Stability Analysis of System with Fixed Structure Controller for Industrial Multi-Stage Separation Process via Vector Lyapunov Function

The present paper is devoted to the evaluation of stability analysis of multi-stage separation process (multicomponent distillation) control system based on the tray-by-tray nonlinear dynamic process model. The vector Lyapunov function (LF) jointly with comparison functions (CF) are proposed for the stated problem solution. The overall system of differential equations is decomposed on the subsystems so that the LF for each subsystem can be determined. It was shown that the unforced subsystems of distillation model are unstable. But the stabilizing effect of composite system is reached in a natural way by the interaction among these subsystems. This gives the possibility to formulate stability conditions using CF. The estimation of stability domain for multivariable fixed-structure composition (temperature) controller for two-product industrial distillation column is given as illustrative example.