Limitations Imposed by the Sign-Equality Assumption in Qualitative Simulation

The second derivative sign-equality assumption has to be made for the derivation of expressions for higher-order derivatives of chattering system variables in the qualitative simulation of models containing monotonic function constraints . Kuipers et al. [1] established this method and showed that prediction failure is possible when the sign-equality assumption is utilized . We present a closer examination of the unwarranted modeling restrictions entailed by this assumption in connected tank systems . We show that all the systems which are validly considered in simulations with HOD constraints necessarily contain tanks with quite atypical shapes . We conclude that the chattering and spurious behavior elimination problem for systems of connected tanks with reasonable shapes is still open.