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The singular-value decomposition has been used to analyze the robustness of closed-loop systems and to determine whether any controllability problems can be expected. Past controllability conditions have been derived in terms of the condition number and the minimum singular value of the process and the condition number of the controller transfer function matrix, in terms of potential sensitivities of the closed-loop system to model uncertainties or problems with saturation of the manipulated variables. This paper considers processes with a large maximum singular value. It is shown that the closed-loop control of such processes can result in poor transient performance as a result of valve accuracy considerations, even if the condition number is small and the minimum singular value is large, which would indicate no performance limitations according to existing controllability criteria. Further, processes with large singular values can be prone to sensor saturation. This indicates that the magnitude of all of the singular values should be considered when assessing the controllability of a process. A new interaction tool based on output correlation is introduced to help select measurements and manipulated variables that have a good range of singular values for practical application. The approach proposed is illustrated on two simple examples and on the Tennessee Eastman process.

In any process plant design, a central question is whether it is possible to achieve acceptable control with the available manipulated variables, while taking into account the disturbances that can be expected. Some little known controllability measures have been proposed to address such issues.^1,2 The main reason these controllability measures have received little attention is probably that, while their mathematical formulation was defined, no algorithms were provided to solve the mathematical problems. This paper shows how to calculate these controllability measures and applies the algorithms to some process examples.

Many of the crystals in the pharmaceuticals, photographic, and other industries are multidimensional; that is, their growth is associated with the change of multiple internal coordinates. The main governing equation for such systems is a highly nonlinear multidimensional population balance equation that must be solved for a wide range of length scales. For population balance equations, it is well-known that the standard first-order schemes give diffusive solutions while the commonly used second-order schemes give spurious oscillations. This paper presents a high-resolution simulation algorithm that provides short computation times and high accuracy. The high-resolution algorithm is compared to the upwind difference and Lax−Wendroff methods through simulations of potassium dihydrogen phosphate (KDP, KH2PO4) crystal nucleation and growth. No spurious oscillations or numerical diffusion occurred, in contrast to the upwind method and Lax−Wendroff methods. The numerical stability of the algorithm is assessed using the Courant−Friedrichs−Lewy condition.

A systematic approach is developed for the in situ control of the crystal size distribution, and is applied to the aqueous crystallization of paracetamol (acetaminophen) as a model pharmaceutical system. This involves the determination of the solubility curve and the metastable limit, and the operation of concentration-controlled batch crystallization. The solution concentration and the solubility curve of paracetamol in water are determined using attenuated total reflection (ATR)-Fourier transform infrared (FTIR) spectroscopy coupled with chemometrics. The metastable zone width of paracetamol is determined using laser backscattering and ATR-FTIR spectroscopy. Seeded batch crystallizations of paracetamol following a desired supersaturation profile near the metastable limit are carried out using in situ solution concentration measurements obtained from ATR-FTIR spectroscopy. The in situ chord length distributions of crystals obtained from laser backscattering are related to characteristics of the crystal size distribution. Product crystals where the supersaturation temporarily exceeded the metastable limit during operation contained agglomerates and exhibited large size variation. Larger product crystals of more uniform size and shape are obtained from operation where supersaturation was successfully controlled to stay within the metastable limit.

In the pharmaceutical industry, a vast number of compounds are produced by solution crystallization, making the design and development of such processes of critical importance. The kinetics of crystal growth and nucleation, the fundamental mechanisms of a solution crystallization process, are strongly dependent on supersaturation (the difference between solution concentration and the saturation concentration). The present study uses attenuated total reflection (ATR) Fourier transform infrared (FTIR) spectroscopy, coupled with robust chemometric techniques, for the on-line measurement of solution concentration of two pharmaceutical compounds in multicomponent systems in the presence of impurities and over a wide range of temperature. To our best knowledge, this is the first time that ATR FTIR spectroscopy has been applied to a multicomponent pharmaceutical system. The resulting models show high accuracy in predicting the solution concentration and are applied successfully in measuring the solubility for the cases of cooling and antisolvent crystallization.

The tailoring of the pore surface chemistry of activated carbon fibers is shown to be an effective method for increasing the removal efficiencies of various contaminants under a fixed bed configuration. An oxidation treatment with nitric and sulfuric acids resulted in a significant increase in the adsorption capacities and breakthrough times. The adsorption kinetics were described by a homogeneous surface diffusion model. Although the effective diffusion coefficients were actually reduced by the oxidation process, the improvement in equilibrium adsorption capacities more than compensated, to result in the overall improved breakthrough times.

The widely published internal model control (IMC) proportional-integral-derivative (PID) tuning rules provide poor load disturbance suppression for processes in which the desired closed-loop dynamics is significantly faster than the open-loop dynamics. The IMC filter is modified to derive low-order controllers that provide effective disturbance suppression irrespective of the location at which the disturbances enter the closed-loop system.

Manipulated variable moves are computed to maximize the information contained in experimental data collected from sheet and film processes. The experimental design procedure minimizes the confidence ellipsoid of the critical model parameters over the manipulated variables subject to their physical constraints. For a simulated blown film process, the model is 1 order of magnitude more accurate than that identified from the industrial standard bump test experiments. The improved accuracy results in a 37% reduction in closed-loop thickness variations. This indicates that substantial benefits can be achieved by incorporating the optimal experimental design algorithm into industrial sheet and film process control algorithms.

We propose the use of pseudo-singular values, which are closely related to singular values but are allowed to have sign, as a convenient approach for developing techniques for the identification and control of large-scale processes. Steady-state controllability can be assessed directly in terms of the pseudo-singular values. It is shown that to control an output disturbance direction with zero steady-state error it is necessary to correctly identify the sign of the corresponding pseudo-singular value. At the identification stage, this motivates the estimation of confidence intervals for the pseudo-singular values from input−output data. A controller with integral action should not attempt to manipulate in process input directions corresponding to output disturbance directions that cannot be controlled with confidence. These principles motivate a controller structure appropriate for providing the robust control of poorly conditioned large-scale processes. Any controller design technique can be applied to produce a controller with the proposed controller structure. The controllability results and the integrated identification/controller design procedure are illustrated using an industrial paper machine example.