Loop analysis

The double loop analysis questions the steering process if any single loop control element seems to be ineffective. So the analysis discriminates between an ineffective single loop control element and an ineffective corresponding (double loop) steering element, where the steering element has the benefit of the doubt. 

Figure 35 The flow schemes for single and double loop analysis.

The additional double loop analysis gives more detailed information regarding the 44 ineffective control elements, distinguishing true ineffective elements of the single loop from the false ineffective elements that in fact concern the double loop learning , i.e. an ineffective steering element. The results of this additional analysis are presented in Figure 37. 

To supplement the SVD analysis, rigorous d mamic simulations under closed loop operation were carried out. For the closed-loop analysis, several issues must be defined first, such as the control loops for each system, the type of process controller to be used, and the values of the controller parameters. 

The simulations involve the solution of the rigorous tray-by-tray model of each sequence, given by equations 1 to 6, together with the standard equations for the PI controllers for each control loop (with the parameters obtained through the minimization of the lAE criterion). The objective of the simulations is to And out how the dynamic behavior of the systems compare under feedback control mode. To carry out the closed-loop analysis, two types of cases were considered i) servo control, in which a step change was induced in the set point for each product composition under SISO feedback control. 

Inspecting Equation (5.29), we notice that three of the state variables (namely, Mr, My, and Ml) are material holdups, which act as integrators and render the system open-loop unstable. Our initial focus will therefore be a pseudo-open loop analysis consisting of simulating the model in Equation (5.29) after the holdup of the reactor, and the vapor and liquid holdup in the condenser, have been stabilized. This task is accomplished by defining the reactor effluent, recycle, and liquid-product flow rates as functions of Mr, My, and Ml via appropriate control laws (specifically, via the proportional controllers (5.42) and (5.48), as discussed later in this section). With this primary control structure in place, we carried out a simulation using initial conditions that were slightly perturbed from the steady-state values in Table 5.1. 

A commonly used network analysis method is loop and mesh analysis, which is generally based on KVL. As defined previously, loop analysis refers to the general method of current analysis for both planar and non-planar networks, whereas mesh analysis is reserved for the analysis of planar networks. In loop or mesh analysis, the circulating currents are selected as the unknowns, and a circulating current is assigned to each independent loop or mesh of the network. Then a series of equations can be formed according to KVL. 

For a first approximation to the solution, we will assume that essentially all the methanol condenses, with only trace amounts appearing in the recycle line. We will also assume that most of the water condenses and that very small amounts of carbon monoxide, carbon dioxide, hydrogen, methane, and nitrogen dissolve in the condensate. To account for methanol and water vapor in the recycle gases and the solubility of the gases in the crade methanol, we would have to include phase equilibrium relationships in the analysis. As stated earlier, several condensable byproducts, high and low-boiling compounds in the cmde methanol, are present in small amounts, as shown in Table 3.5.1. We will not consider these compounds in the synthesis-loop analysis. 

Tests using loop analysis combined with least sums-least squares analysis can also be used to see whether a large-scale revision of data on compounds of a given element is needed or justified. The complexities of such networks can be great, as is the case for the lithium network. This network approach will assist us in evaluating data for flue gas washing processes. 

The study of how any disturbance propagates inside the converter, either getting attenuated or exacerbated in the process, is called feedback loop analysis. As mentioned, in practice, we test a feedback loop by deliberately injecting a small disturbance at an appropriate point inside it (cause), and then seeing at what magnitude and phase it returns to the same point (effect). If, for example, we find that the disturbance reinforces itself (at the right phase), cause-effect separation will be completely lost, and instability will result. 

As we proceed toward our ultimate objective of control loop analysis and compensation network design, we will be multiplying transfer functions of cascaded blocks to get the overall transfer function. That is because the output of one block forms the input for the next block, and so on. 

Note however, that in applying control loop theory to power supplies, we are actually looking only at changes for perturbations), not the dc values (though this was not made obvious in Figure 7-9). It can also be shown that when the error amplifier is a conventional op-amp, the lower resistor of the divider, Rfl, behaves only as a dc biasing resistor and does not play any (direct) part in the ac loop analysis. 

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