||System with Backlash is a kind of nonlinear system, which is studied widely. In the field of industrial manufacture and robotics, those backlashes occur in the motion transmission, which really spoils the performance. The backlash makes the system unconnected at some time when the system is running. In the unconnected period, the control commands can not be transformed to the part separated by backlash. This leads a time delay problem. In this thesis, the dynamic performance of backlash is studied by establishing a model. The impact phenomenon during the dynamic process of backlash is concerned. In the study of model, the velocity of motion is analyzed and shows that it varies fast and greatly in some period. The conventional method, digital differential, introduces great noises in the measurement which makes the control performance poor. A motion measurement system, including an FPGA PC card, is established according to the requirement of measurement. The accuracy analysis of the method is studied, which gives a direction to the design of FPGA program. Also, the sources of noises are studied and methods on eliminating those noises are given. A learning controller based on Fourier analysis is developed and utilized on a backlash system. The learning controller is performed in the frequency domain which can compensate the time delay from backlash, which is a big flow for those systems. The convergence of the controller is also proved. Experiments are operated and the results illustrate the effectiveness of the controller and the improved motion measurement system. Thus, it can be widely used in motion control systems.