Reasoning about energy in qualitative simulation

Qualitative modeling and simulation make it feasible to predict the possible behavior of a mechanism consistent with an incomplete state of knowledge. Though qualitative simulation predicts all possible types of behavior of a system, it can also produce spurious behavior, i.e., behavior that corresponds to no solution of any ordinary differential equation consistent with the qualitative model. A method for reasoning about energy that eliminates an important source of spurious behavior is presented. This method is applied to a nonlinear proportional-integral controller, and it is shown that qualitative simulation captures the main qualitative properties of such a system, such as stability and zero-offset control. It is believed that this is a significant step toward the application of qualitative simulation to model-based monitoring, diagnosis, and design of realistic mechanisms