improvements of pid.pdf

Process Control in the Chemical Industries 85

IMPROVEMENTS OF SINGLE-LOOP PID FEEDBACK CONTROL

Introduction

Single loop feedback controllers often provide satisfactory control performances. Besides their simplicity that reduces engineering effort, its main advantages are:

It requires minimal knowledge about the process to be controlled. In particular, a mathematical model is not necessary, although it is useful for control system design.

The classical PID controllers are versatile and robust. If process conditions

change, re-tuning the controller usually produces satisfactory response. Feedback control has also certain inherent weaknesses:

The feedback controller acts only after the process feels the upset. It therefore can never yield perfect control where the controlled variable does not deviate from the set point during load or set point changes.

Poor feedback tuning may cause instability

PID controller does not always provide the best possible control for all processes

especially for processes with large dead times and/or cascade processes with large time constant.

In some applications the controlled variable can not be measured on line and

consequently feedback control is not feasible.

Feedback control does not provide predictive control action to compensate for the effects of known or measurable disturbances.

In order to enhance the single loop PID feedback control performances, a number of

special control configurations such as cascade control, feed-forward control, and inferential control are often used. Each of these configurations improves the feedback controller design by taking advantage of additional knowledge about process dynamics through one of these means:

Additional process output measurements are used (e.g. cascade ,inferential)

Additional process inputs measurements are used (e.g. feed-forward)

Use explicit modeling in control calculations (e.g. inferential)

Use a different control algorithm than PID (e.g. feed-forward)

Chemical Engineering Department King Saud University, 2002


1. Cascade Control Cascade control is one of the most successful configurations to improve the performances of the single-loop feedback control. It can provide more effective control by reducing both the maximum deviations and integral error for the disturbances response.

As it was explained in the introduction, cascade control uses an additional measurement of a process variable to assist in the control task. This technique is shown in the block diagram of Fig. 1. Two controllers are used but only one process variable is manipulated. The primary (also called outer, master) controller maintains the primary variable y1 at its set point by adjusting the set point ysp2 of the secondary controller. The secondary (also called inner, slave) controller responds both to the output of the primary controller and to the secondary controlled variable y2 .

GcI GcII GPII GPIy1

Primary Loop

Secondary Loop

+

_+ _

dII+

+ +

+dIy1

sp y2sp y2

Figure 1: Cascade control block diagram

1.1 Illustrating Example

Consider the stirred tank heater of Fig. 2 for which the objective is to control the exit temperature T using the heating Fc. For a large disturbance in the heating oil pressure, Figure 3 shows a typical response of the controlled process using a PID feedback controller. As it can be expected the disturbance is ultimately suppressed but the response will be slow since the exit temperature must be disturbed before the feedback controller can respond.

Feed

Product

Heating oil

T

Fc

Figure 2: Stirred Tank Heater with single control loop



To improve the speed of the response, we use a secondary measured process input which is the heating oil flow because it responds faster to the disturbances in the oil pressure. The control system (Fig. 4) uses two feedback controllers that can be standard PID controllers. The output of the exit temperature controller adjusts the set point of the flow controller. That is the set point of the secondary controller is equal to the primary controller output.

Temperature

Flow

Time Figure 3: Dynamic response of stirred tank heater to disturbance in oil pressure using

single loop controller The secondary flow control loop is essentially the manipulated variable for the

primary controller. Figure 5 shows a typical response for the same disturbance using the cascade control. Because the sensor and valve are fast processes, the flow controller can rapidly achieve the desired flow of oil. The secondary controller corrects for the disturbance before the tank exit temperature is significantly affected by it.

TI

TC

FcHeating oil

Sp1 fromoperator

F1

P0

P1

F0T0

Figure 4: Stirred Tank heater with cascade control



Temperature

Flow

Time Figure 5: Dynamic response of stirred tank heater to disturbance in oil pressure with

cascade control

1.2 Advantages The advantages of cascade control can be summarized as follow:

Disturbances felt by the secondary variable is significantly corrected by the secondary controller before it is felt by the process.

The dynamics of the secondary loop are much faster than those of the primary

loop. The cross over of the secondary loop is higher than that of the primary loop. This allows the use of higher gains in the secondary controller to suppress more effectively the effect of the disturbance occurring in the secondary loop without affecting the stability of the system.

1.3 Tuning and Implementation Issues 1.3.1 Selection of the secondary variable The key point in cascade control is the selection of secondary variable. Two guidelines must be observed:

The secondary variable must indicate the occurrence of an important disturbance

The secondary variable dynamics must be faster that the primary variable dynamics

1.4 Types of Cascade Controllers

Cascade control can use the standard PID feedback controllers in the two loops. The secondary loop must have the proportional mode but it does not require the reset mode. Integral model may be used in the secondary controller if it is desired to suppress completely the disturbance entering the primary or when the primary controller is not in operation (sensor not functioning or calibrated, etc). Derivative modes are not advised in the secondary loop since the derivative action is designed to overcome some lag in the controller loop and if applied to set point changes may result in excessive valve motion and overshoot.



The cascade controller is tuned in a sequential manner. The secondary controller is first tuned satisfactorily before the primary is tuned . Conventional tuning guidelines for PID apply for both the control loops. 1.5 Instability and Saturation

Adding cascade control to a process can destabilize the primary loop if most of the process dynamics are within the secondary loop. A common example is the use of a valve positioner in a flow control loop. Closing the loop around the valve increases its gain so that the proportional band of the flow controller has to be increased to maintain stability. This leads to slower response. If large valve motor or long pneumatic transmission lines cause problems a volume booster should be used to load the valve motor rather than a positioner.

Saturation problems can arise when both primary and secondary controllers have automatic reset. The need for anti-reset windup is much greater for cascade designs since once the secondary loop is saturated, the primary controller will also saturate. When putting a cascade system into automatic operation the secondary controller must be first transferred to automatic. 1.6 Examples of Commonly Used Secondary Loops 1.6.1 Valve positioner

Stem friction and/or changes in line pressure can cause a hysteresis between the action of the control signal and its effect on the valve position. i.e. The valve may remain stationary and then jump to a value beyond that necessary to bring the controlled variable to its set point. This can degrade performances.

The effects of a valve sticking can be reduced by the use of a valve positioner

which is included as part of valve equipment (Fig. 6).The primary controller sends it signal to the valve positioner which in turn adjusts the air pressure until the desired stem position is nearly achieved. Valve positioner are proportional controllers with smaller proportional band. This allows for fast dynamics that will reduce the dead zone in the control valve and improve the response of the valve.

Vc

Tc

Remote location

positioner locatedat valve

Figure 6: Schematic of a valve positioner

1.6.2 Flow control To ensure that line pressure fluctuations or undesirable valve characteristics do

not affect the primary loop, flow control can be set in cascade as it is the case in composition control. Flow controllers may have proportional and reset modes.



1.6.3 Temperature Control

When there is need for accurate control of heat transfer such as in jacketed continuous stirred tank reactor (Fig. 7), cascade control is used. The reactor temperature is controlled by manipulating the coolant temperature in cascade.

TT

Tc

TT

set point

Fccoolant Tc

Feed

Product

BA

TT

Tcset point

Fccoolant Tc

Feed

Product

BA

set point

Figure 7: Temperature control: (a) conventional feedback; (b) Cascade control

1.7 Illustrating Example of Design of Cascade Control

Consider the block diagram of a cascade system shown in Fig 1. To simplify the presentation we assume that the transfer functions of the measuring devices is one. The dynamics of the secondary loop are:

Gsecondary = GcII(s)GpI(s) (1) Figure 8 shows a simplified form of the general block diagram where the secondary loop has been considered as a dynamic element. The overall transfer function for the primary loop is

IIIII

IIIIIprimary GpGpGc

GpGcGcG )

1(

+=

(2)

The stability of the primary loop is determined by the characteristic equation,

IIIII

IIIIIprimary GpGpGc

GpGcGcG )1

(11+

+=+ (3)

Let see how the design can be carried out for the following example:

))(.( 11501

++=

ssGpI

and



).( 1101

+=

sGpII

Note that from looking at the time constants that the secondary process is faster than the primary.

GcI GPI y1y1

sp

+_

dII

+

+

+dI

PIIcII

PIIcIIGG

GG+1

PIIcIIGG+11

+

Figure 8: Simplified cascade control block diagram

Simple feedback control Using a simple PI controller with reset time I = 1, the open loop transfer function is

+++

+=

)1)(15.0)(11.0(111

ssssKGpGpGc cIIIII

(4)

The cross over frequency can be found from the equation that sets the total phase lag to 1800

( ) ( ) ( ) 180tan5.0tan1.0tan1tan 1111 =+++

cococo

co

wwww

(5)

This yields:

wco = 4.45 rad/.min The overall amplitude ratio is given by

1

1

150

1

110

1112222 +++

+=wwww

KcAR I).().(

(6)

The ultimate value of the gain KcI can be found from the condition

AR = 1 at w = wco Thus



1

1

150

1

110

11112222 +++

+=cocococo

Iwwww

Kc).().(

(7)

yielding

KcI = 11.88 Therefore when the disturbance dII of the secondary process changes, the simple feedback controller can use a gain up to 11.88 before the system becomes unstable. Also because the overall process is of the third order we expect that the closed loop response of y(t) to change in dII will be rather sluggish. Cascade Control

Consider a cascade control system similar to that of Fig. 1. The open loop transfer function for the secondary loop is given by Eq. 1. Assuming a simple proportional controller yield:

11.01

+=

sKcGpGc IIIII

There is no cross over frequency for the secondary control loop. Large values for the gain KcII can be used that yield fast closed loop responses. Once KcII is selected for the secondary loop, the cross over frequency for the overall process can be obtained as before. Then KcI can be selected for the primary controller using Ziegler-Nichols method. 2. Feed-forward Control

As mentioned in the introduction, feed forward control attempts to enhance the

performance of the single loop feedback control by making use of an additional measurement of process input. Figure 9 shows the general form of feed-forward control configuration. The disturbance is measured directly and the manipulated variable is changed accordingly to eliminate the impact of the disturbance on process output. Recall that feedback controller reacts only after it has detected a deviation of the value of the output from the desired steady state, therefore feedback control can never achieve perfect control. Feed-forward control on the other hand anticipates the effect the disturbance will have on the process output. Therefore feed forward controllers have the potential, at least theoretical, for perfect control.

In many applications, feed flow is the primary component of load because it can

change widely and rapidly. Load elements can also be feed composition when the product composition is to be controlled, or feed flow and temperature when the product temperature is to be controlled.



Process

Controller Disturbance

Manipulatedvariable Controlled variable

Figure 9: Feed-forward controller 2.1 Examples

The objective of the feed-forward controller is to compute the manipulated variable that would balance the load (load balancing). One may anticipate that the logic of the feed-forward will depend on the availability of mathematical equations relating the load to the manipulated variable. These equations are the material and energy balance either at steady state or dynamic.

Consider the example of the stirred tank heater of Fig 10. The objective is to

design a feedforward control for the temperature by measuring the disturbance Ti and using the amount of heat Q provided by the steam as manipulated variable. Since the focus will be only on controlling the temperature we assume that the level L is constant (i.e. Fi does not change).

Ti, Fi

Steam

T, F

L

Figure 10: Stirred Tank Heater

The process variables are related by the dynamic heat balance equation:

CpQTTF

dtdTAL ii

+= )( (8)

2.1.1 Steady state feed-forward controller

The simplest form of feed-forward control is the one based on steady state balance, Setting dT/dt = 0 in Eq. 8, yields:



)( ii TTCpFQ = (9) Therefore in order to keep the controlled variable, i.e. temperature T at the set point Tsp, the manipulated variable i.e. amount of heat should be:

)( isp

i TTCpFQ = (10) This simple relation is the design equation for the static feed-forward controller.

Figure [11a] shows the block diagram for this static feed-forward control. Figure [12a] shows the temperature response to a load change in feed temperature.

CpFi

+

_

1 +sTsp

Ti

Ti, Fi

T, FSteam

Controller

Feedforwardcontrol

CpFi

+

_

1Tsp

Ti

Ti, Fi

Steam

Controller

Feedforwardcontrol

(a)

(b)

T, F

Figure 11: feed-forward of temperature control; (a) static; (b) dynamic

2.1.2Dynamic Feed-forward controller

To improve the controller transient response, we will use the dynamic heat balance to design a dynamic feed-forward controller. Equation (8) can be also put in the following form



CpFQTT

dtdT

FV

ii

i +=+

(11)

where V=AL is the constant liquid volume in the tank. The equation can also be put in deviation variables form as follows:

CpFQTT

dtdT

FV

ii

i +=+

'''' (12)

Taking Laplace transform yields:

CpFsQsTsTssT

FV

ii

i +=+

)(')(')(')(' (13)

Or equivalently:

CpFsQ

sssTsT

i

i

++

+=

)(')(')('1

11

(14)

The objective is to maintain T' at T'sp i.e. T''(s)=T''sp(s), therefore Equation 14 yields:

)](')(')[()(' sTsTsCpFsQ isp

i += 1 (15)

where = V/Fi is the retention time of the liquid in the tank. Equation (15) is the design equation for the dynamic feed forward controller.

For load changes, the steady state and dynamic controllers will be equivalent but dynamic feed-forward will be better for set-point changes as shown in Fig 12b.

time t = 0

TDynamic F.F.

Static F.F.

Response to setpoint step changeResponse to load step

changestatic = dynamic F.F.

(a) (b) Figure 12: Response to load response and set point change using feed-forward control



2.2 Design of Feed-forward Controllers The example before can be generalized for the design of general static and

dynamic feed forward controllers. Consider the block diagram of the process shown in Figure 13, it is easy to see that:

( ) )()()()()()()()()()()()( sdsGsGsGsGsGsysGsGsGsGsy mcpdspspcp ff += (16) Equation (16) determines the form of the feed-forward control and also the two transfer functions for the design of the control mechanism:

Gc

GPy

ysp +_

+

+

d

Gd

Gf

Gm

Process

Final controlelement

Measuring device

Feedforward controlmechanism

Gsp

Figure 13: General block diagram for feed-forward control mechanism For Load suppression, the coefficient in d(s) in equation (16) should be zero. The design equation is therefore

)()()()()(

sGsGsGsGsG

mp

dc

f

= (17)

Similarly, for set point change, the design equation, setting the coefficient of ysp in equation (16) to zero is:

)()()(

sGsGsG

d

msp =

(18)

Figure 14 shows the feed forward control configuration with the control mechanisms. These design equations illustrate some of the basic characteristics of feed forward control.

From Eqs (17,18), it is clear that feed forward controllers can not be conventional PID controller. Instead they should be viewed as special-purpose computing machines.



The design equations (17,18) illustrate that feed forward control depends heavily on the good knowledge of process elements Gp, Gd. Poor knowledge of any of these processes deteriorates the performance of feedforward control and prevent the achievement of perfect control.

GPy

ysp +_

+

+

d

Gd

Gf

Gm

Process

Final controlelement

Measuring device

Feedforward controlmechanism

d

msp G

GG =

mp

dc GGG

GGf

=

Figure 14: block diagram for feed-forward control mechanism 2.2.1 Design of steady state feedforwad elements

To illustrate the design procedure for the stirred tank heater, we will assume that Gm(s) = Gf(s) = 1. From Equation (14) we can identify the process Gp(s) and Gd(s):

11

1

1

+=

+=

sG

sCpFsG dip ;)(

At the steady state only the static elements of the process transfer functions of Gp(s) and Gd(s) are retained; i.e. Gp = 1/Fi Cp Kp; Gd =1 Kd. The design transfer functions (Equations 17 & 18) are reduced in this case to the simple constants:

dsp

p

dc

KsG

KKsG

1=

=

)(

)(

(19) (20)

2.2.2 Design of dynamic feedforwad elements

If the process model Gp(s) and Gd(s) are known we can proceed with using Equations (17,18). If they are not known, it is possible to use approximations to them and still obtain good results over the steady state feed-forward controller. Assume that Gp(s) and Gd(s) are approximated by first order lags:



11

11

+=

+=

ssG

ssG

d

p

)(

)(

(21)

(22)

That is should be equal to the time constant of the controlled variable in

response to the manipulated variable and should be the time constant of the controlled variable in response to the load. The design equations (Eqs. 17,18) yield:

11

11

11

++

=

+

+==ss

s

ssGsGsG

p

dc )(

)()(

(23)

and

11 +== ssG

sGd

sp )()(

(24)

The transfer function of Gsp(s) is called a lead element while that of Gc(s) is a

lead-lag. (i.e. 1/lead lag).The term s+1 introduces phase lead. It tends to improve the rise time and overshoot of the system response but increase the bandwidth. Phase lag introduced by 1/( s+1) improves the steady state response (stability margin) but it results in longer rise time because of the reduced bandwidth. Lead-lag elements are expected therefore to produce satisfactory performance and compensate each other. Lead-lag elements are the most commonly used elements in dynamic feed forward control. Figure 15 shows the response of lead-lag unit to a unit step.

0 2 4 6 8Time (min)

100.0

0.5

1.0

1.5

2.0

Res

pons

e

= 1 min

= 2.01.51.0

0.75

0.0

Figure 15: Unit step response of lead-lag unit



2.3 Tuning of the lead-lag elements The adjustable parameters (, ) of the lead-lag can be selected following this procedure:

1.With no dynamic compensation (lead and lag time constant sets at equal values), Introduce a load change to observe the direction of the error. If the resulting response is in the direction of the load, the lead time should exceed the lag time, i.e. > . It can be seen from Figure 15. that in this case the compensation must over correct at first since the controlled variable responds faster to the disturbance than to the manipulated variable. If the response is not in the direction of the load then the lag time should be grater >. It can be seen in Fig. 15, that in this case the compensator must delay its action in order to prevent correcting too soon since the controlled variable responds faster to the manipulated variable than to the disturbance.

2.Next measure the time required for the controlled variable to reach its

maximum or its minimum value. Set this time to be the smallest of the two time constants. If the lead time is larger this time should be the lag time and vice versa.

3.Set the greater time constant at twice this value and repeat the load change. If

the error curve is still not equally distributed across the set point one should increase the greater time constant and repeat the load change.

4.Once the error area is equally distributed about the set point both settings

should be increased or decreased with their difference constant until a minimum error amplitude is achieved.

Finally, since feed-forward control is more costly and requires more engineering effort, its use is restricted therefore to applications deemed justifiable. Most feedforwad control systems have been applied to processes that are very sensitive to disturbances and slow to respond. Examples include:

Distillation columns

Boilers

Multiple Effect evaporator Solid dryers

3. Feed-forward Feedback Control

Despite its advantages, feedforward control suffers from the following inherent weaknesses:

It requires the identification of all possible disturbances and their direct measurements something that may not be possible for many processes



Any changes in the parameters of the process can not be compensated by a feedforwad controller since their impact can not be detected.

Feed forward control requires a very good model for the process which is not

possible for many processes.

Feedback control on the other hand is insensitive to all three drawback but has poor performance for a number of systems (multicapacity, dead time), and raises question of closed loop stability. We expect that a combination of the two controller would yield better performance

Figure 16 shows how a feedback control can be added to the feedforwad loop.

The open loop transfer function is:

y(s) = Gp(s)m(s) + Gd(s)d(s) (25) The value of the manipulated variable is given by:

m(s) = Gf(s)c(s) = Gf(s) [c1(s)+c2(s)] = Gf(s)Gc1(s)e1(s)+Gf(s)Gc2e2(s) (26) or

m(s) = Gf(s)Gc1(s)[ysp(s)-Gm1y(s)] + Gf(s)Gc2[Gsp(s)ysp(s)-Gm2(s)] (27) Recasting the expression of m from Eq. 25 yields:

( )

)()()()()(

)()()()()()(

)()()()()()()()()(

)( sdsGsGsGsG

sGsGsGsGsGsy

sGsGsGsGsGsGsGsGsG

symcp

mcpdsp

mcp

spccp

11f

22f

11f

21f

11 +

++

+=

(28)

Note that the stability of the closed loop response is determined by the roots of the characteristic equation:

1+Gp(s)Gf(s)Gc1(s)Gm1(s) = 0

which depends on the transfer function of the feedback loop only and does not depend on the addition of the feedforwad loop. The transfer functions of the feedforwad loop Gc2 and Gsp are given by (Eqs. 17,18).

d

msp

mp

dc

GGG

GGGGG

2

2f2

=

=

(28) (29)

If Gp, Gd, Gf and Gm2 are known only approximately, then:

Gd Gp Gf Gc2 Gm2 0 and Gp Gf Gc2 Gsp 1



In such case the feedforwad does not provide perfect control y ysp ( e1 0) and the feedback is activated to offer the necessary compensation.

Gc1 Gf Gp

Gm1

Gc2

Gsp Gm2

Gd

y(s)

d(s)

m(s)c(s)c1(s)

c2(s)

e2(s)

e1(s)ysp(s)

ysp(s)

Feedbackcontroller

Feedforwardcontroller

Sensor meeasuringdisturbance for feedforward

controller

Sensor meeasuring output forfeedback controller

+

++

++

+ _

_

Figure 16: Generalized block diagram for feed-forward feedback controller

3.1 Feed-forward-feedback Control of a Tank Heater

The example for a tank heater with a feed-forward and PI controller is shown in Figure 17. The design equations for feed forward control alone are: Gc2 = Fi Cp and Gsp = s+1.

)(s

KG cc1

111

+=

CpFGc 12 =++

+

_e

+

_

1+= sGsp Tsp

Ti

Ti, Fi

T, F

Figure 17: Example of heated tank with feed-forward-feedback controller

Assume that the density or heat capacity Cp are not known exactly, then the

feed-forward control alone does not provide perfect control. Figure 18 shows the temperature in the tank after a step change in the inlet temperature. Because of the uncertainty in there is offset in the response. With feedback PI control added to the feed forward loop and for the same step change, the deviation has disappeared.



0time

T

Feedforward control

Feedforward-Feedbackcontrol

Deviation remaining fromfeedforward control only

Figure 18: Temperature response

4. Ratio Control

In some aspects ratio control can be considered as a special type of feed-forward

control where two loads are measured and held in a constant ratio to each other. It is mostly used to control the ratio of flow rates of two streams. Both flow rates are measured but only one can be controlled. The stream whose flow rate is not under control is refereed to as wild stream. Considering Figure 19, there are essentially two configurations for ratio controller:

In configuration 1 we measure both flow rates and take their ratio, This ratio is compared to the desired ratio (set point) and the deviation (error) between the measured and desired ratio constitutes the actuating signal for the ratio-controller

In configuration 2 we measure the flow rate of the wild stream and multiply it

by the desired ratio. The result is the flow rate that the stream B should have and constitutes the set point value which is compared to the measured flow rate of stream B. The deviation constitutes the actuating signal for the controller which adjusts appropriately the flow of B.

Ratio control is used for a variety of applications including:

Keep constant the ratio between the feed flow rate and the steam in the reboiler of a distillation column,

Hold constant the reflux ratio in a distillation column.

Control the ratio of two reactants entering a reactor at a desired value.

Hold the ratio of two blended streams constant in order to maintain the

composition of the blend at the desired value.

Hold the ratio of a purge stream to the recycle stream constant.



Keep the ratio of fuel/air in a burner at its optimum value

Maintain the ratio of the liquid flow rate to vapor flow rate in an absorption

constant.

FT

Divider

FT

GR

FA

ValveB

A

FB

MeasuredRatio

Desired Ratio

Error

+_

Wild stream

Controlable stream

Ratiocontroller

FT

FT GR

FA

ValveB

A

FB

DesiredRatio

Error

+_

Wild stream

Controlable stream

Ratiocontroller

Figure 19: Ratio controller configuration

5. Selective/Override Control

Most process control problems have an equal number of controlled variables and

manipulated variables. If a process has fewer manipulated variables than controlled variables, a strategy is needed for sharing the manipulated variables among the controlled variables. A common strategy is to use selectors to choose the appropriate process variables among a number of available measurements. Signal selectors choose either the lowest, median or the highest control signal from among two or more signals. A control loop containing this type of logic is called selective control. In this section we present examples of the use of this type of control.



5.1 Maintaining Safety of the Equipment

When a process variable exceeds certain given hazardous limits, the equipment is automatically shut down by process interlocks. Shutdowns can be avoided by the use of secondary controller that has a higher priority and overrides the normal control operation, thus keeping the process running at some suboptimal conditions. Examples of these situations include:

Safeguard the operation of variable speed pumps.

Safeguard the operation of high temperature or pressure reactors.

Avoid flooding in distillation columns

Safeguard the operation of furnace. Figure 20 illustrate the concept of selective/override control in a pumping system

for a sand-water slurry. During normal operation the level controller (LC) adjusts the slurry exit flow by changing the pump speed. The slurry velocity in the exit line must be however always kept above a minimum value to prevent the line from sanding up. If the flow rate (and hence the velocity) decreases and approaches a lower limit the flow controller takes over from the level controller and speeds up the pump. The strategy is implemented using a high selector and a reverse acting flow controller with a high gain. The selector compares signals P1 and P2 and chooses the highest one. This type of control is also called override control.

FT

FCHS

LCLT

h

Slurry in

Holding Tank

hm

p2

p1

pqm

qSlurry out

Figure 20: A selective control for sand-water slurry system

5.2 Improving Control Performance

A plug flow reactor where an exothermic reaction is taking place is always prone to the developments of hot spots. For good control, the sensor providing the temperature measurement should be located at the hot spot. As the catalyst in the reactor ages or conditions in the reactor change, the hot spot move along the reactor. It is desired to design control scheme so that the measured variable "moves" with the hot spot. A control strategy that accomplishes this goal is shown in Fig 21. The high



selector selects the transmitter (all transmitters assumed to have the same range) with the highest output and the control is based on this temperature.

TT TC

SP

Reactants

Cooling meduim

Products

TTTTTT

HS

Figure 21: A plug flow reactor

5.3 Optimization of the process

Consider the furnace of Fig 22. where fuel oil is used to provide heat to a number of process units. Each individual unit manipulates the flow of oil required to maintain its controlled variable at set point. A bypass control loop is also provided. A bad or inefficient operation of the process is the one for which the oil temperature is heated above the value that would satisfy the need of the users. In this case most of the valves would not be wide open and large quantity of fuel would be burned to reach the unnecessary high oil temperature.

Fuel spsp

sp

sp

sp

Hot oil

Stack gas

T

T

T

h

Figure 22: Hot oil system



The effective operation that would save energy is the one that would maintain the oil leaving the furnace at a temperature just enough to provide the necessary energy to the users with hardly any flow through the bypass valve. In this case most of the temperature control valves would be open most of the time. To achieve this goal, the selective control strategy, shown in Fig. 22, first selects the most open valve using a high selector .The valve position controller controls the selected valve position at large value i.e. 90 % open by manipulating the set point of the furnace temperature. This saves energy because it will maintain the temperature just hot enough to provide needed heat to the users. 5.4 Protecting against sensor/transmitters failures

Selectors are also used to protect against transmitter failures by selecting a valid transmitter signal among several. Redundant transmitters monitor the process variable and the median selector chooses the right one for control. Redundant sensors are commonly used in a hostile environment of high temperature or corrosive where failures rate are high thus avoiding the shutdown of the process.

6. Inferential Control As mentioned in the introduction, inferential control makes use of a secondary

measurement. Quite often the controlled output of a process unit can not be measured directly and also the disturbance is unmeasured. This is the type of control where feedback and feed forward can not be used. Inferential control is the only solution. Consider the block diagram of the process shown in Fig 23, with one unmeasured controlled output y and one secondary measured output z. The manipulated variable m and the disturbance d affect both outputs. The disturbance is assumed to be unmeasured. The open loop transfer function in the block diagram of Fig. 23 is:

y(s) = Gp1(s) m(s) + Gd1(s) d(s) (31)

z(s) = Gp2(s) m(s) + Gd2(s) d(s) (32) We can solve for d(s) in the second equation to find the following estimate of the unmeasured disturbance

)()()(

)()(

)( smsGsG

szsG

sdd

p

d 2

21 = (33)

Substituting back in equation (31) yields,

)()()()(

)()()()( sz

sGsGsmG

sGsGsGsy

d

dp

d

dp

2

12

2

11 +

=

(34)



GP2

ym

+

++

d

Process

Controlled output(unmeasured)

Manipulatedvariable

Gd1

GP1

Gd2

+

z

Unmeasureddisturbance

Secondarymeasurement

Figure 23 Process with need for inferential control

This equation provides the estimator needed which relates the unmeasured

controlled output to measured variables m(s) and z(s). Figure 24 shows the resulting block diagram for the inferential control. Equation (34) also illustrates the basic characteristics of the inferential control: The accuracy of the control scheme depends on the good estimation. This is turn depends on the good knowledge of the process i.e. Gp1(s), Gp2(s), Gd1(s) and Gd2(s). Generally these process elements are not known perfectly and therefore the inferential control would provide control with varying quality.

Generally inferential control is used when composition is the desired controlled

variable. Temperature in the most common secondary measurement. Examples of these situations include: chemical reactor, distillation columns, driers, absorber, etc.

ysp m

+

+_

Estimator

Set point

+

z

Controller

Estimates of unmeasuredoutput y

Gc Process

y

221

1 pGdGdG

pG =

21

dGdG

Figure 24: Process under inferential control system

Example: Inferential control of a distillation column

Consider a distillation column which separates a mixture of propane-butane in two products. The feed composition is the unmeasured disturbance and the control objective is to maintain the overhead product molar composition 95% propane. The



reflux ratio is the manipulated variable. The feed and overhead composition are unmeasured so there is need for inferential control. The secondary measurement to infer the overhead composition is the temperature at the top tray. The process inputs are the feed composition (disturbance)and reflux ratio (manipulated variable) while the outputs are the overhead propane composition (unmeasured controlled variable) and temperature of top tray (secondary measurement). The transfer functions (Figure 25a) between the process inputs and outputs are given in the block diagram. Following the procedure established before we derive the following input-output relations,

)(.)(.)( smsesd

sesy

ss

13021

17090 2

++

+=

(35)

)()(.)(.

sms

sdsesz

s

1201

16020 20

++

+=

(36)

The resulting block diagram can be shown in Figure 25b.

ym

+

++

d

Process

Overheadcomposition

Manipulatedvariable

+

z

Unmeasureddisturbance

Temperatureof top tray

130

1211 +

=

s

ssepG

.

1201

2 +=

spG

170

2901 +

=

s

ssedG

.160

2202 +

=

s

ssedG

.

(a)

ysp m

+

+_

Estimator

Set point

+

z

Controller

Estimates of unmeasuredoutput y

Gc Process

y

17016054

++

ss.

))(()(..

12017016054

13021

+++

+

sss

s

se

(b) Figure 25: (a) Block diagram of distillation column; (b) corresponding inferential

control system



References Marlin, T., Process Control: Designing Processes and Control Systems for Dynamic Performance, McGraw Hill, New York, 1995. Seborg, D., Edgar, T., and Mellichamp, D., Process Dynamics and Control, Wiley & sons, New York, 1989. Stephanopoulos, G., Chemical Process Control: An Introduction to Theory and Practice, Prentice Hall, 1984. Smith, C. and Corripio, A., Principles and Practice of Automatic Process Control, Wiley & sons, New York, 1997. Shinsky, F., Process Control Systems, McGraw Hill, New York, 1988. Jones, B., Instrumentation, Measurement and Feedback, McGraw Hill, New York, 1977. Wightman, E., Instrumentation in Process Control, Butterworth, 1972. Ogunnaike, B. and Ray, W., Process Dynamics, Modeling and Control, Oxford University Press, UK, 1994. Murrill, P., Application Concept of Process Control, ISA, NC, USA, 1988. Murrill, P., Fundamentals of Process Control Theory, ISA, NC, USA, 1991. Luyben, W.,Process Modeling, Simulation and Control for Chemical Engineers, McGraw Hill, New York, 1990.


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