<正>A nano-displacement measurement system with duo-gratings is analyzed by using optics theory,a math- ematic model for the system is established,and the characteristic of laser Moirésignals is studied through CAD simu- lation.To improve signal sensitivity and positioning accuracy,two methods of precision positioning are brought for- ward:differential Moirépositioning method and modified Moirépositioning method.A compound control system for precision positioning is set up by combining these 2 Moiréalignment methods,in which the modified Moiréalignment technique is used for coarse alignment and the differential Moiréalignment technique is used for fine alignment,and the system obtains positioning accuracy of±10 nm in±500μm positioning range with shot response time.