Example 2.4For the tank heater system (Figure 1.1), the inputs F, and T, are

disturbances, while Fst and F are manipulated inputs. The output vari­ables V and T can be measured easily and they are considered measuredoutputs.

Example 2.3Suppose that the inlet stream in the CSTR system (Figure 1.7) comes

from an upstream unit over which we have no control. Then CAi' Fi, andTi are disturbances. If the coolant flow rate is controlled by a controlvalve, then Fe is a manipulated variable, while Tei is a disturbance. Also,if the flow rate of the effluent stream is controlled by a valve, F is amanipulated variable; otherwise, it is an output variable.

With respect to the output variables we have the following: T, F, Teo,and V are measured outputs since their values can be known easily usingthermocouples (T, Teo)' a venturi meter (F), and a differential pressurecell (V).

The concentration C A can be a measured variable if an analyzer (gaschromatograph, infrared spectrometer, etc.) is attached to the effluentstream. In many industrial plants such analyzers are not availablebecause they are expensive and/or have low reliability (give poor meas­urements or break down easily). Consequently, in such cases CA is anunmeasured output variable.

Output variables: F, V,T

The input variables can be further classified into the following cate­gories:

1.Manipulated (or adjustable) variables, if their values can beadjusted freely by the human operator or a control mechanism

2. Disturbances, if their values are not the result of adjustment by anoperator or a control system

The output variables are also classified into the following categories:1.Measured output variables, if their values are known by directlymeasuring them

2. Unmeasured output variables, if they are not or cannot be meas­ured directly

Fi, t: FSh (F)Input variables:

Example 2.2For the tank heater discussed in Example 1.1 (Figure 1.1) we have

DesignAspects of a ProcessControl System 13Chap. 2

Output variables: CA, T,F, Teo' V

Notice that the effluent flow rate F can be considered either as input oroutput. If there is a control valve on the effluent stream so that its flowrate can be manipulated by a controller, the variable F is an input, sincethe opening of the valve is adjusted externally; otherwise, F is an outputvariable.

Input variables:

Example 2.1For the CSTR reactor discussed in Example 1.2 (Figure 1.7) we have

The variables (flow rates, temperatures, pressures, concentrations, etc.)associated with a chemical process are divided into two groups:

1. Input variables, which denote the effect of the surroundings onthe chemical process

2. Output variables, which denote the effect of the process on thesurroundings

2.1 Classificationof the Variablesin a ChemicalProcess

2Design Aspectsof a Process Control

System

Whatever our control objectives are, we need some means to moni­tor the performance of the chemical process. This is done by measuringthe values of certain processing variables (temperatures, pressures, con­centrations, flow rates, etc.). The second question that arises is:

Select measurements

Example 2.8For the batch reactor of Example 1.3, the qualitative control objective

is the maximization of the profit. The quantitative description of thisobjective is rather complex. It requires the solution of a maximizationproblem, which will yield the value of the steam flow rate, Q(t), at eachinstant during the reaction period.

Example 2.7For the stirred tank heater of Example 1.1, the control objectives are to

maintain the temperature of the outlet (T) and the volume of the fluid(V) in the tank at desired values. For this example the quantification ofthe control objectives is direct and straightforward: that is,

T= r,V= Vs

where T, and Vs are given, desired values.

Example 2.6For the CSTR system discussed in Example 1.2 (Figure 1.7),the con­

trol objective (qualitatively defined) is to ensure the stability of themiddle, unstable steady state. But such a qualitative description of thecontrol objectives is not useful for the design of a control system andmust be quantified. A quantitative translation of the qualitative controlobjective requires that the temperature (an output variable) not deviatemore than 5%from its nominal value at the unstable steady state.

At the beginning the control objectives are defined qualitatively; subse­quently, they are quantified, usually in terms of the output variables.

Ensuring the stability of the process, orSuppressing the influence of external disturbances, orOptimizing the economic performance of a plant, orA combination of the above.

The answer to this question determines the control objectives. Theymay have to do with:

15DesignAspects of a ProcessControl SystemChap. 2

Question 1: What are the operational objectives that a control sys­tem is called upon to achieve?

The central element in any control configuration is the process thatwe want to control. The first question raised by the control designer is:

Define control objectives

Let us look next at the basic questions that we must ask and try toanswer, while attempting to design a control system that will satisfy thecontrol needs for a chemical process.

2.2 Design Elementsof a Control System

Figure 2.1 summarizes all the classes of variables that we havearound a chemical process.

Example 2.5The disturbances F, and T, of the stirred tank heater (Figure 1.1) are

easily measured; thus they are considered measured disturbances. On theother hand, the feed composition for a distillation column, an extractionunit, reactors, and the like, is not normally measured and consequently isconsidered an unmeasured disturbance. As we will see later, unmeasureddisturbances generate more difficult control problems.

According to their direct measurability, the disturbances are classi­fied into two categories: measured and unmeasured disturbances.

Figure 2.1 Input and output variables around a chemical process.

Unmeasured outputs (z)

1--- Measured1--_ outputs

(y)Processing system

Manipulated --+-Ivariables(m)

Unmeasured (d ')Measured (d)

External disturbances

Part IControl of a Chemical Process: Characteristics and Associated Problems14

Figure 2.2 Three different systems for the distillate composition controlofa simple distillation column: (a) feedback; (b) feedforward; (c) inferen­tial.

(c)

(b)

L---4.----- ....Bottoms

(a)

17DesiqnAspects of a ProcessControl SystemChap. 2

Example 2.10Consider a simple distillation column separating a binary mixture of

pentane and hexane into two product streams of pentane (distillate) andhexane (bottoms). Our control objective is to maintain the production ofa distillate stream with 95 mole % pentane in the presence of changes inthe feed composition.

It is clear that our first reaction is to use a composition analyzer tomeasure the concentration of pentane in the distillate and then usingfeedback control to manipulate the reflux ratio, so that we can keep thedistillate 95%in pentane. This control scheme is shown in Figure 2.2a.Analternative control system is to use a composition analyzer to monitor theconcentration of pentane in the feed. Then in a feedforward arrangementwe can change the reflux ratio to achieve our objective. This control

It sometimes happens that our control objectives are not measurablequantities; that is, they belong to the class of unmeasured outputs. Insuch cases we must measure other variables which can be measuredeasily and reliably. Such supporting measurements are called secondarymeasurements.

Then we develop mathematical relationships between the unmeas­ured outputs and the secondary measurements; that is,

unmeasured output = f(secondary measurements)which allows us to determine the values of the unmeasured outputs(once the values of the secondary measurements are available). In asubsequent chapter we will see that the mathematical relationshipbetween measured and unmeasured outputs results from empirical,experimental, or theoretical considerations.

Consequently, our first attempt is to install measuring devices that willmonitor T and V directly. For the present system this is simple by using athermocouple (for T) and a differential pressure cell (for V).

and

Example 2.9For the tank heater system (Example 1.1) our control objectives are to

keep the volume and the temperature of the liquid in the tank at desiredlevels, that is, keep

It is self-evident that we would like to monitor directly the variablesthat represent our control objectives, and this is what is done wheneverpossible. Such measurements are called primary measurements.

Question 2: What variables should we measure in order to monitorthe operational performance of a plant?

Part IControl of a Chemical Process: Characteristics and Associated Problems16

Question 4: What is the best control configuration for a givenchemical process control situation?

It is clear from the previous examples that normally we will havemany different control configurations for a given chemical process,which raises the following question:

A control configuration is the information structure that is used toconnect the available measurements to the available manipulatedvariables.

After the control objectives, the possible measurements, and theavailable manipulated variables have been identified, the final problemto be solved is that of defining the control configuration. Before wedefine a control configuration, let us look at some control systems withdifferent control configurations.

The two feedback control systems in Figure 1.3a and b constitutetwo different control configurations. Thus the same information (mea­surement of liquid level) flows to different manipulated variables [i.e.,F (Figure 1.3a) and F, (Figure 1.3b»).Similarly, the feedback controlsystem (Figure 1.2)and the feedforward control system (Figure l.~) forthe tank heater constitute two distinctly different control configura­tions. For these two control systems we use the same manipulatedvariable (i.e., Fst) but different measurements. Thus for the feedbacksystem of Figure 1.2we use the temperature of the liquid in the tank,whereas for the feedforward system of Figure 1.4we measure the tem­perature of the inlet.

In the examples above we notice that two control configurationsdiffer either in:

1.The information (measurement) flowing to the same manipulatedvariable, or

2. The manipulated variable to which the same information flows.Thus for the two feedback control systems in Figure 1.3a and b we

use the same information (measurement of the liquid level) but differ­ent manipulated variables (F or Fi)' On the contrary, for the controlsystems in Figures 1.2 and 1.4,we have different measurements (T orTi) which are used to adjust the value of the same manipulated variable(Fst).

Later, wewill study other types of control configurations, but for thetime being we can define a control configuration (or control structure)as follows:

Select the control configuration

19Chap. 2 Design Aspects of a ProcessControl System,

Example 2.11To control the level of liquid in a tank we can adjust either the flow

rate of the inlet stream (Figure 1.3b) or the flow rate of the outlet stream(Figure I.3a). Which is better is an important question that we will ana­lyze later.

Usually in a process we have a number of available input variableswhich can be adjusted freely.Which ones we select to use as manipu­lated variables is a crucial question, as the choice will affect the qualityof the control actions we take.

Question 3: What are the manipulated variables to be used to con­trol a chemical process?

Once the control objectives have been specified and the variousmeasurements identified, the next question relates to how we effect achange in the process:

Select manipulated variables

The third class of measurements that we can make to monitor thebehavior of a chemical process includes direct measurement of theexternal disturbances. Measuring the disturbances before they enter theprocess can be highly advantageous because it allows us to know apriori what the behavior of the chemical process will be and thus takeremedial control action to alleviate any undesired consequences. Feed­forward control uses direct measurements of the disturbances (see Fig­ure 1.4).

scheme is shown in Figure 2.2b. Both of the control systems noted abovedepend on the composition analyzers. It is possible that such measuringdevices are either very costly or of very low reliability for an industrialenvironment (failing quite often or not providing accurate measure­ments). In such cases we can measure the temperature of the liquid atvarious trays along the length of the column quite reliably, using simplethermocouples. Then using the material and energy balances around thetrays of the column and the thermodynamic equilibrium relationshipsbetween liquid and vapor streams, we can develop a mathematical rela­tionship that gives us the composition of the distillate if the temperaturesof some selected trays are known. Figure 2.2c shows such a controlscheme that uses temperature measurements (secondary measurements)to estimate or infer the composition of pentane in the distillate (i.e., thevalue ofthe control objective).

Part IControl of a Chemical Process: Characteristics and Associated Problems18

ables at desired levels (set points). Examples of feedback controlare shown in Figures 1.2and 1.3.

2. InJerential control configuration: uses secondary measurements(because the controlled variables cannot be measured) to adjustthe values of the manipulated variables (Figure 2.4). The objec­tive here is to keep the (unmeasured) controlled variables atdesired levels.

The estimator uses the values of the available measured out­puts, together with the material and energy balances that governthe process, to compute mathematically (estimate) the values ofthe unmeasured controlled variables. These estimates, in turn, areused by the controller to adjust the values of the manipulatedvariables. An example of inferential control configuration isshown in Figure 2.2c.

3. FeedJorwardcontrol configuration: uses direct measurement ofthe disturbances to adjust the values of the manipulated variables(Figure 2.5). The objective here is to keep the values of the con­trolled output variables at desired levels. An example of feedfor­ward control configuration is shown in Figure 1.4.

Figure 2.4 General structure of inferential control configurations.

Estimatesof theunmeasuredcontrolledvariables

Estimator:computes an estimateof the values of theunmeasured controlledvariables

Set points----

Unmeasuredoutputs(controlledvariables)

Measuredoutputs

...

r I

! t Process 1 !• I • i I II I I ... I I II I I I I I

Manipulatedvariables

Disturbances

21DesiqnAspects of a ProcessControl SystemChap 2

Figure 2.3 General structure of feedback control configurations.

- - - - - Set p-oints

III

J I_J I__ ..J

I Unmeasured outputs

II II IIL

I L_L__

Measured outputs(controlled variables)

...

l ,~t Process I I

I II : t -. I II I I II I I

., . I I II I I I I I

Manipulatedvariables

Disturbances

In the chemical industry most of the processing systems are multi­ple-input, multiple-output systems. Since the design of SISO systems issimpler, we will start first with them and progressively cover the designof MIMO systems.

Let us close this section by defining three general types of controlconfigurations.

1. Feedback control configuration: uses direct measurements ofthe controlled variables to adjust the values of the manipulatedvariables (Figure 2.3).The objective is to keep the controlled vari-

The answer to this question is very critical for the quality of the controlsystem we are asked to design.

Depending on how many controlled outputs and manipulatedinputs we have in a chemical process, we can distinguish the controlconfigurations as either single-input, single-output (SISO) or multiple­input, multiple-output (MIMO) control systems.

For example, for the tank heater system:(a) If the control objective (controlled output) is to keep the liquid

level at a desired value by manipulating the effluent flow rate, wehave a SISO system.

(b) On the contrary, if our control objectives are (more than one) tokeep the level and the temperature of the liquid at desired values,by manipulating (more than one) the steam flow rate and theeffluent flow rate, we have a MIMO system.

Part IControl of a Chemical Process: Characteristics and Associated Problems20

Substitute again Q from eq. (2.6) into (2.3) and take

Equation (2.5) is solved for (T - Ts), and for various values of gain 0:yields the solutions shown in Figure 2.7. We notice that none of thesolutions is satisfactory since T - T,* O. Thus we conclude that theproportional control law is not acceptable.

Considerable improvement in the quality of the resulting control canbe obtained if we use a different control law known as integral control. Inthis case Q is proportional to the time integral of (T - Ts):

Q ""- 0:' i' (T - T,,)dt + o, (2.6)

This law is known as proportional control and parameter 0: is calledproportional gain. Substitute eq. (2.4) into (2.3) and take

d(T - Ts)Vpcp dt ""Fpcp[(Ti-Ti,s)-(T-Ts)]-o:(T-Ts) (2.5)

(2.4)Q ""- 0:( T - Ts) + Qs

Note that d( T - Ts)/ dt ""dT/dt, since T,""constant.The difference E "" T - T, denotes the error or deviation of liquid's

temperature from the desired value T;Wewant to drive this error to zeroby manipulating appropriately the value of heat input Q. The simplestcontrol law is to require that Q changes proportionally to the errorT- t;

(2.3)

Subtract eq. (2.1)from (2.2) and taked(T- Ts)

Vpc, dt ""Fpcp[(Ti - Ti,s) - (T - Ts)] + (Q - Qs)

(2.2)

and the liquid's heat capacity, respectively. T; Ti,s, and Qs are thecorresponding steady-state values. Suppose that suddenly T, increases asshown in Figure 2.6. If nothing is done on Q, the temperature T will startrising with time. How T changes with time will be given by the transientenergy balance around the tank: that is,

dTVpcp - ""Fpcp(Ti - T) + Q

dt

Figure 2.6 Temperature step change.

Time

23DesignAspects of a ProcessControl SystemChap 2

where F, p, and Cp are the inlet (or outlet) flow rate, density ofthe liquid,

(2.1)0"" Fpcp(Ti,S - Ts) + Qs

Example 2.12Let us consider the problem of controlling the temperature T of a

liquid in a tank (Figure 1.1) when the inlet temperature T, changes.Assume that the inlet and outlet flow rates are equal. Our measurementwill be the liquid temperature and the manipulated variable the rate ofheat input, Q, provided by steam. The question is: How should Q changein order to keep temperature T constant, when T, changes? In otherwords, we want to develop the control law.

Assume that the heater has been operating for some time and that theliquid temperature has been kept constant at T" while the volume of theliquid has remained constant at a value V.We say that the heater hasbeen operating at steady state (where nothing changes). Under theseconditions the energy balance around the tank yields

The answer to this question constitutes the control law, which isimplemented automatically by the controller.

Question 5: How is the information, takenfrom the measurements,used to adjust the values of the manipulated variables?

In every control configuration, the controller is the active elementthat receives the information from the measurements and takes appro­priate control actions to adjust the values of the manipulated variables.For the design ofthe controller we must answer the following question:

Design the controller

Figure 2.S General structure of feedforward control configurations.

Unmeasuredoutputs

t--- MeasuredoutputsProcess

Manipulated _ ......._ ...... -ivariables

Disturbances

Part IControl of a Chemical Process: Characteristics and Associated Problems22

Figure 2.9 The simple chemical plant of Example 2.13.

C

A+B+C

Steam-

column

Consider a simple chemical plant composed of two units: a CSTR anda distillation column (Figure 2.9). The raw materials entering the reactor

Example 1.13

The examples that we discussed in previous sections were concernedwith the control of single units such as CSTR, a tank heater, and a batchreactor. It should be emphasized as early as possible that rarely if ever isa chemical process composed of one unit only. On the contrary, achemical process is composed of a large number of units (reactors,separators, heat exchangers, tanks, pumps, compressors, etc.) which areinterconnected with each other through the flow of materials andenergy. For such a process the problem of designing a control system isnot simple but requires experience and good chemical engineering back­ground.

Without dwelling too much on the control problems of integratedchemical processes, let us see some of their characteristic features whichdo not show up in the control of single units.

2.3 Control Aspects of a CompleteChemicalPlant

25DesignAspects of a ProcessControl SystemChap. 2

Figure 2.8 Temperature response under integral feedback control.

Time

No control(a' = 0)

Error(T- T,)

In Part IV (Chapters 13through 18)we will study the characteristicsof various control laws, but it should be remembered that the selectionof the appropriate control law is an important question to be answeredby the chemical engineer control designer.

(2.8)

V d( T - Ts) , it dpc, = Fpcp[(Ti - Ti,s)- (T - Ts)] - a (T - Ts) t (2.7)dt 0

The solution of eq. (2.7) for various values of the parameter a' is shownin Figure 2.8. We notice that integral control is acceptable since it drivesthe error T - T, to zero.Wealso notice that depending on the value of a',the error T - T, returns to zero faster or slower, oscillates for longer orshorter time, and so on. In other words, the quality of control depends onthe value of a'. [Note: In Chapter 8 we will learn how to solve integral­differential equations such as (2.7).]

Combining the proportional with the integral action we take a newcontrol law known as proportional-integral control. According to this lawthe value of heat input Q is given by

Q = -a(T - T,)- a'it (T - Ts) dt + Q,

Figure 2.7 Temperature response under proportional feedback control.

Timeo

a=2

a=l

(a= 0)

No controlError(T- T,)

Part IControl of a Chemical Process: Characteristics and Associated Problems24

The control of integrated processes is the basic objective for a chem­ical engineer. Due to its complexity, though, we will start by analyzingthe control problems for single units and eventually we will treat theintegrated processes.

the desired level, we try to keep the ratio F AIF B = constant and thetemperature T in the CSTR constant. Any changes in F AIF B or T willaffect the conversion in the reactor and thus the composition of the feedin the distillation column. A change in the feed composition of the col­umn will affect the purity of the two product streams.

27DesignAspects of a ProcessControl SystemChap. 2

At first glance the problem of designing a control system even for thissimple plant looks very complex. Indeed it is. The basically new featurefor the control design of such a system is the interaction between the units(reactor, column). The output of the reactor affects the operation of thecolumn in a profound way and the overhead product of the columninfluences the conversion in the CSTR. This tight interaction between thetwo units seriously complicates the design of the control system for theoverall process.

Suppose that we want to control the composition of the bottomsproduct by manipulating the steam in the reboiler. This control actionwill affect the composition of the overhead product (A + B),which in turnwill affect the reaction conversion in the CSTR.

On the other hand, to keep the conversion in the CSTR constant at

(a) The flow rates, compositions, and temperatures of the streams ofthe two raw materials.

(b) The pressure in the distillation column.(c) The temperature of the coolant used in the condenser of the distil­

lation column: (For example, if the coolant is water, it will have adifferent temperature during the day than during the night.)

are:

The reaction is endothermic and the heat is supplied by steam whichflows through the jacket of the reactor. The mixture of C and unreacted Aand B enters the distillation column, where A + B is separated from thetop as the overhead product and C is taken as the bottom product.

The operational objectives for this simple plant are:

I. Product specifications:(a) Keep the flow rate of the desired product stream Fr at the

specified level.(b) Keep the required purity ofC in the product stream.

2. Operational constraints:(a) Do not overflow the CSTR.(b) Do not flood the distillation column or let it go dry.

3. Economic considerations:Maximize the profit from the operation of this plant. Since the flowrate and the composition of the product stream are specified, max­imizing the profit is equivalent to minimizing the operating costs.It should be noted that the operating cost involves the cost forpurchasing the raw materials, the cost of steam used in the CSTRand the reboiler of the distillation column, and the cost of thecooling water used in the condenser.

The disturbances that will affect the foregoing operational objectives

are A and B with flow rates FA and F B and temperatures T A and T B,

respectively. They react to yield C:

A+B-C

Part IControl of a Chemical Process: Characteristics and Associated Problems26