Dynamic Analysis and Control of a Polymerization Reaction

In this paper detailed dynamic analysis of a quantitative mathematical model of a polymerization process is presented. The process serves as an appropriate paradigm of multi-variable dynamic systems of strong non-linear coupling in the control of which the state propagation of various internal degrees of freedom cannot directly be controlled: the desired output is nonlinear function of these quantities. In the present example only a single input variable is used as the control signal (process input), and a single output variable is observed (process output) for this purpose. In contrast to a former approach in which the stability of the steady states was proved by perturbation calculus and the process was approximately treated as a 1^st order problem in its quasi-stationary limit by an ARMAX-type (autoregressive moving average model with external input) control, in the present paper the "exact" 2^nd order dynamics of the transitions between different steady states is considered. It is observed that the response of the system is negative definite function of the process input. On this basis a special adaptive controller is constructed the operation of which far excels that of the quasi-stationary 1^st order one. It is concluded that with a sampling time of about 0.067/2, 0.067, and 2 times 0.067 s quite precise control can be achieved. This sampling rate is smaller but almost comparable with the 0.2 s sampling time commonly applied for such reactions in the industry. The conclusions are justified by simulation results