Constant control policy

Seodigeng, T., Hausberger, B., Hildebrandt, D., Glasser, D., 2009. Recursive constant control policy algorithm for attainable regions analysis. Comput. Chem. Eng. 33, 309-320. 

The toxic chemicals in inhalants are stored in fatty tissue in the body for weeks. Thus, when long-term abusers attempt to quit, they may develop withdrawal symptoms several hours to a few days afterward. The Office of National Drug Control Policy and the American Academy of Pediatrics list these common withdrawal symptoms hand tremors, excessive sweating, constant... 

Kerkhof and Vissers showed that for difficult separations an optimal reflux control policy yields up to 5% more distillate, corresponding to 20-40% higher profit, than either constant distillate composition or constant reflux ratio policies. 

Also note that if Ns is chosen sufficiently large, the piecewise constant optimal control policy will be sufficiently close to the continuous optimal control policy. 

It is clear from Table 5.9 that the results obtained are in very good agreement with the objectives set for each individual optimisation problem. Table 5.9 also deary shows the advantages of optimal reflux policies over the conventional constant reflux operation. Table 5.9 shows that the time optimal control policy (variable reflux) saves about 63% of the operation time compared to that required in the simulation (Table 4.6). Even the time optimal constant reflux policy saves about 33% of the operation time compared to the original simulation... 

For the development of neural network models simulated process operation data from 50 batches with different feeding profiles were generated using the mechanistic model of the process. In each batch, the batch duration is divided into 10 equal stages. Within each stage, the feed rate is kept constant. The control policy for a batch consists of the feed rates at these 10 stages. 

The optimal temperature policy in a batch reactor, for a first order irreversible reaction was formulated by Szepe and Levenspiel (1968). The optimal situation was found to be either operating at the maximum allowable temperature, or with a rising temperature policy, Chou el al. (1967) have discussed the problem of simple optimal control policies of isothermal tubular reactors with catalyst decay. They found that the optimal policy is to maintain a constant conversion assuming that the decay is dependent on temperature. Ogunye and Ray (1968) found that, for both reversible and irreversible reactions, the simple optimal policies for the maximization of a total yield of a reactor over a period of catalyst decay were not always optimal. The optimal policy can be mixed containing both constrained and unconstrained parts as well as being purely constrained. 

Ogunye and Ray (1971a,b) have formulated the optimal control problem for tubular reactors with catalyst decay via a weak maximum principle for this distributed system. Detailed numerical examples have been calculated for both adiabatic and isothermal reactors. For irreversible reactions, constant conversion policies are found to not always be optimal. A practical technique for on-line optimal control for fixed bed catalytic reactors, has been suggested by Brisk and Barton (1977). Lovland (1977) derived a simple maximum principle for the optimal flow control of plug flow processes. 

Introduction In Chapter 7, under the context of batch reaction, it is demonstrated how the fed-batch reactor may be used to approximate the behavior of both the PFR and CSTR, and how the fed-batch reactor is the batch analogue of a DSR. It is therefore possible to construct a candidate AR, composed of all three fundamental reactor types, using only DSR trajectories. This is the basic premise behind the recursive constant control (RCC) policy algorithm (Seodi-geng et al., 2009). 

A new method for selecting controlled variables (c) as linear combination of measurements (y) is proposed based on the idea of self-optimizing control. The objective is to find controlled variables, such that a constant setpoint policy leads to near optimal operation in the presence of low frequency disturbances d). We propose to combine as many measurements as there are unconstrained degrees of freedom (inputs, u) and major disturbances such that opi d) = 0. To illustrate the ideas a gas-lift allocation example is included. The example show that the method proposed here give controlled variables with good self-optimizing properties. 

The weak maximum principle can certainly be used to maximize the performance index of Eq. 13.33, for instance, for the independent deactivation problem given by Eqs. 13.40 through 13.45 with the addition of a heat balance at the pellet-bulk fluid interface for the pellet surface temperature 7 [( )s]. Nevertheless, the optimal inlet temperature will be a function of time. Thus, the inlet temperature is to be manipulated in a prescribed manner in time without any regard to what happens to the reactor. This open-loop control is rarely practiced in actual applications because of the uncertainties regarding the model, measurements, and disturbances. Rather, closed-loop control using feedback from the process is usually practiced. This fact should not discourage one from using the maximum principle for optimization, for it will at least indicate what the best possible performance is in a relative sense. At the same time it can yield in some simple cases a very powerful optimal policy such as the constant conversion policy, which can be implemented by a feedback control scheme. 

The overall activity factor can be used in a straightforward manner for a piecewise feedback control. Suppose that the control policy is to maintain a constant outlet conversion. Suppose further that the inlet temperature is manipulated intermittently, as in the usual operation of an adiabatic reactor, so as to maintain the constant outlet conversion. If one lets the subscript c denote the current quantities... 

During polymerization, when Initiator Is Introduced continuously following a predetermined feed schedule, or when heat removal Is completely controllable so that temperature can be programmed with a predetermined temperature policy, we may regard functions [mo(t ], or T(t), as reaction parameters. A common special case of T(t) Is the Isothernral mode, T = constant. In the present analysis, however, we treat only uncontrolled, batch polymerizations In which [mo(t)] and T(t) are reaction variables, subject to variation In accordance with the conservation laws (balances). Thus, only their Initial (feed) values, Imo] andTo, are true parameters. 

To minimize damage due to power outage, the Celanese Corporation in their plant at Newark, N.J., instituted a policy of always generating half its own power. Merck Company installed additional auxiliary steam power to insure constant refrigeration for its biochemicals at its West Point, Pa., plant. At Allied Chemical s phenol plant in Frankfort, Pa., electric devices on air compressors and pumps were replaced by steam-operated controls, and diesel generators were installed to maintain cooling water circulation. 19... 

The control strategies for determining the feed policies were decided on the basis of a numerical solution of the terpolymerisations described by equations 1 - 3 using a microcomputer and a general purpose simulation package, BEEBSOC (10). Where necessary, these data were acquired in the course of this study, otherwise literature values were used. The apparent first order rate constants in terpolymerisations have been shown to be composition dependent. The variation in rate constants with... 

The nitrogen oxide reaction gas stream cannot be directly controlled from the steam superheater. Instead the flowrate, temperature and pressure are predetermined by the reactor feed conditions. No direct control exists on this stream as far as the production of steam is concerned, both inlet and outlet lines possess isolation valves for plant shutdown. These lines would be blanked before any platinum recovery work was attempted on the steam superheater. Inlet and outlet linesalsofeature temperature indicators, consistent with the policy of constant monitoring of this parameter throughout the process. 

An alternative to the constant-reflux-ratio policy described above is to maintain a constant-molar-vapor rate, but continuously vary the reflux ratio to achieve a constant distillate composition that meets the specified purity. This policy requires a more complex control system, which may be justified only for large batch distillation systems. 

At steady state the chemical species must enter and leave the plant in a manner that satisfies perfectly the material balance. If chemical reactions are present, the make-up policy of the reactants must fulfil the stoichiometry of various chemical reactions. However, in practice the material balance of components has always a dynamic character. When several reactants are involved, not all can be fed on flow control. Firstly, because of inherent measurement errors and variability of raw materials, the reactants cannot be exactly counted in the stoichiometric ratio. Secondly, the reaction conditions are not constant. Accumulation will take place, and over longer period could lead to dysfunctions or even to plant upset. Somewhere in the plant the inventory of the reactants and products should be measured or estimated, and the make-up policy adapted accordingly. 

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