Study on the Load‐Adaptive Control Method of Quasizero Stiffness Vibration Isolator Based on the Semi‐Analytical Solution

For the quasizero stiffness (QZS) isolators, the mismatch between the stiffness and the load will significantly impact the vibration isolation performance, greatly reducing the isolation efficiency and complicating the load motion. Therefore, a load‐adaptive method is designed innovatively based on a semianalytical solution of the QZS isolator, which adjusts the stiffness to match the load while simultaneously controlling the load’s motion. The advantage of this control method is that it can fully leverage the excellent vibration isolation performance of the QZS isolator while eliminating the need for continuous control intervention. To match the changing load, air springs with adjusting stiffness are chosen to construct the positive and negative stiffness structures of the QZS isolator. The static and dynamic models are established to analyze the influences of the mismatched load on the stiffness and vibration isolation characteristics of the QZS isolator with constant stiffness. Then, based on the Lyapunov stability theorem, a two‐stage load‐adaptive control method is developed by setting the control target to be the semianalytical solution of the steady‐state orbit solved by the averaging method. Guiding by the control method, the unknown changed load is estimated, the stiffness of the air springs is adjusted to match the load, and the load vibration state is stabled to the quasizero steady‐state orbit with small amplitude. Finally, numerical simulations are given to verify the effectiveness of the control method. The results demonstrate that the load‐adaptive control method can eliminate the effect of load variation on the deterioration of the QZS isolator. Since the QZS isolator has an excellent vibration isolation performance, when the state reaches the quasizero steady orbit, the vibration of the load can stay small without controlling energy input. The proposed load‐adaptive control method solves the problem of the load sensitivity of the QZS isolator and broadens the field of its industrial applications.