Transforming dynamic system models between two-axis reference frames rotating at different angular frequencies

This paper introduces a general method to transform dynamic system models between two-axis reference frames that are rotating at different angular frequencies. Such a transformation is needed in the analysis and implementation of a control system where the entire system is not presented in the same reference frame. Detailed derivation of the transformation for transfer function matrices is presented. Contrary to the previous solutions, the suggested transformation is not limited by the structure of the transfer function matrix of the system. Application examples illustrate the theory. Theoretical analysis indicates important design limitations especially for multiple frame control systems. Experimental results verify the analysis.