Parallel Cascades

If only a single controller flj ed to control X by manipulating M, the closedloop characteristic equation is the conventional 

however, a cascade control system is used, as sketched in Fig. ll.3b, the closedloop characteristic equation is not that given in Eq, (11.21). To derive it, let us start with the secondary loop. 

Note the difference between the series cascade [Eq. (11.4)] and the parallel cascade [Eq. (11.25)] characteristic equations. 

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We will also talk in Chap. 11 about the two types of cascade control series cascade and parallel cascade. The two examples discussed above are both series cascade systems because the manipulated variable affects the secondary controlled variable, which then affects the primary variable. In a parallel cascade system the manipulated variable affects both the primary and the secondary controlled variables directly. Thus the two processes are basically different and result in different dynamic characteristics. We will quantify these ideas later. 

There are two types of process structures for which cascade control can be applied. If the manipidated variable affects one variable and then this variable affects a second controlled variable, the structure leads to series cascade control. If the manipulated variable affects both y iables directly, the structure leads to parallel cascade. 

Figure 11.3d shows a process where the manipulated variable affects the two controlled variables and in parallel. An important example is in distilla tion column control where reflux flow aSecte both distillate composition and a tray temperature. The process has a parallel structure and this leads to a parallel cascade control system. 

However, acascade system is used where another proportional controllerXj is used to control X2 by changing the setpoint of the K, controller. Thus we have a parallel cascade system. 

Fig. 2.10. Alternative electric configurations of a fuel cell cascade, a) Parallel cascade with independent cell voltage and cell current of each cell b) series cascade with independent cell voltage and equal cell current.

There are two types of third-order cascades that can lead to an overall fifth-order signal. Ladder diagrams for the two types of cascades are shown in Fig. 2a and b, and we label them sequential and parallel. A sequential cascade (Fig. 2a) involves the emission of a field from the first vibrational coherence that then participates in driving a vibrational coherence on a different chromophore. A parallel cascade (Fig. 2b) begins with the preparation of vibrational coherences on separate chromophores as a result of interactions with the first and second pairs of laser fields. The probing interaction on one of the chromophores then results in a field that is involved in a probing interaction on the other chromophore. 

Figure 2 Representative ladder diagrams for the possible cascading fifth-order pathways, (a) The sequential cascade pathway, (b) The parallel cascade pathways.

Figure 11 Cascaded 2D fifth-order Raman spectra for CCU simulated directly from the ID spectrum shown in Fig. 4. (a) The sequential cascade spectrum, (b) The parallel cascade spectrum, (c) A best fit to the 2D spectrum in Fig. 10a using a linear combination of the sequential and parallel cascaded spectra. The ratio is 0.8 1 sequentiahparallel. 

Parallel cascade, (a) Openloop process, (b) Parallel cascade control, (c) Reduced block diagram. 

Series Cascade / 9.1. 2 Parallel Cascade Feedforward Control... 

In a source/filter vocal model such as LPC or parallel/cascade formant synthesis, periodic impulses are used to excite resonant filters to produce vowels. We could construct a simple alternative model using three, four, or more tables storing the impulse responses of the individual vowel formants. Note that it isn t necessary for the tables to contain pure exponentially decaying sinusoids. We could include aspects of the voice source, etc., as long as those effects are periodic. FOFs (originally introduced as Formant Onde Functions in French, translates to Formant Wave Functions in English) were created for... 

Korenberg, M.J. 1991. Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng. 19 429. 

Parallel/cyclic cascade. The second scheme is where one or more additional enz5unes are used to assist a primary enzyme. This is done in order to achieve a degree of self-sufficiency in cofactors or reagents. There are two t5qjes of scheme, referred to either as parallel cascades (Figure 20.2b) or cyclic cascades (Figure 20.2c). Such schemes are also be found in nature to balance redox in microbial metabolic pathways. 

For practical implementation the use of parallel cascades is of great value for cofactor recycle. For example, van Hecke and coworkers [45] report the synthesis of lactobi-onic acid from lactose using cellobiose dehydrogenase. The enzyme requires an electron acceptor, and using ABTS and laccase in a parallel cascade, such a system was effectively operated and modeled. 

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