Controller parameters dependence on model information through dimensional analysis

In this article we make use of dimensional analysis in order to investigate the controller parameters dependence on model information (i.e. model parameters). The objective is to relate the influence that each model parameter has on each controller parameter. In order to accomplish this goal the model transfer function is first analyzed using dimensional analysis and characterized by means of of dimensionless numbers. Secondly each controller parameter is related with the model parameters. As a result it is derived the underlaying structure that any homogeneous tuning rule must follow. The general results are particularized for PID control of first order and second order systems. The results can be applied to PID tuning and PID tuning rules comparison.