyapunov function, solving a virtual controller, an actual controller and an adaptive law which enable V (t) to tend to zero when t tends to be infinite, and finally obtaining the predetermined performance 
controller design method for suppressing rolling mill vertical vibration. According to the method, the rolling mill vertical vibration 
nonlinear model more conforming to the actual working condition is established, the characteristic that the 
servo valve has adead zone and the limitation on roller vibration displacement are considered, the rolling mill vertical vibration 
suppressor is designed, vertical vibration occurring in the high-speed rolling processis rapidly and actively suppressed, and the stability of the high-speed plate and strip rolling process is guaranteed.