Dynamic process model

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

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 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. 

The example simulation THERMFF illustrates this method of using a dynamic process model to develop a feedforward control strategy. At the desired setpoint the process will be at steady-state. Therefore the steady-state form of the model is used to make the feedforward calculations. This example involves a continuous tank reactor with exothermic reaction and jacket cooling. It is assumed here that variations of inlet concentration and inlet temperature will disturb the reactor operation. As shown in the example description, the steady state material balance is used to calculate the required response of flowrate and the steady state energy balance is used to calculate the required variation in jacket temperature. This feedforward strategy results in perfect control of the simulated process, but limitations required on the jacket temperature lead to imperfections in the control. 

The dynamic process model involves a component balance, energy balance, kinetics and Arrhenius relationship. Hence... 

The program THERMFF solves the same dynamic process model equations as THERM, where it was shown that all the parameters, including the inlet temperature and concentration will influence the steady state. In the case of multiple steady states the values of the steady state parameters cannot be set, because they are not unique. This example should, therefore, be mn under parameter conditions that will guarantee a single steady state for all expected values of the CA0 and T0. These can be selected with the aid of the programs THERMPLOT and THERM. 

The nonlinear observers developed in the previous sections may be then applied to the dynamical process model (23) defining the state vector in the following way ... 

The MPC strategy can be summarized as follows. A dynamic process model (usually linear) is used to predict the expected behavior of the controlled output variable over a finite horizon into the future. On-line measurement of the output is used to make corrections to this predicted output trajectory, and hence provide a feedback correction. The moves of the manipulated variable required in the near future are computed to bring the predicted output as close to the desired target as possible without violating the constraints. The procedure is repeated each time a new output measurement becomes available. 

In contrast to the sequential solution method, the simultaneous strategy solves the dynamic process model and the optimization problem at one step. This avoids solving the model equations at each iteration in the optimization algorithm as in the sequential approach. In this approach, the dynamic process model constraints in the optimal control problem are transformed to a set of algebraic equations which is treated as equality constraints in NLP problem [20], To apply the simultaneous strategy, both state and control variable profiles are discretized by approximating functions and treated as the decision variables in optimization algorithms. 

Consider a dynamic process model as in the form of an implicit function... 

Physical Models versus Empirical Models In developing a dynamic process model, there are two distinct approaches that can be taken. The first involves models based on first principles, called physical or first principles models, and the second involves empirical models. The conservation laws of mass, energy, and momentum form the basis for developing physical models. The resulting models typically involve sets of differential and algebraic equations that must be solved simultaneously. Empirical models, by contrast, involve postulating the form of a dynamic model, usually as a transfer function, which is discussed below. This transfer function contains a number of parameters that need to be estimated from data. For the development of both physical and empirical models, the most expensive step normally involves verification of their accuracy in predicting plant behavior. 

In most process control courses for chemical engineers, the first part of the course normally deals with the development of dynamic process models from first principles (mass and energy balances), since these are used in the analysis of process dynamics and often also for controller tuning. In this chapter, however, the focus will be on process control and modelling will not be considered. Neither will the chapter consider... 

Lehtonen et al. (1998) considered polyesterification of maleic acid with propylene glycol in an experimental batch reactive distillation system. There were two side reactions in addition to the main esterification reaction. The equipment consists of a 4000 ml batch reactor with a one theoretical plate distillation column and a condenser. The reactions took place in the liquid phase of the reactor. By removing the water by distillation, the reaction equilibrium was shifted to the production of more esters. The reaction temperatures were 150-190° C and the catalyst concentrations were varied between 0.01 and 0.1 mol%. The kinetic and mass transfer parameters were estimated via the experiments. These were then used to develop a full-scale dynamic process model for the system. 

Egly et al. (1979) considered the minimum time optimisation problem using a detailed dynamic process model (Type V) but no details were given regarding the input and kinetic data of the problem. 

In Mujtaba and Hussain (1998), the detailed dynamic model was assumed to be the exact representation of the process while the difference in predictions of the process behaviour using a simple model and the detailed model was assumed to be the dynamic process-model mismatches. Theses dynamic mismatches were modelled using neural network techniques and were coupled with the simple model... 

In Greaves et al. (2001) and Greaves (2003), instead of using a rigorous model (as in the methodology described above), an actual pilot plant batch distillation column is used. The differences in predictions between the actual plant and the simple model (Type III and also in Mujtaba, 1997) are defined as the dynamic process-model mismatches. The mismatches are modelled using neural network techniques as described in earlier sections and are incorporated in the simple model to develop the hybrid model that represents the predictions of the actual column. 

Figure 12.6. Experimental Simulation Results and Dynamic Process-model Mismatch Model (Rexp= 2).

Dynamic process modelling is being developed to be used on the macroscopic scale. Full complex plant models may involve up to 5.0 x variables, 2.0 x 10 equations and over 1.0 X 10 optimisation variables. 

Previously reported work describes dynamic process model for ice cream freezers (Bongers, 2006) and extruders (Bongers and Campbell, 2008) to relate operating conditions, equipment geometry with physical attributes, such as extrusion temperature. 

Dose to Dose PBPK modeling permits reasonable extrapolation from one dose to another, if adequate information on physiology, physicochemical properties, and biochemistry is available. If the dynamic processes modeled by the PBPK approach are all directly proportional to administered concentrations, then the extrapolation can be relatively straightforward. However, this is not often the case, especially at higher doses, where saturation of metabolic or clearance processes can occur [14,19]. Further causes of nonlinearity of chemical kinetics include the induction and inhibition of metabolic enzymes [14], Despite these difficulties successful applications of dose extrapolation using PBPK models for many chemicals have been published [20,21], and... 

As discussed above, the task of the controller is to optimize the performance of the process over a certain horizon in the future, the prediction horizon. Specifications of product purities, equipment limitations and the dynamic process model (a full hybrid model of the process, including the switching of the ports and a general rate model of all columns) appear as constraints. The control algorithm solves the following nonlinear optimization problem online ... 

To include the information about process d3mamics in the models, the data matrix can be augmented with lagged values of data vectors, or model identification techniques such as subspace state-space modeling can be used (Section 4.5). Negiz and Cinar [209] have proposed the use of state variables developed with canonical variates based realization to implement SPM to multivariable continuous processes. Another approach is based on the use of Kalman filter residuals [326]. MSPM with dynamic process models is discussed in Section 5.3. The last section (Section 5.4) of the chapter gives a brief survey of other approaches proposed for MSPM. 

Y You and M Nikolaou. Dynamic process modeling with recurrent neural networks. AIChE J., 39(10) 1654-1667, 1993. 

---