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Vibration is a significant factor that influences the performance of the long-range ultra-precise positioning system. Due to the intense nonlinearity and parameter uncertainties, it is difficult to eliminate the vibration by using a conventional PID controller. In this paper, the intelligent PID controller based on BP neural network with the ability of self-learning and strong robustness is introduced into the positioning system. Simulation and experiment are conducted and the results show that the vibration is effectively suppressed and the positioning accuracy has reached within 5.8nm.

Base on the significance of understanding research objects, modeling and validation of ultra precision positioning system is studied in this paper. Taking different reduction methods of leaf springs into consideration, a rigid body model and an elastic body model has been developed. Identifying unknown parameters by the least square method, the validation results of two models are compared. The conclusion indicates that the elastic body model is better when the dynamic characteristics of the positioning system before the stable state are concerned and the rigid body model is more appropriate if the accuracy of the whole model is focused.

Based on data from internet, investigation was conducted to verify the relationship between the ratio of fake parts and the number of automobile holdings. A complete information game was modeled to reveal the impact of piracy on product life cycle of automobile parts. Numerical analysis showed that automobile manufacturers, threatened by piracy, may get maximum profits by appropriate regenerating key parts.