Open-loop dynamics

The expander train supplier shall assist with the selection of the expander inlet and bypass valve configurations and closure rates by performing an open loop dynamic simulation study. For a main air blower train dais could be closed loop. 

The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

Open hollow fiber membranes, 16 2, 3 Open-loop control systems, 9 56-57 Open-loop dynamics, 20 694... 

PID controller tunings for this model have been given by a number of researchers [9-13], Chen and Fruehauf [9] have given an industrial example of the level control in a distillation column where the open loop dynamics follows the IPTD model with parameters kp = 0.2 and d = 1A min. 

Figure 4.9 Open-loop dynamic response of oxidation reactor.

Figure 5.29 Open-loop dynamic behavior of packed adiabatic plug-flow reactor with FEHE.

We use the default tuning parameters, as follows LCl with Kc=20 %/% and t,=10 min., and PC2 with Kc=20 %/%. Fig. 4.8 displays the closed loop response for the same scenario of disturbances as in Example 4.2. This time the liquid level is kept around the set point with small deviations. The response of the output streams is different from open loop dynamics the outlet liquid flow rate decreases at increasing temperature, and vice versa. An inverse response is noted in both cases. Hence, keeping constant the liquid level will produce disturbances in the outlet flows, which might be undesirable... 

Figure 17.18 Open loop dynamic responses in the base case...

NEQ simulations also show that the dynamic response of a RD column is also sensitive to the hardware choice (tray or packing type). The open loop dynamics are predominately influenced by the storage capacities (at steady state) and resi-... 

In the previous case study, the focus was on control structure selection. As control algorithms standard linear Pl-controllers were used. In a second case study, the focus is on control algorithms. For that purpose we compare different control algorithms for a fixed control stmcture. The process to be considered is an industrial benchmark problem, which was treated in joint research with Bayer AG [21, 33]. The process and its open loop dynamic behavior is illustrated in Fig. 10.29. Components B and C are the reactants. They react in two consecutive equilibrium reactions to products A and E. The main product E is obtained in the bottoms of the column and the other product A in the distillate. 

Fig. 10.30 gives a comparison between open loop dynamics and closed loop dynamics for linear multi-input multi-output PI controllers and an advanced nonlinear controller. The nonlinear controller is based on asymptotic etsact input/out-put linearization as proposed by Gilles and coworkers [29]. This is a model based controller, where the concentration profiles inside the column are reconstructed online from the two temperature measurements by means of a nonlinear state observer [21, 33]. 

In this chapter, an overview on the present knowledge of nonlinear dynamics and control of RD columns was given. First, focus was on open-loop dynamics. It was shown that these processes can show a distinct nonlinear behavior including multiple steady states, selfsustained oscillations, and nonlinear wave propagation. Different patterns of behavior were identified depending on the properties of the reaction system and the operating conditions. 

In the second part of this chapter, focus was on control of continuously operated RD processes. So far most control studies focus on processes that are operated close to chemical equilibrium. Emphasis was on the well-known esterification and etherification systems. The methods employed are similar to non-RD column control. It is worth noting that this is consistent with our conclusions on open-loop dynamics as drawn above. Additional problems may rise in indirect control schemes, where product compositions are inferred from temperature measurements. It was shown that these problems can be handled if in addition some direct or indirect measure of conversion is taken into account. 

The valve coefficients for the four valves are fixed at the values given by (10.63), (10.64), (10.66) and (10.67) to obtain the open-loop dynamic response of the SOFC. Step changes are made in the load current from 100 to 80 A at 500 s and from 80 to 90 A at 2000 s. The dynamic responses of the cell voltage, current, FU and OU to the step changes of load current, the data being normalised with respect to the initial steady-state conditions (Voltage = 0.609036 V, Current = 100 A, FU = 0.8 and OU = 0.125), are shown in Fig. 10.8a. 

Linearize the open-loop dynamic model of the process at the two fixed points in Table 4. Then perform model reduction [38,39] to derive two reduced linear 4-state models. From the Jacobian of the full state model, balanced truncation was used to reduce the model order. The... 

The effects of interactions on plant dynamics can in general be attributed to feedback effects imposed by recycle flows. Thus, similar to what is done for feedbaek control systems, it is relevant to decompose the system by deriving models for the system dynamies in the absence of feedback ( open-loop ), and then study the effect of closing the loop ( closed-loop ). Note that, in physical terms, the open-loop dynamics will correspond to the case in which the recycle flow conditions are kept constant, i.e., changes in the system are not fed back through the recycle flow. 

From the block-diagram in Fig. 4 we can now derive the closed-loop dynamics and compare it to the open-loop dynamics represented by G s). In this way we can directly compute the effect of the feedback, provided by the recycle flow, on the overall dynamics. To simplify the exposition, we here limit ourselves to consider the case in which all variables are scalar. However, similar results apply when considering the more general multivariable case. With all variables scalar, G s) is a 2 x 2 matrix and can be written... 

From this we see that all transfer-functions involving at least one loop-variable, W2 or y2, is simply the open-loop dynamics multiplied by the factor... 

Reboilers—Open-Loop Dynamics If steam flow is noncritical,... 

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