The LQG controllers, designed for the NASA Deep Space Network antennas have small tracking errors and are resistant to wind disturbances. However, during antenna slewing, they induce limit cycling caused by the violation of the antenna rate and acceleration limits. This problem can be avoided by introduction of a command that does not exceed the limits. The command preprocessor presented in this paper generates a command that is equal to the original command if the latter does not exceed the limits, and varies with the maximal (or minimal) allowable rate and acceleration if the limits are met or exceeded. It is comparatively simple since it requires only knowledge of the command at the current and the previous time instants, while other known preprocessors require knowledge of the terminal state and the acquisition time. Thus, the presented preprocessor is more suitable for implementation. In this article analysis of the preprocessor is presented. Also the performances of the preprocessor itself, and of the antenna with the preprocessor is illustrated with typical antenna commands.