Rigorous analytical methods for consistent modeling of control structures for multivariable processes are presented. The continuous distillation process is used to illustrate the methods, but the basic ideas, and more specifically the transformations and consistency relations derived, are valid in general.If steady-state operating data and the process gains of an arbitrary control structure are known, it is possible to calculate the process gains of any feasible control structure. A general expression relating the process gains of different control structures is derived. In general, the process gains must also satisfy certain consistency relationships which can be derived from first principles, e.g., steady-state material balances.The usefulness of the results is illustrated by control structure transformations and reconciliation of process gains, by an application to process dynamics, by synthesis of noninteracting control loops, and by derivation of analytical relationships useful in relative gain analysis.

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A good deal of the research on distillation control during the last decade has concerned the structure of the control system, i.e., which inputs should be connected to which outputs (Waller, 1986). One example is the discussion of the relative merits of so-called material balance control and conventional control in dual-composition control of distillation (McAvoy and Weischedel, 1981).Not only the manipulator part of the control scheme has been discussed. Various choices of the controlled variables have been sug,gested, such as sums of and differences between compositions or temperatures .The various structures have usually been discussed and compared on the basis of interaction, i.e., the structure giving the smallest (steady state) interaction between the control loops has been considered the preferable one.This note treats the importance of disturbance sensitivity, especially in relation to interaction, when choosing a control system structure. An important difference between control structures is that the compositions (or temperatures) to be controlled may be affected very differently by the same disturbances. This can be shown theoretically by control structure transformations (HiXggblom, 1986;Haggblom and Waller, 1987a), and it has been verified experimentally (Finnerman and Sandelin, 1986;. The subject has also been discussed by Shinskey (1985).In the following, four different control structures are used to illustrate how the control qualities obtained correlate with the degree of interaction and the disturbance sensitivity implied by the open-loop schemes. Control Structures StudiedA pilot-plant distillation column was used in the experimental part of this study. The column has 15 bubble cap plates, is 30 cm in diameter, and separates a mixture of ethanol and water. The nominal steady state at which the column was operated is given in Table 1. The control objective is to keep the temperatures on plates 4 and 14 as constant as possible in spite of disturbances in feed composition.The four control configurations studied are denoted by the manipulators used to control the two temperatures, the first manipulator controlling the top temperature, T4 (or y , for short), and the second the bottom temperature, T,, (or x). The control structures are (see Table 1 , 1982, 1984Shinskey, 1984), with inventory controlled by L + D a n d BTransfer functions (first order plus dead time) for the four control structures were obtained experimentally, with only inventory control loops (accumulator level and column base level) closed. Due to nonlinear process behavior and inexact measurements, the experimentally obtained process gains did not satisfy certain consistency relationships that must hold for both physical and mathematical reasons (Hlggblom 1986;Haggblom and Waller 1986, 1987a,b). The process gains were therefore reconciled by optimization subject to these consistency relationships (Haggblom, 1987). The reconciled transfer functions, which are used in the simulations below, are given in Table 2. The gains between the...

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The process gains for different distillation control structures can be calculated through transformations from known gains of one arbitrary structure.In this paper the transformation is utilized for calculation of a two-point distillation control structure which, in the steady state, simultaneously rejects disturbances in the feed composition and in the feed flow rate and results in implicit decoupling between the two product control loops. This disturbance rejecting and decoupling (DRD) structure is tested on a model of a 15-plate pilot-plant distillation column. It compares favorably with standard structures for dual composition control. Experimental results agree with the simulation results.