Model-based control theory

New research advances in control theory that are bringing it closer to practical problems are promising dramatic new developments and attracting widespread industrial interest. One of these advances is the development of "robust" systems. A robust control system is a stable, closed-loop system that can operate successfully even if the model on which it is based does not adequately describe the plant. A second advance is the use of powerful semiempirical formalisms in control problems, particularly where the range of possible process variables is constrained. 

Further stability models based on surface area, equilibrium water-content-pressure relationships, and electric double-layer theory can successfully characterize borehole stability problems [1842]. The application of surface area, swelling pressure, and water requirements of solids can be integrated into swelling models and mud process control approaches to improve the design of water-based mud in active or older shales. 

In view of this, a robust scheme based on the Hoo control theory [24] is developed in the present work. The algorithm guarantees both stability and performance for a family of perturbed plants with model uncertainties and exogenous inputs (i.e., chamber disturbances and sensor noises) over a wide range of operating conditions, an advantage especially desired for combustion dynamics problems. 

The system dynamics uncertainty A(s) contains parametric and model uncertainties, and its L2 gain bounded as A(s) oo < 1/7- Based on the L2"gain control theory, the first task of a robust controller for stabilizing perturbed plants is to endow the closed-loop system with the following property ... 

This simple mass transfer model based on simplified film theory has been proposed to describe the process of facilitated transport of penicillin-G across a SLM system [53]. In the authors laboratory, CPC transport using Aliquat-336 as the carrier was studied [56] using microporous hydrophobic polypropylene membrane (Celgard 2400) support and the permeation rate was found to be controlled by diffusion across the membrane. 

A valid kinetic model of stage 3 emulsion polymerization must account for diffusion-controlled termination and propagation reactions. Marten and Hamielec (J) have proposed such a model based on a free-volune theory and have confirmed its validity for the bulk polymerization of methyl methacrylate (7). Herein is reported an evaluation of this model for the emulsion... 

The present modeling approach to circadian cancer chronotherapy is based on an automaton model for the cell cycle. Continuous approaches to cell cycle progression have also been used to study the link between cell proliferation and circadian rhythms [44] and to determine, in conjunction with optimal control theory, the most efficient circadian schedules of anticancer drug administration [45]. Including more molecular details of the cell cycle in continuous models for cell populations represents a promising line for future research. Hybrid models incorporating molecular details into the automaton approach presented here will also likely be developed. 

Insights from nonlinear wave theory can also be used for designing new control strategies. A major problem in controlling product purities in separation as well as integrated reaction separation processes is often the lack of a cheap, reliable and fast online concentration measurement. This problem can be solved in two different ways (i) through simple inferential control, or (ii) model-based measurement. 

The success of MPC is based on a number of factors. First, the technique requires neither state space models (and Riccati equations) nor transfer matrix models (and spectral factorization techniques) but utilizes the step or impulse response as a simple and intuitive process description. This nonpara-metric process description allows time delays and complex dynamics to be represented with equal ease. No advanced knowledge of modeling and identification techniques is necessary. Instead of the observer or state estimator of classic optimal control theory, a model of the process is employed directly in the algorithm to predict the future process outputs. 

Model-based approaches allow fast derivative computation by relying on a process model, yet only approximate derivatives are obtained. In self-optimizing control [12,21], the idea is to use a plant model to select linear combinations of outputs, the tracking of which results in optimal performance, also in the presence of uncertainty in other words, these linear combinations of outputs approximate the process derivatives. Also, a way of calculating the gradient based on the theory of neighbouring extremals has been presented in [13] however, an important limitation of this approach is that it provides only a first-order approximation and that the accuracy of the derivatives depends strongly on the reliability of the plant model. 

Schramm et al. (2001) have presented a model-based control approach for direct control of the product purities of SMB processes. Based on wave theory, relationships between the front movements and the flow rates of the equivalent TMB process were derived. Using these relationships, a simple control concept with two PI controllers was proposed. This concept is very easy to implement however, it does not address the issue of optimizing the operating regime in the presence of disturbances or model mismatch. 

The control of silica sol coagulation by pH and by addition of simple electrolytes is said to be anomalous in that it is not simply predicted by conventional Derjaguin-Landau-Verwey-Overbeck (DLVO) theory. This chapter describes a model based on the control of coagulation by surface steric barriers of polysilicate and bound cations. The model suggests new experimental directions. 

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