Nominal plant model

The nominal plant model was shown to exhibit an infinite number of RHPT zeros [7], which as discussed in Section 2, can result from the distribution of time delays in a MIMO system. It... 

Unstructured model uncertainty relates to unmodelled effects such as plant disturbances and are related to the nominal plant CmCv) as either additive uncertainty (s)... 

Simulation studies carried out to compare the amount of desired product C obtained from on-line dynamic optimization strategy with that from off-line strategy, are cases where the perfect model (all parameters correctly specified) is used (nominal case), and where plant/model mismatch is introduced by changing parameters in actual plant i.e. pre-exponential rate constant (kf) decreased by 50% and activation energy (Ea) increased by 20% from their nominal values, as shown in Table 5. 

Figures 7.23-7.27 show the closed-loop profiles for a 10% increase in the production rate at operating point I (attained by increasing Fo), and a decrease in the purity setpoint to Cb,Sp = 1.888 mol/1 - this reduction is necessary since the nominal purity is beyond the maximum attainable purity for the increased throughput. Although controller design was carried out to account for the inverse response exhibited by the system at operating points II and III, and in spite of the plant-model parameter mismatch, the proposed control structure clearly yields good performance at operating point I as well.

After the identification of a model, the open-loop optimal control policy for the nominal plant can be determined by solving the following optimization problem. 

An open-loop control policy is effective only if the model can accurately predict the behavior of the plant and if there are no large external disturbances. The introduction of feedback would allow compensation for plant/model mismatch and perturbations from the nominal control profile. Nevertheless, there have been only a few attempts to use feedback in a control algorithm for batch crystallizers these are briefly outlined below. 

The linearized plant model used in this analysis was derived from a rigorous dynamic nonlinear model by linearization around a stationary point. The linear model has 85 state variables and there are two manipulated variables the reflux ratio (nominal value / =0.597)... 

A.6. Perform structural analysis based on a steady-state model and evaluate the possibilities for decomposition of the control problem. To simply this step, we assume that the pressure and temperature control loops are essentially decoupled from the plant holdups (integrating modes), the compositions, and the liquid flows. If this assumption is approximately valid, we can analyze a core plant model ( core model ) that comprises the reactor, flash unit, and recycle tank—all assumed to operate isothermally and isobarically (see Fig. H.5). Thus, the approximate plant model consists only of material balances but includes the key flows, levels, and compositions. This type of approach, in which temperatures and pressures are assumed to remain constant at their nominal values, was employed by Robinson et al. (2001) in their analysis of a similar plant. 

In general, however, robust control system design uses an idealized, or nominal model of the plant Uncertainty in the nominal model is taken into account by... 

Consider a Nyquist contour for the nominal open-loop system Gm(iLu)C(iuj) with the model uncertainty given by equation (9.119). Let fa( ) be the bound of additive uncertainty and therefore be the radius of a disk superimposed upon the nominal Nyquist contour. This means that G(iuj) lies within a family of plants 7r(C(ja ) e tt) described by the disk, defined mathematically as... 

Phase three of a typical HRA begins with developing human error probabilities that can he applied to the selected model. In some cases, a set of nominal human errors can be derived 1mm plant data, however, due to the sparseness and low confidence of these data industry generic information may be used. Chapter 20 of NUREG/CR-1278 includes a typical set of. such data. 

NN applications, perhaps more important, is process control. Processes that are poorly understood or ill defined can hardly be simulated by empirical methods. The problem of particular importance for this review is the use of NN in chemical engineering to model nonlinear steady-state solvent extraction processes in extraction columns [112] or in batteries of counter-current mixer-settlers [113]. It has been shown on the example of zirconium/ hafnium separation that the knowledge acquired by the network in the learning process may be used for accurate prediction of the response of dependent process variables to a change of the independent variables in the extraction plant. If implemented in the real process, the NN would alert the operator to deviations from the nominal values and would predict the expected value if no corrective action was taken. As a processing time of a trained NN is short, less than a second, the NN can be used as a real-time sensor [113]. 

The reactor model available in Aspen Dynamics [16] only provides the possibility of changing the coolant temperature. Figure 10.12 shows results dynamic simulation results, for the following scenario the plant is operated at the nominal steady state for lh. Then, the coolant temperature is increased from 413 to 425 K and simulation is continued for 2 h. The maximum temperature inside the reactor... 

Before considering methods of finding a, let us review how the concept of model distortion has allowed us to move from comparison between model and plant to a comparison between two models, in one of which we allow the nominally constant parameters to be varied. Suppo.se we drive the system to follow the recorded transients exactly. Using the superscript 0 to label the vectors associated with exact matching, the parameter variations will be given by (/), the states by X"(/) and the outputs by Y (f). Exact matching implies ... 

In order to investigate the regulatory operability of the process, additionally the anticipated ranges of disturbances needs to be specified, that will define the Expected Disturbance Space (EDS). For the steady-state case, the EDS may also reflect the uncertainties in some of the important model parameters employed in the design, such as kinetic constants, heats of reaction, heat-transfer coefficients, etc. The regulatory operability index is defined from the inputs required to compensate for the effect of disturbances while maintaining the plant at its nominal set point, as ... 

G.2 In this exercise, you will evaluate the individual units at the nominal steady state for purposes of understanding how the plant would operate without recycle. Use Simulink to simulate the full differential equation model given in Table G.l. Then, for purposes of this problem only, tear the recycle stream to the reactor—that is, disconnect the distillate line and replace it with a constant stream to the reactor that is set at the recycle stream s nominal conditions of flow rate and concentration. 

For an integral PSA model of a plant, it is significant to adequately define the interface between power PSA and SLP PSA. This interface does not necessarily coincide with the definition of the operating modes. Typically, the power PSA considers 100% nominal power. In terms of the thermal hydraulic response to an initiating event, there is not much difference between 100% power and lower power levels, except that at lower power levels the time available for selected corrective actions may be somewhat greater. The 100% power case is therefore conservatively a representative of the whole spectrum of power levels. 

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