Kurt V. Waller

Dynamic modeling and reaction invariant control of pH

Abstract A systematic treatment of the dynamics and control of acid-base reactions is presented. A state model consisting of mass balances for the species present is formed. Through a linear transformation of the concentration vector a new model is set up. The state vector of this model is partitioned into a reaction invariant and a reaction variant part. The model is thus split into two parts, one describing the physical properties of the reactor system independent of chemical reactions, the other describing the chemical reactions. For fast acid-base reactions the reaction invariant part of the model is sufficient to define the thermodynamic state of the system. The reaction rate vector is thus eliminated from the model. In this case the reaction variant part of the model consists of a static equation, relating pH to the reaction invariant state variables. The model obtained provides a sound basis for design of control loops for feedback and feedforward control of pH. As a direct application a new scheme for adaptive control of pH is proposed.

Robust multiobjective linear quadratic control of distillation using low-order controllers

Abstract A robust multimodel multiobjective linear quadratic design technique is applied to the design of robust distillation control systems. A range of operating conditions of the process is considered. A single constant low-order controller is then designed to give satisfactory performance at all operating points. This is achieved via a minimax multicriterion optimal control problem, in which the worst values of quadratic cost functions over the range of operating points are minimized. The process studied is an experimental distillation column at Abo Akademi showing nonlinear behavior in the desired operating range. First-order time delay models were available for the process at different operating points. A deterministic servo problem is studied, involving set-point changes between two operating conditions, and robustness as concerns the nonlinearities is desired. The control objectives involve keeping the outputs close to the desired ones and simultaneously keeping the variations of the inputs small. Modifications of the objectives studied include reducing variations of the output as well as trying to follow specified trajectories. Various controller structures are studied: multiloop PI, multiloop PID, and (full order) multivariable PI. The controllers are evaluated both through simulations and experiments. The results show that by the technique studied, it is possible to design robust multivariable control systems with attractive properties for the distillation system in question.

Multivariable control of ill-conditioned distillation columns utilizing process knowledge

Abstract In distillation, a reliable model of the column is generally considered as a prerequisite for the design of efficient two-product control by multivariable methods. However, such models are often very hard to obtain. In fact, even very small identification errors may introduce features which are in conflict with physical knowledge, and which make the model useless. Instead of focusing on the development of consistent models, this work is concerned with the utilization of physical process knowledge directly for multivariable control, even if a reliable input-output model is lacking. Such knowledge is, for example, the sign of the RGA-values and an estimate of the input-directionality. It is shown that such structural information of the process can form an entity of control-relevant knowledge that is sufficiently rich for the design of a multivariable SVD controller.

On using sums and differences to control distillation

The idea to use sums and differences of compositions (or temperatures) to improve dual-composition control of distillation has been suggested a number of times in the literature, at least since 1962. The main advantage of the scheme has been claimed to be that it results in noninteraction, i.e. the two composition control loops act as noninteracting SISO-Ioops. Most of the schemes suggested have used distillate flow D and vapor boilup V as manipulators for the composition loops, although also other manipulators have been suggested, Some new theoretical results (Haggblom and Waller, 1987) show that noninteraction (triangular system matrix) at steady state is obtained for separations where the distillate flow D is equal to the bottoms flow B when the sum of product composition is controlled by D or by B. Dynamic simulations for one such case show that, compared to the usual approach of using D to control top composition and vapor boilup V to control bottoms composition, an improvement in control may be obta...

TWO-WAY OR ONE-WAY DECOUPLING IN DISTILLATION?†

Abstract A systematic simulation study of dual composition control of distillation has been carried out in order to compare different decoupling strategies and contrast them with well-tuned SISO-controllers. Two column models are studied. One describes the experimental pilot plant used by Wood and Berry (1973) and the other the experimental pilot plant investigated by Luyben and Vinante (1972). A better control quality–compared to the control quality obtained by SISO-control–may be achieved if suitably chosen decoupling elements are introduced. The best control quality does not, however, necessarily correspond to the best decoupling. In the studied systems, where the controllers of the decoupled systems have been tuned according to the Ziegler-Nichols settings for the effective process transfer functions, there is no incentive to use two decouplers (two-way decoupling): the same or better control quality is obtained with the simpler scheme utilizing only one decoupler (one-way decoupling). Actually, for t...

Control Structures, Consistency, and Transformations

The operation of a multivariable process like a distillation column has to satisfy several control objectives. Typical objectives are to ensure the stability of the process, to produce specified products, and to optimize the operation economically. As the various objectives may be of quite different importance and normally require control actions at different time rates, it is usually desirable to decompose the full system into a number of subsystems according to the objectives.

ON MODELING ACCURACY FOR MULTIVARIABLE DISTILLATION CONTROL

Modeling of the process dynamics needed for (linear-quadratic) design of multivariable composition control schemes in distillation is treated. It is illustrated how an (experimentally obtained) model consisting of simple transfer functions containing dead times is transformed into a sampled model, suitable for controller computation. Two distillation systems, with quite different properties, are used in the simulations, illustrating the controller properties: a column modeled by Toijala and Fagervik (1972) and the experimental system modeled by Wood and Berry (1973). The paper is focused on how errors in the process models affect the control properties of the multivariable control system. The relations between the model structure, the performance index, the control quality, and the sensitivity are discussed.

Performance indices for multivariable PI-control with incomplete feedback

Abstract The formulation of performance indices is discussed for control problems typical of the chemical process industry. Emphasis is put on the common situation of incomplete feedback, i.e. the situation where only part of the state vector is measured or estimated. It is suggested that performance indices for regulator problems should include the time derivative of a chosen output vector in addition to the time derivative of the control vector and the chosen output vector. For a quadratic performance index and a linear system subject to unknown constant (step) disturbances, an optimal multivariable PI-controller is derived. Examples illustrate that an essential improvement of the output response for incomplete feedback can be obtained if weight in the performance index is put on the time derivative of the chosen output vector.

Relations between Steady-state Properties of Distillation Control System Structures

Abstract Recent research in dual composition control of distillation has, to a large extent, treated various control system structures. Special attention has been paid to configurations where the manipulative variables have been chosen so as to minimize interaction between the control loops. In the present paper consistency relationships between the process gains of single control structures are derived. It is also shown how the process gains of arbitrary control structures can be calculated from the process gains and steady-state data of just one suitable base structure. The equations obtained are exact relations based on fundamental first principles. By means of these relations it is possible easily to investigate (e.g. calculate relative gains (RGA) for) a large number of control system structures. A structure where the reflux flow and the boilup, or functions of them, are the composition manipulators is a suitable base structure. The reason for this is that a model for such a scheme contains more information than does e.g. a model, such as it usually is given, for a material balance scheme. The latter one cannot therefore be utilized to the same extent for variable transformation purposes as the former. The consistency relationships also provide useful constraints for parameter estimation.

ILL-CONDITIONEDNESS AND PROCESS DIRECTIONALITY - THE USE OF CONDITION NUMBERS IN PROCESS CONTROL

Abstract The concepts of process directionality and ill-conditionedness as commonly used in the literature might be confusing. Therefore, a refinement of the definition of process directionality is suggested. The refinement divides the concept of directionality into two parts, connected to stability and performance aspects, respectively. The refinement clarifies the connection between condition numbers and control difficulties and makes it possible to define general scaling methods for directionality analysis.