Propagator controller system

P. Fife. Propagator-controller systems and chemical patterns. In C. Vidal and A. Pacault, editors, Non-equilibrium dynamics in chemical systems, pages 76-88. Springer-Verlag, Berlin, 1984. 

Fife, P. Propagator-Controller Systems and Chemical Patterns in Nonequilibrium Dynamics in Chemical Systems Vidal, C. Pacault, A., Ed. Springer-Verlag Berlin, 1984 pp 76-88. 

Fife refers to a set of partial differential equations like eqs. (6.28) as a propagator—controller system, for reasons that will become clear later. We recall that the small parameter e 1 makes u change much more rapidly than v. It also makes the time scale of the chemical change much shorter than that of the diffusion that is, the diffusion terms are small compared with the chemical rates of change. Note that all the chemistry is in the functions / and g, which are constructed so that neither concentration can grow to infinity. We will want to consider either a one-dimensional geometry (spatial variable x) or a radially symmetric two-dimensional system, like a Petri dish. 

Springer-Verlag, Berlin, 1984, pp. 76-88. Propagator-Controller Systems and Chemical Patterns. 

Detonation arresters are typically used in conjunction with other measures to decrease the risk of flame propagation. For example, in vapor control systems, the vapor is often enriched, diluted, or inerted, with appropriate instrumentation and control (see Effluent Disposal Systems, 1993). In cases where ignition sources are present or pre-dic table (such as most vapor destruct systems), the detonation arrester is used as a last-resort method anticipating possible failure of vapor composition control. Where vent collec tion systems have several vapor/oxidant sources, stream compositions can be highly variable and... 

However, for many systems, more sophisticated control systems capable of overcoming these restrictions are likely to be desirable. To develop such systems, we need to expand the predictive models mentioned above to incorporate the dynamic effects of input, control, and process variables. The model needs to be able to answer questions such as how quickly do deviations in input conditions propagate through the system, how does the system respond over time under different control policies, and what is the... 

Steps 1 and 2 establish the objectives of the control system and the available degrees of freedom. Step 3 ensures that any production of heat (entropy) within the process is properly dissipated and that the propagation of thermal disturbances is prevented. In Steps 4 and 5 we... 

From a dynamic viewpoint, whenever all flows in a recycle loop are set by level controllers, wide dynamic excursions can occur in these flows because the total system inventory is not regulated. The control system is attempting to control the inventory in each individual vessel by changing the flowrate to its downstream neighbor. In a recycle loop, all level controllers see load disturbances coming from the upstream unit. This causes the flowrate disturbances to propagate around the recycle loop. Thus any disturbance that tends to increase the total inventory in the process (such as an increase in the fresh feed flowrate) will produce large increases in all flowrates around the recycle loop. 

However, we have noticed in previous chapters that the more coupled the process is, the more potential difficulties we have with operation and control. The reason has to do with snowballing, trapping of components, and propagation of composition and thermal disturbances. These issues are definitely still present in reactive distillation, making the control system design for these systems a challenging problem. 

Two major entry models - the diffusion-controlled and propagation-controlled models - are widely used at present. However, Liotta et al. [28] claim that the collision entry is more probable. They developed a dynamic competitive growth model to understand the particle growth process and used it to simulate the growth of two monodisperse polystyrene populations (bidisperse system) at 50 °C. Validation of the model with on-line density and on-line particle diameter measurements demonstrated that radical entry into polymer particles is more likely to occur by a collision mechanism than by either a propagation or diffusion mechanism. 

The most important fact about piston flow is that disturbances at the inlet are propagated down the tube with no dissipation due to mixing. They arrive at the outlet t seconds later. This pure time delay is known as dead time. Systems with substantial amounts of dead time oscillate when feedback control is attempted. This is caused by the controller responding to an output caused by an input t seconds ago. The current input may be completely different. Feedforward control represents a theoretically sound approach to controlling systems with appreciable dead time. Sensors are installed at the inlet to the reactor to measure fluctuating inputs. The... 

Olaj et al. (27) rekindled interest in the issue of chain-length-dependent propagation (CLDP), an issue that Hants and coworkers have pursued most recently 28-31). CLDP results in veiy small radicals growing relatively quickly 28), and thus - opposite to CLDT - it causes narrowing of a MWD 29). The effect can be substantial, with PDl of 1.5 having been observed for transfer-controlled systems withDPn- 15 30), as opposed to the classical kinetics value... 

Nonlinear waves are very useful for a qualitative understanding of the concentration and temperature dynamics in an RD column. So far, only an incomplete understanding of the relation between the physicochemical complexity of the mixture, the design and operation of the column, and the observed spatiotemporal patterns is available. Much research is required to resolve the open issues. In addition, the phenomenon of a propagating wave can also be exploited to derive a simplified quantitative description of the column dynamics in the non-reactive [27, 67] as well as in the reactive [4, 51, 52] case. These reduced nonlinear models are most suitable to design and implement advanced model based control systems as discussed in the next section. 

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