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A low-order modeling technique for separation processes is developed by considering a staged column as a compartmental system in which a number of stages are lumped to form an equivalent stage. This method leads to low-order models of separation processes directly and without linearization. Moreover, the resulting models have state variables and parameters that are physically significant. In contrast t o alternative model reduction methods, compartmental analysis guarantees preservation of both material balances and steady states for arbitrary changes in the input variables.A comparison of compartmental analysis to a recently proposed technique based on orthogonal collocation, both methods incorporating an equimolal overflow assumption, shows the efficiency and robustness of the compartmental method.A. Benallou SCOPELow-order, dynamic models of separation processes are desirable for a number of reasons including the evaluation of alternative control strategies, the development of on-line applications of advanced control schemes, and the training of plant personnel.Most of the available methods for building low-order models of separation processes are deficient because they are so abstract and complicated, require linearization of the system equations, or yield models with parameters or state variables having no physical significance.The most recent of these methods uses orthogonal collocation to derive reduced models (Wong and Luus, 1980;Cho and Joseph, 1980, 1983;Stewart et al., 1981). This approach introduces mathematical complications and leads to state variables that may not necessarily correspond to tray locations.Another approach, linearization techniques combined with model reduction, can lead to low-order models in a state space or transfer function form (Mockzek et al.. 1965;Wahl and Harriott, 1970;Weigand et al., 1972; Waller, 1972 Waller, , 1979Crockett, 1978). This class of methods offers a simpler alternative, but leads to models in which the parameters have no physical significance.By considering a separation column as a compartmented system, it is possible to derive low-order models that avoid these deficiencies. At the same time, steady state characteristics of high-and low-order models can be matched exactly, and transient characteristics of the low-order models can closely approximate the high-order system dynamics. Moreover, the model parameters retain their physical significance, permitting broad use of the model, especially when operating conditions change. In this development of the basic theory, several simplifying assumptions are made, including equimolal overflow, in order to compare results with those from collocation methods. Benallou (1 982) presents extensions of the method to more realistic systems. CONCLUSIONS AND SIGNIFICANCECompartmental modeling techniques are based on the physical characteristics of separation processes. They are suitable for developing low-order models for AIChE JournalJuly 1986 Vol. 32, No. 7 1067 simulation or control purposes that are valid, with no fur...

In several recent studies a discrete convolution representation of a dynamic system has been used to develop new digital control algorithms based on the prediction of future outputs. This paper presents a fundamental analysis of the concepts involved In designing both predictor and control elements for such algorithms. For single-input, single-output systems, the predicted controller Is equivalent to a discrete feedback controller which operates on the current output and past input signals. Simulation and experimental results for several single-input, single-output systems provide a comparison of a predictive control technique with standard RID control. The predictive controller Is shown to be quite effective even for systems with inverse response characteristics.

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