Optimally Invariant Variable Combinations for Nonlinear Systems

AbstractIn this article we present an “explicit RTO” approach for achieving optimal steady state operation without requiring expensive online calculations. After identifying regions of constant active constraints, it is shown that there exist some optimally invariant variable combination for each region. If the unknown variables can be eliminated by measurements and system equations, the invariant combinations can be used for control. Moreover, we show that the measurement invariants can be used for detecting changes in the active set and for finding the right region to switch to. This explicit RTO approach is applied to a CSTR described by a set of rational equations. We show how the invariant variable combinations are derived, and use polynomial reduction to eliminate the unknown variables to obtain the measurement invariants which are used for control.