Approximate dynamic models for recycle systems

There has been recent interest in the dynamics and control of plants with recycle, due particularly to the complex dynamics that these plants can exhibit. While the transfer functions for the recycle system may be constructed from the individual linear transfer functions for each of the subunits comprising the plant, the resultant overall plant transfer function will often contain denominator deadtime terms. These denominator deadtime terms preclude the use of time-domain simulations and most of the common advanced controller design algorithms as the mathematical methods employed by these techniques require transfer functions with rational denominators. It is therefore necessary to simplify these models before they can be used, and the purpose of this paper is to present a technique suitable for these model simplifications which retains the original system stability and has a strong intuitive appeal.