Models process

The 78 equality constraints in the complete model were thus reduced to 6 nonlinear equations as the genetic algorithm, NSGA-II-aJG is not effective in handling multiple equality constraints. Its inadequateness was also observed even when the equations had been reduced to 6 equations. Hence, the Broyden s update and finite-difference Jacobian function (DNEQBF) of the IMSL Library was embedded in the objective evaluation to solve the nonlinear equations 10.1 to 10.6. 

The above model equations are validated by reproducing the results in Pintaric and Kravanja (2006) for single objective optimization, using NSGA-II-aJG. For this, the 4 decision variables are V, 7) and t]. For 

Solver has to satisfy while the selected economic objective was optimized. If the initial guesses of the 10 variables are random. Solver experienced difficulty in converging to the optimal solution thus, it is essential that the initial guesses are close to the optimal values for Solver to produce the correct optimal solution. When the solutions of the Solver are compared with the results given by Pintaric and Kravanja (2006), the mean and maximum difference is 0.094% and 0.36% (in IRR for max. PBT) respectively. Note that the programme used by Pintaric and Kravanja (2006) is GAMS/CONOPT. 

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IMPOSITION OF BOUNDARY CONDITIONS IN POLYMER PROCESSING MODELS... 

In the finite element solution of the energy equation it is sometimes necessary to impose heat transfer across a section of the domain wall as a boundary condition in the process model. This type of convection (Robins) boundary condition is given as... 

Process Modeling. The complexity of emulsion polymerization makes rehable computer models valuable. Many attempts have been made to simulate the emulsion polymerization process for different monomer systems (76—78). 

W. L. Luyben, Process Modeling, Simulation, and Controlfor Chemical Engineers, McGraw-HiU, Book Co., Inc., New York, 1973. 

Obtain real-time process data confirm process models... 

Documentation of experimental method so that work can be reproduced at a later time Appropriate data handling statistical methods conclusions based on fact, supportable by data Define and execute critical experiments to prove or disprove hypothesis Mechanistic or fundamental interpretation of data preferred Communication of Conclusions to Incorporate Technical Learning in Organization Experimental W rk Done in Support of New or Existing Processes Should be Captured in Process Models... 

Fig. 8. The innovation process model seen as a series of feedback loops involving technology transfer and the merging of cooperative efforts on a global...

Transport Models. Many mechanistic and mathematical models have been proposed to describe reverse osmosis membranes. Some of these descriptions rely on relatively simple concepts others are far more complex and require sophisticated solution techniques. Models that adequately describe the performance of RO membranes are important to the design of RO processes. Models that predict separation characteristics also minimize the number of experiments that must be performed to describe a particular system. Excellent reviews of membrane transport models and mechanisms are available (9,14,25-29). 

For optimisation of process design and process control, the efficiency and effectiveness of the various methods depend on the process being modeled and the process modeling software that is used. 

In using a spreadsheet for process modeling, the engineer usually finds it preferable to use constant physical properties, to express reactor performance as a constant "conversion per pass," and to use constant relative volatiHties for distillation calculations such simplifications do not affect observed trends in parametric studies and permit the user quickly to obtain useful insights into the process being modeled (74,75). 

In the chemical engineering domain, neural nets have been appHed to a variety of problems. Examples include diagnosis (66,67), process modeling (68,69), process control (70,71), and data interpretation (72,73). Industrial appHcation areas include distillation column operation (74), fluidized-bed combustion (75), petroleum refining (76), and composites manufacture (77). 

N. Bhat and T. J. McAvoy, "Dynamic Process Modeling via Neural Computing," paper presented atMJOE National Meeting, San Francisco, 1989. 

Tuning Methods Based on Known Process Models. 8-14... 

Tuning Methods When Process Model Is Unknown. 8-15... 

Physical Models versus Empirical Models In developing a dynamic process model, there are two distinct approaches that can be... 

Simulation of Dynamic Models Linear dynamic models are particularly useful for analyzing control-system behavior. The insight gained through linear analysis is invaluable. However, accurate dynamic process models can involve large sets of nonlinear equations. Analytical solution of these models is not possible. Thus, in these cases, one must turn to simulation approaches to study process dynamics and the effect of process control. Equation (8-3) will be used to illustrate the simulation of nonhnear processes. If dcjdi on the left-hand side of Eq. (8-3) is replaced with its finite difference approximation, one gets ... 

The principal limitation to using these rules is that the true process parameters are often unknown. Steady-state gain K can be calculated from a process model or determined from the steady-state results of a step test as Ac/Au, as shown in Fig. 8-28. The test will not be viable, however, if the time constant of the process is longer than a few... 

Does not introduce instability in the closed-loop response Sensitive to process/model error... 

Does not require an explicit process model Unsatisfactory for processes with large time constants and frequent disturbances... 

The Smith predictor is a model-based control strategy that involves a more complicated block diagram than that for a conventional feedback controller, although a PID controller is still central to the control strategy (see Fig. 8-37). The key concept is based on better coordination of the timing of manipulated variable action. The loop configuration takes into account the facd that the current controlled variable measurement is not a result of the current manipulated variable action, but the value taken 0 time units earlier. Time-delay compensation can yield excellent performance however, if the process model parameters change (especially the time delay), the Smith predictor performance will deteriorate and is not recommended unless other precautions are taken. 

FIG. 8-37 Block diagram of the Smith predictor. The process model used in the controller is G = G°e (G = model without delay = time delay element). 

Foxboro developed a self-tuning PID controller that is based on a so-called expert system approach for adjustment of the controller parameters. The on-line tuning of K, Xi, and Xo is based on the closed-loop transient response to a step change in set point. By evaluating the salient characteristics of the response (e.g., the decay ratio, overshoot, and closed-loop period), the controller parameters can be updated without actually finding a new process model. The details of the algorithm, however, are proprietary... 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

RGA Method for 2X2 Control Problems To illustrate the use of the RGA method, consider a control problem with two inputs and two outputs. The more general case of N X N control problems is considered elsewhere (McAvoy, Interaction Analysis, ISA, Research Triangle Park, North Carohna, 1983). As a starting point, it is assumed that a linear, steady-state process model is available. 

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

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