Nonlinear decouplers

The advantage of static decoupling is that less process information is required namely, only steady-state gains. Nonlinear decouplers can be used when the process behavior is nonlinear. 

J. Alvarez, R. Suarez, and A. Sanchez. Nonlinear decoupling control of free radical polymerization continuous stirred tank reactors. Chem. Enq. Sci., 45 3341-3354, 1990. 

For nonlinear decoupling schemes, the G " (w) are evaluated most conveniently by symbolic programming, and they involve polynomials of accordingly higher order of (w it/)" in their denominators. Analytic expressions are necessary for G (w) in order to take advantage of the relation [79]... 

A control algorithm has been derived that has improved the dynamic decoupling of the two outputs MW and S while maintaining a minimum "cost of operation" at the steady state. This algorithm combines precompensation on the flow rate to the reactor with state variable feedback to improve the overall speed of response. Although based on the linearized model, the algorithm has been demonstrated to work well for the nonlinear reactor model. 

Kim et al. (1990) proposed a nested, nonlinear EVM, following ideas similar to those of Reilly and Patino-Leal (1981). In this approach, the parameter estimation is decoupled from the data reconciliation problem however, the reconciliation problem is optimized at each iteration of the parameter estimation problem. 

As pointed out by Kim et al. (1990), the difference between this algorithm and that of Patino-Leal is that the successive linearization solution is replaced with the nonlinear programming problem in Eq. (9.23). The nested NLP is solved as a set of decoupled NLPs, and the size of the largest optimization problem to be solved is reduced to the order of n. 

R. Sehger and P.M. Prank. Pault diagnosis by disturbance decoupled nonlinear observers. In IEEE Conf. Decision and Control (CDC), volume 3, pages 2248-2253, Brighton, Englant, 1991. 

In spite of the potential advantages, useful organic NLO materials have not yet been developed because the necessary molecular and macroscopic characteristics have only recently begun to be understood. However, because bulk NLO properties in organic materials arise directly from the constituent molecular nonlinearities, it is possible to decouple molecular and supramolecular contributions to the NLO properties. One can then semiquantitatively predict relative macroscopic nonlinearities based on theoretical analyses of the individual molecules (7). Reliable predictions of this kind are vital for the efficiency of a program aimed towards developing new organic materials with tailored NLO properties. 

Several process control design methods, such as the Generic Model Control (GMC) [41], the Globally Linearizing Control (GLC) [37], the Internal Decoupling Control (IDC) [7], the reference system synthesis [8], and the Nonlinear Internal Model Control (NIMC) [29], are based on input-output linearization. 

J.B. Balchen, B. Lie, and I. Solberg. Internal decoupling in nonlinear process control. Modeling Identification and Control, 9 137-148, 1988. 

The net effect is a large reduction in the time needed to obtain a decoupled spectrum as compared with a coupled spectrum. Furthermore, this contribution to intensity increase is a nonlinear function of the number of protons directly attached to the particular 13C nucleus. 13C nuclei without an attached proton are characterized by peaks of distinctly low intensities (see Figure 4.1b). These erratic contributions make peak intensities unrelated to the number of 13C nuclei that they should represent. 

The important advantage of this strategy is that the reactor behaves as decoupled from the rest of the plant The production is manipulated indirectly, by changing the recycle flows, which could be seen as a disadvantage. However, it handles nonlinear phenomena better, such as for example the snowball effect or state multiplicity. Additionally, this strategy guarantees the stability of the whole recycle system if the individual units are stable or stabilized by local control. 

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