Use of Feedback for Indirect Optimizing Control: Application to Petlyuk Distillation

We address the problem of optimizing operation of a process where there are extra degrees of freedom, and where the optimum is not at some constraint. In practice, there are always unknown disturbances and model uncertainties which make this task complicated. The key idea of this paper is to turn the non-linear optimization control problem into a setpoint control problem so that we achieve “selfoptimizing control”. If this can be done, the task of optimizing operation can be realized by simple standard control loops, without the need of solving complex nonlinear optimization problems on-line. The integrated “Petlyuk” or “dividing-wall” distillation column is used as an example process. The column has two extra degrees of freedom at steady state, and the challenge is to find a set of feedback variables, which makes the operation insensitive to disturbances so that the reported 30% energy savings can be achieved in practice. DYCOPS-5 Symposium: Corfu, Greece, June 8-10, 1998 Page 2 of 6 2. THE PETLYUK DISTILLATION COLUMN The thermally integrated “Petlyuk” arrangement implemented in a single distillation column shell has several appealing features. For the separation of a three-component mixture, Triantafyllou and Smith (1992) report savings in the order of 30% in both capital and energy costs compared to traditional arrangements with binary columns in series. An important question remains: Is this process units difficult to operate and is it possible to achieve in practice the energy savings? The Petlyuk column, shown in Fig. 1, has at steady state, five independent manipulated inputs: Boilup (V), reflux (L), mid product side-stream flow (S), liquid split ( ) and vapor split ( ). There may be up to four product specifications: Purities of top ( ) and bottom ( ) products, purity of side-stream product ( )and the ratio of the light and heavy impurity components in the side-stream product ( ). However, based on the results of Wolff and Skogestad (1996), which shows the possibility of infeasible operation (“holes in the operating range”) we will only use the first three product specifications. We then have two remaining degrees of freedom and the optimization objective is to use these inputs (e.g. and ) to minimize the energy consumption ( ). The issue is then to find a set of variables which, when kept constant at their setpoints, indirectly ensures optimal operation. One seemingly viable solution would be to simply implement the optimal minimum heat input in an open loop fashion (i. e. set ). However, there are at least three serious problems: 1) Since operation is infeasible if we have , we would need to set . 2) Measurement or estimation of the actual V is generally difficult and inaccurate, which makes it even more difficult to keep V close to Vmin. 3) The optimal value changes with operation, and it would require a good model and measurements of the disturbances to recompute it. Thus, this open-loop policy is clearly not viable. As good candidate variables for feedback control we want variables which avoid the three problems above: 1) The optimal candidate feedback value should not be at a limit, that is, the variable should not have an extremum inside the normal operating range, and in particular not when 2) The accuracy of the measurement of the variable should be good. 3) The relation of the variable and the optimum should be insensitive to disturbances. Finally, the variable should be easy to control, using the available extra degrees of freedom. Often we may find variables which have an extremum when the criterion functions is at its minimum. These cannot be used for feedback, but may be used in experimental methods, or simply as indicators to process operators. 3. THE PETLYUK COLUMN MODEL We use a dynamic tray model with the following simplifying assumptions: Constant pressure, constant relative volatilities, constant molar flows, constant tray efficiency, no heat transfer through the dividing wall. This is a very simple model, but it contains the most important properties of a column. The column data can be found in Halvorsen and Skogestad (1997). The column shown in Fig. 1 is modeled with 6 sections (the numbers inside the column are section numbers). A three-component feed, with components a, b and c is separated into almost pure a (97%) in the top product D, almost pure b (97%) in the in the side stream S, and almost pure c (97%) in the bottom product B. For our column the total number of states is 150 (48 trays plus reboiler and condenser). The input, output and disturbance vectors are defined as: