Quality control of binary distillation columns via nonlinear aggregated models

A robust nonlinear control law is designed to reject unknown feed composition disturbances with overall stability. Implementation to real columns as well as comparisons with classical control strategies, show the robustness and flexibility improvements of the method. Almtracq-Using singular perturbation techniques on a physical model of distillation column, an aggregated model is proposed for control purposes. Nonlinear perturbation rejection techniques via static feedback are then applied to this model to reject the feed composition disturbances: around every slowly varying reference trajectory, the existence of such a control law and the stability of the overall closed-loop system are proven. Moreover, the obtained control law can be synthesized with measurements commonly available on distillation columns: the product compositions and two inner temperatures. An industrial implementation on a refinery depropanizer of 42 trays is presented. Simulation comparisons with linear and nonlinear geometric control laws, both using the physical model of high dimension, show the robustness and flexibility improvements provided by our method. Notation f = (fi)~=l n: state function of the physical model (1). f = ~)j=ti~,i~,n: state function of the reduced model (18). fj: function defmed by (2) for j = 1,..., n and corresponding to the physical model, or function defined by (19) for j = 1, r, jp s, n and corresponding to the reduced model. F: mole flow of the feed. F: steady-state value of F. Hj: fiquid holdup of tray j. Hi: liquid holdup of tray j for the compartment of m trays. m /~= X Hi. 1 J~ /~" = ~2/'/j: the liquid holdup of the rectifying compartment. n-1 /~, = ~ P/j: the liquid holdup of the stripping compartment. h /~n = Hn. j: tray index. Ja: index of the aggregation tray relative to the compartment of m trays. jr: index of the feed tray. j,: defines the rectifying compartment (2 <j, <Jl)" Js: defines the stripping compartment (jr <j, < n-1). k: the equilibrium function. k(i,,+l): mole composition of the vapor entering the compartment of m trays. k(xj): vapor mole fraction on tray j. L: reflux flow. L: steady state value of L. L: liquid flow in the compartment of m trays. m: number of trays of the compartment. n: number of trays of the column. r: index of the aggregation tray relative to the rectifying compartment. s: index of the aggregation tray relative to the stripping compartment. t: the time. Tj = O(xj): temperature …