Robust H₂ /H_∞ Control Of Vibration Isolation Platform For High-pricision Equipment Based On LMI

Along with the rapid development of science and technology, the modern machining has entered precision, even ultra-precise period. Thus there emerging a variety of high-precision equipment. However, the equipment requires a special working environment with limited vibration, and the equipment cost is very high. Thus, it is imperative to find an effective way to ensure the functionality of high-tech equipment against micro-vibration.The research theme of this dissertation is multiple-degree-of-freedom micro-vibration hybrid control system for high technology facilities based on the project of National Science Foundation of China-"Micro-vibration hybrid control system for high technology facilities subject to urban railway traffic-induced ground motion". By using air springs and magnetostrictive actuators, a multi-degree-of-freedom hybrid control system is developed and its dynamic model of platform and the control system model is established. Based on H_∞robust control theory and LMI (linear matrix inequality) technique, we investigate the vibration isolation platform system. The main research work of this paper is listed as follows:The first part is the structural design of multiple-degree-of-freedom hybrid control system. Firstly, the geometric dimensions of the platform and the number and direction of air springs and magnetostrictive actuators are introduced. Then, the analytical models of the stiffness and damping of air springs are investigated. Finally, the relation graph of electric current—output force for the magnetostrictive actuators are investigated. According to these prerequisites, the vibration model and dynamic function are obtained.The second part is the transformation from dynamic function to state-space function. By using H_∞robust control theory based on LMI, the simulation on the vertical vibration, horizontal vibration and 6-degree-of-freedom platform vibration is considered respectively. The simulation demonstrates the validity and advantage of the proposed method.The third part is optimization of the H_∞robust control result using H2/H_∞robust control based on LMI. The simulation results demonstrate that the H2/H_∞ control is offers much better robustness in performance. but there need bigger control force for the control system.The last part is H∞robust control for the vibration isolation platform system which consists of perturbed identified parameters. Its aim is to narrow the gap between the simplified model and realistic model. The simulation results show that the control system also exhibits good robustness.