Process-model mismatches

Sorensen and Skogestad (1994) developed control strategies for BREAD processes by repetitive simulation strategy using a simple model in SPEEDUP package. Wilson and Martinez (1997) developed EKF (Extended Kalman Filter) based composition estimator to control BREAD processes. The estimator was found to be quite robust and was able to estimate composition within acceptable accuracy, even in the face of process/model mismatches. Balasubramhanya and Doyle III... 

Modelling process-model mismatches and hybrid modelling in batch distillation (Mujtaba and Hussain, 1998 Greaves et al., 2001)... 

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 many chemical processes, especially inherently dynamic processes, it is not always possible to model the actual process. Therefore, the states predicted by using the model (Equation 12.1) will be different than that of the actual process and will result in process-model mismatches. The implementation of the optimal operating policies obtained using the model will not result in a true optimal operation. Regardless of the nature of the mismatches, a true process can be described (Agarwal, 1996) as ... 

The error ex(t) is in general time dependent and describes the entire deviation due to process-model mismatches. Structural incompleteness in the model,... 

At any time t, the true estimation of the state variables requires instantaneous values of the unknown mismatches eft). To find the optimal control policies in terms of any decision variables (say z) of a dynamic process using the model will require accurate estimation of ex(t) for each iteration on z during repetitive solution of the optimisation problem (see Chapter 5). Although estimation of process-model mismatches for a fixed operating condition (i.e. for one set of z variables) can be obtained easily, the prediction of mismatches over a wide range of the operating conditions can be very difficult. 

Greaves et al. (2001) modelled the actual process (Equation 12.2) by combining a simple dynamic model (of type Equation 12.1) and the process-model mismatches (eft)) model. 

Here, neural network techniques are used to model these process-model mismatches. The neural network is fed with various input data to predict the process-model mismatch (for each state variable) at the present discrete time. The general input-output map for the neural network training can be seen in Figure 12.2. The data are fed in a moving window scheme. In this scheme, all the data are moved forward at one discrete-time interval until all of them are fed into the network. The whole batch of data is fed into the network repeatedly until the required error criterion is achieved. 

Figure 12.4 illustrates a general optimisation framework (developed by Mujtaba and Hussain, 1998) to obtain optimal operation policies for dynamic processes with process-model mismatches. 

Dynamic sets of process-model mismatches data is generated for a wide range of the optimisation variables (z). These data are then used to train the neural network. The trained network predicts the process-model mismatches for any set of values of z at discrete-time intervals. During the solution of the dynamic optimisation problem, the model has to be integrated many times, each time using a different set of z. The estimated process-model mismatch profiles at discrete-time intervals are then added to the simple dynamic model during the optimisation process. To achieve this, the discrete process-model mismatches are converted to continuous function of time using linear interpolation technique so that they can easily be added to the model (to make the hybrid model) within the optimisation routine. One of the important features of the framework is that it allows the use of discrete process data in a continuous model to predict discrete and/or continuous mismatch profiles. 

Figure 12.4. General Optimisation Framework For Dynamic Processes with Process-model Mismatch...

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. 

B show the model and pilot plant predictions respectively. Figure 12.6 clearly shows that there are large process-model mismatches in the composition profiles although for a given batch time of tdiS = 220 min the amount of distillate achieved by the experiment was the same as that obtained by the simulation. These process-model mismatches can be attributed to factors such as use of constant Vmodei instead of a dynamic one constant relative volatility parameter used in the model and uncertainties associated with it actual efficiency of the plates. 

The four experiments done previously with Rnp (= 0.5, 1, 3, 4) were used to train the neural network and the experiment with / exp = 2 was used to validate the system. Dynamic models of process-model mismatches for three state variables (i.e. X) of the system are considered here. They are the instant distillate composition (xD), accumulated distillate composition (xa) and the amount of distillate (Ha). The inputs and outputs of the network are as in Figure 12.2. A multilayered feed forward network, which is trained with the back propagation method using a momentum term as well as an adaptive learning rate to speed up the rate of convergence, is used in this work. The error between the actual mismatch (obtained from simulation and experiments) and that predicted by the network is used as the error signal to train the network as described earlier. 

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

Figure 12.6 also shows the instant distillate composition profile for / exp = 2 (which is used to validate the network) using the simple model coupled with the dynamic model for the process-model mismatches (curve C). The predicted profile (curve C) shows very good agreement with the experimental profile (curve B). Similar agreements have been obtained for the accumulated distillate amount and composition profiles (Greaves, 2003). 

If the output constraint, Eq. (4), were not present, then the choice m = 1 and a sufficiently large p n + m would stabilize the closed loop, in the absence of process/model mismatch. However, the presence of the output constraint destabilizes the closed loop. As p, the closed loop largest... 

Process Model Mismatches The decision to use default values for testing (both by LMA FAST lab and by Analex-Denver) was based on a misunderstanding about the development and test environment and what was capable of being tested. Both the LMA FAST lab and Analex-Denver could have used the real load tape values, but did not think they could. 

Figure 3.12 Closed-loop response of the process flow rates for a 15% increase in production rate and 1.5% decrease of the product-purity setpoint, in the presence of plant-model mismatch, (a) Product flow rate and (b) reactor effluent, recycle, and column boilup flow rates.

This last class of methods provides a way of avoiding the repeated optimization of a process model by transforming it into a feedback control problem that directly manipulates the input variables. This is motivated by the fact that practitioners like to use feedback control of selected variables as a way to cormteract plant-model mismatch and plant disturbances, due to its simphcity and reliability compared to on-line optimization. The challenge is to find functions of the measured variables which, when held constant by adjusting the input variables, enforce optimal plant performance [19,21]. Said differently, the goal of the control structure is to achieve a similar steady-state performance as would be realized by an (fictitious) on-line optimizing controller. 

Parameter identification is complicated by several factors (i) the complexity of the models and the nonconvexity of the parameter estimation problems, and (ii) the need for the model parameters to be identifiable from the available measurements. Moreover, in the presence of structural plant-model mismatch, parameter identification does not necessarily lead to model improvement. In order to avoid the task of identifying a model on-line, fixed-model methods have been proposed. The idea therein is to utilize both the available measurements and a (possibly inaccurate) steady-state model to drive the process towards a desirable operating point. In constraint-adaptation schemes (Forbes and Marlin, 1994 Chachuat et al., 2007), for instance, the measurements are used to correct the constraint functions in the RTO problem, whereas a process model is used to... 

Schramm et al. (2001) have presented a model-based control approach for direct control of the product purities of SMB processes. Based on wave theory, relationships between the front movements and the flow rates of the equivalent TMB process were derived. Using these relationships, a simple control concept with two PI controllers was proposed. This concept is very easy to implement however, it does not address the issue of optimizing the operating regime in the presence of disturbances or model mismatch. 

Song et al (2006) proposed a multivariable purity control scheme using the m-parameters as manipulated variables and a model predictive control scheme based on linear models that are identified from nonlinear simulations. The approach proposed by Schramm, Griiner, and Kienle (2003) for purity control has been modified by several authors (Kleinert and Lunze, 2008 Fiitterer, 2008). It gives rise to relatively simple, decentralized controllers for the front positions, but an additional purity control layer is needed to cope with plant-model mismatch and sensor errors. Vilas and Van de Wouwer (2011) augmented it by an MPG controller based on a POD (proper orthogonal collocation) model of the plant for parameter tuning of the local PI controllers to cope with the process nonlinearity. 

The findings of this study reinforce a model of error management that emphasizes the process of mismatch emergence as the driver of error detection, problem identification and error resolution (see Figitre 15.1). 

To further cope with process nonlinearities, the disturbance term d can be expressed by combining two terms which is the disturbance due to plant/model mismatch, and d, the disturbance due to nonlinearities, d, can be deter-mined at every sampling time by minimizing the output prediction error between the linear and nonlinear models [5]. 

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