Control degrees of freedom

The number of manipulated variables is called the control degrees of freedom, which is equal to the number of control valves. In a conventional distillation column system there are six control valves feed, condenser coohng water, reboiler steam, reflux, distillate, and bottoms. One control degree of freedom must be used to control throughput. This is usually the feed, but it can be a product stream in an on-demand control structure. One control degree of freedom must be used to control pressure (typically condenser 

Reactive Distillation Design and Control. By William L. Luyben and Cheng-Ching Yu 

In the two-temperature control structure studied in Chapter 10, the 7 control degrees of freedom are allocated as follows  

Reflux-drum level controlled by distillate flowrate 

Reflux ratio maintained by measuring distillate flowrate and adjusting reflux flowrate 

In this section we discuss some basic concepts concerning distillation control degrees of freedom, basic manipulated variables, and constraints. 

There are six control valves associated with the column, therefore 

Two of the control degrees of freedom must be consumed to control the two liquid levels in the process reflux drum level and base level. Reflux drum level can be held by changing the flowrate of the distillate, the reflux, the vapor boilup, the condenser cooling, or the feed (if the feed is partially vapor). Each of these flows has a direct impact on reflux drum level. The most common selection is to use distillate to control reflux drum level, except in high reflux-ratio columns (RR 4) where Richardson s rule7 suggests that reflux should be used. 

Column base level (or reboiler level in a kettle reboiler) can be held by the flowrate of the bottoms, the vapor boilup, or the feed (if the feed is partially liquid and the stripping section does not contain too many trays). Since the typical hydraulic lag is 3 to 6 seconds per tray, a 20-tray stripping section introduces a deadtime of 1 to 2 minutes in the feed-to-base-level loop. Because of these hydraulic lags, reflux is only very7 rarely used to control base level. For this loop to work successfully, the column must be relatively short (less than 30 trays) and the holdup in the base must be large (more than 10 minutes). 

A fourth degree of freedom is consumed to control column pressure. The valves available are condenser cooling (by far the most commonly7 used), reboiler heat input, and feed (if the feed is partially vapor). If a flooded condenser is used, the cooling water valve is wide open and an additional valve, typically located between the condenser and the reflux drum, is used to cover or expose heat-transfer area in the condenser. 

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The process with two reactants offers a design and control degree of freedom that can be utilized to improve dynamic controllability if required. This degree of freedom is the concentration of the limiting reactant. The concentration of B in the 100-m3 reactor process considered in the previous section is only 0.0844 kmol/m3 compared to the concentration of A, which is 1.706 kmol/m3, so B is the limiting reactant. 

In this flowsheet the presence of the furnace provides an additional control degree of freedom, and there are now two controllers. The first G( (X) controls 7 lmx by manipulating bypass flow Fby. The second Gc2(s) controls Tm by manipulating furnace firing QF. The second controller sees the furnace transfer function GF2(S) which we assume to be a furnace first-order lag and three small lags (see Fig. 7.4b) ... 

Luyben, W.L., Design and control degrees of freedom, Ind. Eng. Chem. 

The control structure implication is that we do not attempt to regulate the gas recycle flow and we do not worry about what we control with its manipulation. We simply maximize its flow. This removes one control degree of freedom and simplifies the control problem. 

Establish the best way to use the remaining control degrees of freedom. 

We have discussed in detail each of the nine steps in our plantwide control design procedure. The first two steps establish the control objectives and control degrees of freedom for the plant. In the third step we discuss how the plantwide energy management problem can be converted to a local unit operation energy management problem by using the plant utility system. 

However we choose to look at it, a basic distillation column has two control degrees of freedom. When we turn to more complex column configurations with sidestreams, side strippers, side rectifiers, intermediate reboilers and condensers, and the like, we add additional control degrees of freedom. These more complex systems are discussed in Sec. 6.8. 

Since we have two control degrees of freedom, our objectives in distillation are to control the amount of LK impurity in the bottoms product ( b.lk) and the amount of HK impurity in the distillate ( 5>Hk) Controlling these compositions directly requires that we have composition analyzers to measure them. Instead of doing this, it is often possible to achieve fairly good product quality control by controlling the temperature on some tray in the column and keeping one manipulated variable constant. Quite often the best variable to fix is the reflux flowrate, but other possibilities include holding heat input or reflux ratio constant. 

Figure 6.20 gives a control scheme for a single sidestream column. The flowrate of the sidestream can be manipulated, so we have an additional control degree of freedom. Three compositions can be controlled the impurity of B in the distillate (xDiS). the purity of B in the sidestream (xsS), and the impurity of B in the bottoms xBS). Note that we cannot control the two impurity levels (A and C) in the sidestream xsa and Xs,c because there are not enough degrees of freedom. 

Most distillation columns have two control degrees of freedom, once pressure and feed conditions are set. The typical control structure holds the composition profile in the column by controlling a tray temperature somewhere in the column. The other degree of freedom is then normally consumed by fixing some other variable such as the flowrate of reflux, the reflux ratio, or the heat input. 

Step 2. This process has 14 control degrees of freedom. They include fresh feed valve DIB column steam, cooling water, reflux, distillate, and bottoms valves purge column steam, cooling water, reflux, distillate, and bottoms valves furnace fuel valve flooded condenser cooling water valve and DIB column feed valve. 

Step 2. There are 23 control degrees of freedom. They include two fresh feed valves for hydrogen and toluene purge valve separator base and overhead valves cooler cooling water valve liquid quench valve furnace fuel valve stabilizer column steam., bottoms, reflux, cooling water, and vapor product valves product column steam, bottoms, reflux, distillate, and cooling water valves and recycle column steam, bottoms, reflux, distillate, and cooling water valves. 

Step 2. There are 26 control degrees of freedom in this process. They include three feed valves for oxygen, ethylene, and acetic acid vaporizer and heater steam valves reactor steam drum liquid makeup and exit vapor valves vaporizer overhead valve two coolers and absorber cooling water valves separator base and overhead valves absorber overhead, base, wash acid, and liquid recirculation valves gas valve to CO removal system gas purge valve distillation column steam and cooling water valves column base, reflux, and vent valves and decanter organic and aqueous product valves. 

Control system. For subsequent selection and sizing of pumps and compressors, we need to map out the number and location of the control valves. Since the number of control valves is related to the number of control degrees of freedom, identify the control degrees of freedom. For example, a typical hydrodealkyllation process with a reactor, furnace, vapor-liquid separator, recycle compressor, two heat exchangers, and three distillation columns has 23 control degrees of freedom (Luyben et al., 1997). This requires 23 control valves whose location affects the rest of the design and the safety and hazards (see Section 16.7). 

Establish the best way to use the remaining control degrees of freedom. After satisfying the basic control requirement described above, there are some degrees of freedom left. 

The choice of the controlled and manipulated variables can be based on engineering judgement, or on methods that are more systematic. In any case we recommend those that regard in the first place the material balance. This gives valuable insight into the number of control degrees of freedom, functional controllability, I/O pairing for decentralized control. 

The number of variables that can be controlled in any plant equals the number of control valves. Most of these control degrees of freedom must be used to set production rate, control product quality, account for safety and environmental constraints, control liquid levels, and control gas pressures. Any remaining degrees of freedom can be used to achieve economic or dynamic objectives. 

Count the number of control valves (make sure all are legitimate, i.e., only one valve in a liquid-filled line). This is the number of control degrees of,freedom. 

Step 2. Determine the control degrees of freedom. Twenty control valves have been positioned in the PFD, as shown in Figure 20.17. 

In single-end control structures, only one composition or one temperature is controlled. The remaining control degree of freedom is selected to provide the least amount of product quality variability. For example, a constant reflux ratio RR can be maintained or the reflux-to-feed ratio R/F can be fixed. The control engineer must find out whether this more simple approach will provide effective control of the compositions of both product streams. One approach to this problem is to use steady-state simulations to see how much the reflux ratio and the reflux flow rate must change to maintain the specified impurity levels in both product streams (heavy-key impurity in the distillate X/>(hk) and light-key impurity in the bottoms Xb(lk)) when changes in feed composition occur. The procedure is call feed composition sensitivity analysis. ... 

Minimum Product Variability Criterion Choose the Tray that Produces the Smallest Changes in Product Purities When it is Held Constant in the Face of Feed Composition Disturbances. Several candidate tray locations are selected. The temperature on one specific tray is fixed, and a second control degree of freedom is fixed such as reflux ratio or reflux flow rate. Then the feed composition is changed over the expected range of values, and the resulting product compositions are calculated. The procedure is repeated for several control tray locations. The tray is selected that produces the smallest changes in product purities when it is held constant in the face of feed composition disturbances. 

Minimum Product Variability Criterion. Figure 6.8 shows how product impurities change when the temperature on a specific tray is held constant and feed composition changes. The second control degree of freedom that is fixed in this figure is the reflux flow rate. 

In the last three chapters, we have developed a number of conventional control structures dual-composition, single-end with RR, single-end with rellux-to-feed, tray temperature control, and so on. Structures with steam-to-feed ratios have also been demonstrated to reduce transient disturbances. Four out of the six control degrees of freedom (six available valves) are used to control the four variables of throughput, pressure, reflux-drum level, and base level. Throughput is normally controlled by the feed valve. In on-demand control structures, throughput is set by the flow rate of one of the product streams. Pressure is typically controlled by condenser heat removal. Base liquid level is normally controlled by bottoms flow rate. 

The other two control degrees of freedoms are typically reboiler duty and reflux flow rate (or distillate flow rate in high RR columns). ReboUer heat input is an effective... 

These four control degrees of freedom can be used to control four variables. Ideally the purities (or impurities) of all three product streams should be controlled. The fourth degree of freedom can be used to achieve some other objective. In the control structure discussed later in this chapter, it is used to achieve implicitly minimum energy consumption as feed... 

There are two remaining control degrees of freedom. The ideal dual-composition control structure would control C5 impurity in the distillate by manipulating reflux flow rate and C4 impurity in the bottoms by manipulating reboiler duty. However, this ideal control structure is the exception not the rule in industrial applications. We usually try to find a more simple control structure in which a single-end control scheme provides adequate regulatory control using a suitable tray temperature. 

FIGURE 32.18 Schematic of the prehension patterns of the hand as defined by Keller, Taylor, and Zahn (1947) (al) palmar prehension (three-jaw chuck), (o2) palmar prehension (two finger), (b) tip prehension, (c) lateral prehension, (<0 hook prehension, (e) spherical prehension, (/) cylindrical prehension. In a handlike prosthesis, it takes two to four independently controlled degrees of freedom to implement these prehension patterns. In a non-hand-like device, a single-degiee-of-free-dom device such as a split hook can be used. 

Detennine control degrees of freedom Establish energy management system Set production rate... 

For the designed plant with no heat integration, there are 38 control degrees of freedom in this process. These degrees of freedom represents the available manipulated variables in the process and can be characterised as follow four feed valves, direct reaction and oxy-reaction coolers valves, direct reaction and oxy-reaction product valves, oxy quench cooler valve, three decanter product valves, pyrolysis preheater and heater valves, pyrolysis product valve, pyrolysis quench cooler valve, HCl heater valve, eight valves for the heating and cooling systems of the four distillation columns, thirteen valves for the base, top and reflux streams of the four distillation columns. 

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