Control structures loops

In the previous chapter we discussed the elements of a conventional single-input-single-output (SISO) feedback control loop. This configuration forms the backbone of almost all process control structures. 

These same notions can be extended to an entire plant in which several unit operations are connected together. The HDA process for hydrodealkylation of toluene to form benzene is a good example of where an eigenstructure can be found that provides a more easily and simply controlled plant. See Fig. 8.15. Assuming that the toluene feed rate to the unit is fixed, this plant has 22 valves that must be set. There are 11 inventory loops (levels and pressures), so they require 11 valves. One possible conventional control structure is shown in Fig. 8.15. 

In this case, the typical CSTR control structure is as shown in Figure 9, with a single-loop control of the composition and a cascade control of the temperature. The block diagram is shown in Figure 10. 

Summary. In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. 

Now, from its essential notion, we have the feedback interconnection implies that a portion of the information from a given system returns back into the system. In this chapter, two processes are discussed in context of the feedback interconnection. The former is a typical feedback control systems, and consists in a bioreactor for waste water treatment. The bioreactor is controlled by robust asymptotic approach [33], [34]. The first study case in this chapter is focused in the bioreactor temperature. A heat exchanger is interconnected with the bioreactor in order to lead temperature into the digester around a constant value for avoiding stress in bacteria. The latter process is a fluid mechanics one, and has feedforward control structure. The process was constructed to study kinetics and dynamics of the gas-liquid flow in vertical column. In this second system, the interconnection is related to recycling liquid flow. The experiment comprises several superficial gas velocity. Thus, the control acting on the gas-liquid column can be seen as an open-loop system where the control variable is the velocity of the gas entering into the column. There is no measurements of the gas velocity to compute a fluid dynamics... 

The connection of secondary structures in native proteins is controlled by ordered structures, turns, or imordered structures, loops. In protein design the... 

Process design modifications usually have a bigger impact on operability (dynamic resilience). Dynamic resilience depends on controller structure, choice of measurements, and manipulated variables. Multivariable frequency-response techniques have been used to determine resilience properties. A primary result is that closed-loop control quality is limited by system invertability (nonmin-imum phase elements). Additionally, it has been shown that steady-state optimal designs are not necessarily optimal in dynamic operation. 

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. 

The first (distributed) layer of the control structure proposed in Section 5.4 was implemented as described in Equation (5.42), i.e., by stabilizing the holdups of the units within the recycle loop (the reactor and the vapor phase of the condenser) with proportional control laws. The liquid holdup in the condenser... 

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.

In this section we replace the CSTR by a plug-flow reactor and consider the conventional control structure. Section 4.5 presents the model equations. The energy balance equations can be discarded when the heat of reaction is negligible or when a control loop keeps constant reactor temperature manipulating, for example, the coolant flow rate. The model of the reactor/separation/recycle system can be solved analytically to obtain (the reader is encouraged to prove this) ... 

If the reactants A and B are lighter and heavier, respectively, than the product P, the flowsheet involves two distillation columns and two recycle streams (Figure 4.5). The control structure includes loops for reactor level and temperature, as well as for distillation columns top and bottom purity. The following dimensionless equations can be derived ... 

Figure 4.11 present the complete flowsheet together with the control structure. The reaction takes place in an adiabatic tubular reactor. To avoid fouling, the temperature of the reactor-outlet stream is reduced by quenching. A feed-effluent heat exchanger (FEHE) recovers part of the reaction heat. For control purposes, a furnace is included in the loop. The heat-integrated reaction system is stabilized... 

The plantwide control deals, mainly, with the mass balance of the species involved in the process. The species inventory can be maintained based on two different principles, namely self-regulation and feedback control. Control structures based on self-regulation set the flow rates of fresh reactants at values determined by the production rate and stoichiometry. Control of inventory by feedback consists of fixing one flow rate in each recycle loop, evaluating the inventory by means of concentration or level measurements, and reducing the deviations from the setpoint by change of the feed rate of fresh reactants. 

Summing up, if the inventory of the main components can be handled by local control loops, the inventory of impurities has essentially a plantwide character. The rates of generation, mainly in chemical reactors, and of depletion (exit streams and chemical conversion), as well as the accumulation (liquid-phase reactors, distillation columns and reservoirs) can be balanced by the effect of recycles in order to achieve an acceptable equilibrium state. Interactions through recycles can be exploited to create plantwide control structures that are not possible from a standalone unit viewpoint. 

We call this high sensitivity of the recycle flowrates to small disturbances the snowball effect. We illustrate its occurrence in the simple example below, It is important to note that this is not a dynamic effect it is a steady-state phenomenon. But it does have dynamic implications for disturbance propagation and for inventory control. It has nothing to do with closed-loop stability. However, this does not imply that it is independent of the plant s control structure. On the contrary, the extent of the snowball effect is very strongly dependent upon the control structure used. 

Conventional control structure. As shown in Fig. 2.6, the following control loops are chosen ... 

However, we see in this strategy that there is no flow controller anywhere in the recycle loop. The flows around the loop are set based upon level control in the reactor and reflux drum. Given what we said above, we expect to find that this control structure exhibits the snowball effect. By writing the various overall steady-state mass and component balances around the whole process and around the reactor and column. wre can calculate the flow of the recycle stream, at steady state, for any given fresh reactant feed flow and composition. The parameter values used in this specific numerical case are in Table 2.1. 

Figure 2,13a and b shows two control structures that work (CS4 and CS1), Both of these provide a mechanism for adjusting the fresh feed reactant flowrates so that the overall stoichiometry can be satisfied. In CS4 this is accomplished by measuring reactor composition. In CS1 it is accomplished by deducing the amounts of the reactants in the process from two levels in the two recycle loops. 

The two nonlinear ordinary differential equations can be linearized around the steady-state values of the reactor compositions zA and zs. Laplace transforming gives the characteristic equation of the system. It is important to remember that we are looking at the closed-loop system with control structure CS2 in place. Therefore Eq. (2.13) is the closed-loop characteristic equation of the process ... 

It should be noted that establishing the product-quality loops first, before the material balance control structure, is a fundamental difference between our plantwide control design procedure and Buckley s procedure. Since product quality considerations have become more important in recent years, this shift in emphasis follows naturally. 

When the unit control structure has been established, we would like to design the process such that the control loops are as responsive as possible. Interestingly enough, we can get clues on how to do this from the area of irreversible thermodynamics. The details are spelled out in Appendix A but let us give a brief introduction here, based on a very simple analog. 

Case 2 includes many of the example systems studied in this book. For example, reactors with temperature as the only controlled variable fall into this category. Also, the isothermal ternary scheme CS4 shown in Fig. 2.13a has a local composition controller on one of the dominant variables, the composition of component A. However, Case 2 is characterized by the fact that other dominant variables are not controlled at the reactor. Instead, the plantwide control structure plays a significant role in its ability to influence these uncontrolled variables. When the uncontrolled compositions become disturbances and the controlled dominant variables are too weak, we have difficulties. On the other hand, the plantwide control structure can be arranged to provide indirect control of the dominant composition variables, thereby augmenting the unit control loops. The HDA process provides a good illustration. The dominant variables are reactor inlet temperature and toluene composi-... 

Now the liquid level loops must also be modified, since we no longer can specify production rate and reactor level control cannot use TV This is easily accomplished by using low level override controllers on each of the three levels. Low stripper level pinches product base product flowrate B. Low separator level pinches separator liquid flowrate L. Low reactor level pinches the condenser cooling water flowrate CWc. In an override situation the level control structure has been reversed from the basic structure and now levels are held in the direction of flow. 

Had we started to assign the DIB column base level control first, we would have ended up with the same inventory control structure. The reason is as follows. Assume we had chosen the DIB column base valve to control base level. After resolving the purge column inventory loops, we would have found that we needed to control the purge column base or reflux drum level with the fresh feed flow to the DIB column. The dynamic lags associated with these loops would have forced us back to the control strategy as described above. 

Figure 10.2 gives the base-case plantwide control structure developed. Total toluene flowrate to the reaction section is flow-controlled. We will make step changes in this flow controller setpoint. Reactor inlet temperature is controlled by the firing rate in the furnace. No heat-exchanger bypass is shown in Fig. 10.2, but we will look at the effect of bypassing the FEHE. Control structure CS2 discussed in Chap. 5 adds a temperature control loop that controls furnace inlet temperature by manipulating the bypass flowrate around the FEHE. See Fig. 5.25. 

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