Nominal operating point

Step 1. Select a finite number of periods of operation (i.e., sets of values of the uncertain supply temperatures and flow rates). Typically, the nominal operating point is selected, as well as some combinations of upper and lower bounds on the uncertain variables [e.g., bounds corresponding to maximum heating, maximum cooling, maximum heat exchange, and maximum required heat transfer area, as suggested by Marselle et al. (1982)]. 

Similarly, if the nominal operating point is at high excess of A, the reactor-inlet flow rate of B can be used to manipulate the production. 

In the following, we compare the performance of these control structures. The results of dynamic simulation are presented in Figures 5.23 to 5.28. A summary is displayed in Table 5.15, where the nominal point is given in the first line, the streams on flow control are in the grey cells, while italic values show changes from the nominal operating point. 

Figure 12.5 Performance of the BioDeNOx process as a function of the bioreactor performance. The nominal operating point is represented by the black dot.

RTO performance metrics on which such systematic approaches would be based currently use linear approximation to estimate performance and, as a result, are only valid in a small region near the test point. Incorporation of nonlinearity into RTO performance would help the designers make more informed design decisions and may decrease the design effort, because fewer nominal operating points would have to be tested. 

Because the mathematical theory of nonlinear dynamic systems is complex, such models are used more for dynamic simulation purposes than for the analysis and design of control systems. Simpler models can be obtained by linearisation around a nominal operating point. 

Before performing a controllability analysis, ensure the stability of the plant. The first step is to close all inventory control loops, by means of level and pressure controllers. Then, check the stability, by dynamic simulation. If the plant is unstable, it will drift away from the nominal operating point. Eventually, the dynamic simulator will report variables exceeding bounds, or will fail due to numerical errors. Try to Identify the reasons and add stabilizing control loops. Often a simple explanation can be found in uncontrolled inventories. In other situations the origin is subtler. Some units are inherently unstable, as with CSTR s or the heat-integrated reactors. The special case when the instability has a plantwide origin will be discussed in Chapter 13. 

Firstly, a steady state simulation is built in AspenPlus. The feed stream consists of F = 200 kg/h containing 19.41 % mol methanol. The column has 15 trays. At the nominal operating point, reflux and reboiler duty are R = 60 kg/h and Q = 41.84 kW,... 

Small disturbances of 0.5% around the nominal operating point are considered in distillate (D), reflux flow rate (L), reboiler duty (V), bottom product (B), and feed (F). The gain matrix is given below, where scaled values are marked by a star ... 

The tuning may follow a simplified procedure. Let Af ax and Awmax be the maximum allowed control error and control action, respectively. Then the variable ranges are y and u Au, Pl-controllers are used, with the gain Kf = A iax / Af ax) and integration time TI = 20 min. Table 17.9 presents the nominal operating point of the three controllers, at a nominal toluene plant throughput of 125 kmol/h. 

Table 17.9 Nominal operating point of the reaction loop control...

Because of different recycle structures, the base-case and the alternatives A, B and C will have slightly different nominal operating points. Table 17.14 shows the scaled static gains for the base-case. The reboiler duty (Q2) has the highest influence on the all... 

A scaled linearised state-space description around the nominal operating point of the dynamic model has been generated. The matrices A, B, C, and D have been exported in MATLAB , where a controllability analysis as fimction of fi equency has been performed. Alternatively, transfer fimctions have been generated. The results are similar. 

In arteries, pressure is usually positive with small oscillations about a nominal operating point (point A in Figure 10.2). Hence the piecewise linear approximation can be reduced to a single line with constant slope 1/C ... 

The material and energy balances, in the steady state, are solved for the complete flowsheet at the nominal operating point. 

Disadvantages of this topology are the limited cost-reduction potentials, as two full inverters are needed, as well as the voltage levels of the market available battery inverters for residential applications, which are in the range 24-48 V. Therefore, the inverters possess transformers and offer only relatively low efficiencies ( 94%) at nominal operating point and efficiencies much below this value at a wide range of the typical operating window. 

The units were designed and rigorous steady-state simulation was performed. The flowsheet was exported to AspenDynamics, where control loops were provided and tuned. It turned out that the nominal operating point is unstable. Figure 10 shows the shift from low to high conversion branch. This occurs after a long period of misleading stationary behaviour. 

Alternately, we could calculate the region of disturbances that can be tolerated with the available inputs, keeping the plant at the nominal operating point. This is denoted as the Tolerable Disturbance Space (TDS) defined as ... 

The last formulation aims to find the optimum steady state (nominal) operating point, the optimum topology of the plant and the optimum topology of the control system for a given set of scenarios. For fixed topology, Eq. (1) is simplified to the following... 

The goal will be to determine optimal equipment parameters and an optimal steady-state operating point such that feasible operation is maintained for all realizations of uncertain parameters within a specified uncertainty region, with a set of outputs controlled at their nominal values. The use of controller parametrization provides a performance limit for linear control. Feasibility with respect to imcertain parameter variation is handled by posing the problem directly within a multi-period framework. The plant will be assumed to be open-loop stable at the nominal operating point, permitting use of the control structure of Fig. 5. Note that while the search is restricted to linear controllers, path constraints are enforced for the nonlinear plant... 

Design parameters for candidate flowsheet configurations at nominal operating point (DeSC design modifications in italics). 

At the nominal operating point (where 0 = d = 95) the optimal solution is to have... 

Moving from the nominal operating point toward increasing energy removal, the temperature at the heat sink boundary of the core will decrease, and power generation will increase. When the temperature at... 

Fig. 5.14. Reactor s self-adjusting operating trajectory with heat sink at the core/reflector boundary equilibrium power vs temperatures at the heat sink, core averaged, and peak. The large black dots represent the nominal operating point (500 kW). The large square dots correspond to equilibrium with heat removal at the outside surface of the reflector at 300 K (see Table 5.5).

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