Qualitative Simulation for Process Modeling and Control

Qualitative simulation is a promising technique for analyzing dynamic systems with incomplete knowledge. The QSIM algorithm provides a framework for constructing qualitative versions of process models normally represented by ordinary differential equations. In this work, a qualitative model is developed for a first-order system with a PI controller without precise knowledge of the process or controller parameters. Simulation of the qualitative model yields all of the solutions to the system equations. In developing the qualitative model, a necessary condition for the occurrence of oscillatory behavior is identified. Initializations that cannot exhibit oscillatory behaviors produce a finite set of behaviors. When the phase space behavior of the oscillatory behaviors is properly constrained, these initializations produce an infinite but comprehensible set of asymptotically stable behaviors. While the predictions include all possible behaviors of the real system, a class of spurious behaviors has been identified. When limited numerical information is included in the model, the number of predictions is significantly reduced.