Adaptive Control of a Polymerization Process

In this paper a simplified ARMAX-type (Autoregressive Moving Average model with eXternal input) adaptive control of a polymerization process approximately in its quasi-stationary limit is presented. This process serves as an appropriate paradigm of multivariable dynamic systems of strong non-linear coupling in the control of which the state propagation of various internal degrees of freedom cannot be directly controlled: the desired output is nonlinear function of these quantities. In the present example only a single input variable is used for control purposes. In the paper detailed mathematical analysis of a quantitative model of the process is presented. It is concluded that at the time-scale commonly used in industrial control of such reactions (about 0.1-0.2 s sampling time) following the variation of the process input (control signal) the internal dynamics of the system achieves its stable stationary state with a rough approximation, therefore in the applied ARMAX-type control instead of the internal dynamics of the system the “dynamics” of the desired output is revealed, i.e. the controlled process is more or less similar to the concept of the “quasi-stationary processes” of Classical Thermodynamics. This fact sets certain limit to the available precision of the control if the desired control actions are faster than the characteristic variation of the internal dynamics. Improving this control requires far more detailed analysis and modelling of the process, and does not allow neglecting the dynamics of the internal degrees of freedom.