group t4 - expt c3

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National University of Singapore

Department of Chemical and Biomolecular Engineering

CN3019 Chemical Engineering Process Laboratory III

Experiment C3Feedforward and Cascade Control

Group T4

Ang Yan Shan (Leader) U083592W

Chandni Chellappa (Experimenter) U083655U

Loo Ching Choo (Data Analyst) U084262H

Yew Kian Wei (Data Analyst) U083694R

Khoo Kian Guan (Literature Reviewer) U083698M

Date of Experiment: 2nd

/6thSeptember 2011

Demonstratorssignature:

GRADE:

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Summary

Process control is important in ensuring the smooth functioning of industrial operations.

Choice and design of control system is crucial in order for appropriate corrective actions to

be taken once a deviation sets in. In this experiment, two types of control, i.e. feedforward

control and cascade control, are studied and evaluated based on their ability to maintain the

vessel level at set point value in a miniaturized plant system. Various deviations, e.g. set

point change, primary and secondary disturbances, were introduced to the system and the

corresponding response curves plotted to track level changes and controller action over time.

The performance of the two control systems were assessed based on three criteria, i.e. the

maximum deviation magnitude, time required for re-stabilization and integral of absolute

error value. Based on the data collected, it is concluded that cascade control shows betterperformance in the control of level than the feedforward control for this system. This is due

to the presence of the slave loop in the former case which allows for quick acting response.

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Table of Contents

1. Introduction ........................................................................................................................ 1

2. Theoretical Background ..................................................................................................... 22.1. Terminology and Basic Control Equipment................................................................ 2

2.2. Control Strategies ........................................................................................................ 3

2.2.1. Feedback Control ................................................................................................. 3

2.2.2. Feedforward Control ............................................................................................ 3

2.2.3. Cascade Control ................................................................................................... 4

2.3. Transfer function of control strategy ........................................................................... 5

2.3.1. Transfer function of feedforward-feedback control ............................................. 5

2.3.2. Design of cascade control .................................................................................... 6

2.4. Methods for the Evaluation of System Response........................................................ 7

2.4.1. Characteristics of system response curve ................................................................ 7

2.4.2. Integral error criteria ................................................................................................ 8

3. Experiment........................................................................................................................ 10

3.1. Apparatus List ........................................................................................................... 10

3.2. Experimental Procedures........................................................................................... 10

3.2.1. Feedforward Control .......................................................................................... 10

3.2.2. Cascade Control ................................................................................................. 12

3.3. Safety Analysis .............................................................................................................. 14

4. Results and Calculations ................................................................................................... 15

4.1. Feedforward Control ................................................................................................. 15

4.1.1. Feedforward Control with Feedforward Gain = 0 ............................................. 15

4.1.2. Feedforward Control with Feedforward Gain = 0.2 .......................................... 17





4.1.7. Summary of Parameters Used to Evaluate Control System Performance ......... 22

4.2. Cascade Control ........................................................................................................ 24

4.2.1. Set point Change Perturbation ........................................................................... 24

4.2.2. Disturbance to SystemChange in Inflow Rate ............................................... 27

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4.2.3. Disturbance to SystemChange in Outflow Rate ............................................ 29

5. Discussion and Analysis ................................................................................................... 32

5.1. Feedforward Control ................................................................................................. 32

5.1.1. Block Diagram of Feedforward Control ............................................................ 32

5.1.2. Limitations of Simple Feedback Control ........................................................... 32

5.1.3. Limitations of Cascade Control ......................................................................... 33

5.1.4. Circumstances that feedforward control is recommended ................................. 33

5.1.5. Limitations of Feedforward Controller .............................................................. 34

5.2. Cascade control ......................................................................................................... 35

5.2.1. Block Diagram of Cascade Control ................................................................... 35

5.2.2. Advantages of Cascade control compared with single loop feedback control .. 36

5.2.3. Limitations of Cascade Control ......................................................................... 36

5.2.4. Classification of Feedforward Control as Cascade Control ............................... 37

5.3. Error Analysis ............................................................................................................... 38

6. Conclusion ........................................................................................................................... 39

References ................................................................................................................................ 40

Table of Notation ..................................................................................................................... 40

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Table of Figures

Figure 1. A general block diagram for feedback control loop ................................................................ 3

Figure 2. A general block diagram for Feedforward Control ................................................................. 4

Figure 3. A simplified block diagram of Cascade control ...................................................................... 5Figure 4. A block diagram for a feedforward-feedback control system (Adapted from Process

Dynamics and Control by Seborg et al) .................................................................................................. 6

Figure 5. A block diagram for a cascade control system (Adapted from Process Dynamics and Control

by Seborg et al) ....................................................................................................................................... 7

Figure 6. Basic characteristics of a system performance curve. ............................................................. 8

Figure 7. Picture of CE117 Process Trainer - (Top) Miniaturized plant set up (Bottom) Mimic control

panel. ..................................................................................................................................................... 10

Figure 8. Schematic layout of connections made for feedforward control experiment. ....................... 10

Figure 9. Flowchart for feedforward control experiment. ..................................................................... 11

Figure 10. Schematic layout of connections made for cascade control experiment. ............................ 12Figure 11. Flowchart for cascade control experiment. .......................................................................... 13

Figure 12. Response graph for feedforward control with gain = 0. ...................................................... 15

Figure 13. Response Graph for Feedforward Control with feedforward gain 0 (400s till 1247.9s) .... 16

Figure 14. Response Graph for Feedforward Control with feedforward gain 0.2 ............................... 17

Figure 15. Response Graph for Feedforward Control with feedforward gain 0.2 (400s till 799.2s) ... 17

Figure 16. Response Graph for Feedforward Control with feedforward gain 0.4. .............................. 18




Figure 20. Response Graph for Feedforward Control with feedforward gain 0.8 ............................... 20Figure 21. Response Graph for Feedforward Control with feedforward gain 0.8 (200s till 729.5s) ... 20



Figure 24. Response graph for (a) initial start and (b) level set point changes (From 7V to 8V and

back to 7V). ........................................................................................................................................... 26

Figure 25. Response graph for inflow rate change 10V8V10V ................................................ 27




Figure 29. Response graph for outflow rate change (drain valve fully open1/3 closedfullyopen) ..................................................................................................................................................... 30

Figure 30. Response graph for outflow rate change (drain valve fully open2/3 closedfully

open) ..................................................................................................................................................... 31

Figure 31. A control amplifier connected to proportional valve ........................................................... 37

Table 1. Comparison of the various feed forward gains 0, 0.2, 0.4, 0.6and 0.8 .................................. 22

Table 2. Summary of IAE at respective feedforward gain value .......................................................... 24

Table 3. Output variable (water level) response to setpoint changes .................................................... 26
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1. Introduction

Control in process industries refers to the regulation of various operating parameters in a

process, such as temperature, level, pressure and flow rates. Precise control over these

conditions is important in ensuring that the system is running efficiently and cost-effectively

at its optimum conditions and for product quality assurance. Also equally important, if not

more important application of process control is in ensuring the process is running within the

safety limit and in compliance with environmental regulatory standards. It is therefore

important to choose the types of control system and design the corresponding parameters

carefully with respect to the system in control to fulfill the abovementioned requirements.

There are three main types of control systems commonly used in the industry, i.e. feedback

control, feedforward control and cascade control. They differ in terms of the type of input

measured, i.e. control variable, secondary variable and disturbance respectively, which has

subsequent implications on the speed and quality of control. Each has its own pros and cons,

which will be elaborated in later sections, and discretion has to be exercised in making a

choice for different systems under control.

In this experiment, the scope of investigation is focused on studying feedforward and cascade

control. There are two main objectives in this experiment:- (1) to study the limitation of

feedforward control and (2) to study how cascade control can improve control of level. Using

CE117 Mimic Panel, a simple miniaturized plant system consisting of a vessel, pump and

valves is put under control. The aim of control is to maintain the water level in the vessel

(controlled variable) at a specified set-point value. To achieve the first objective, disturbance

in the form of change in pump voltage was introduced to the system at various feedforward

gain values and the response of water level and controller action was plotted over time. In thesecond part of the experiment, disturbances in the form of outflow rate and inflow rate were

introduced to the system to study the improvement in level control due to the presence of the

slave loop in cascade control.

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2. Theoretical Background

2.1.Terminology and Basic Control Equipment

To understand process control, it is vital for one get familiarized with the basic components

of a control system which are mainly:

a) Sensor: It is a detection device uses to measure variables (such as pressure,

temperature, level etc.) and transmits signals to the comparator.

b) Comparator: When signals are received from the sensor, a comparator compares the

set point and the measured value and transmits the difference of values as an error to

the controller for controllers action.

c)

Controller: It takes corrective action as soon as possible if the controlled variable/measured disturbances deviated from the set point.

d) Actuator: The actuator serves as a final control element. Depending on the controller

output, the control elements can be control valves, cooling rate, energy input and etc.

Another three important terms that for analysing control systems are the following:

e)

Manipulated variables: The process variables that the controller adjusts to keep the

controlled variables at their desired values. These include the input flow rate, fuel

flow rate and etc.

f) Disturbance variables: The variables that disturbed the system which is undesirable.

Disturbance variables may be known or unknown variables. The presence of

disturbances causes the fluctuation of the system response and thus the need for

automatic control system.

g) Controlled variables: The variable that the controller controlled. They are usually

output variables of a process.

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2.2.

Control Strategies

2.2.1. Feedback Control

Feedback is the process of measuring the deviation of controlled variable from the set point

and utilizing the measured information to exert control on the controlled variable itself.

A simplified block diagram as shown in

Figure 1below shows a typical feedback control system. Measured deviation, which is the

difference between output and set point, is shown as E in the figure. The deviation is then

transmitted to controller and the controller responds to deviation by controlling actuator. The

process is corrected and thus output returns to set point eventually.

Figure 1. A general block diagram for feedback control loop

2.2.2. Feedforward Control

Feedforward control, on the other hand, is the process of measuring disturbance and taking

action based on the measured disturbance to ensure the disturbance does not upset the system

response. Output is not measured in this strategy.

A simple block diagram depicting how feedforward control takes action on disturbance isshown in

Set PointController Process

Disturbance

Sensor

Actuator

-

E Output

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Figure 2.Disturbance is directly measured by sensor and the result is transmitted to

feedforward controller. An accurate process model is then used by controller to control

actuator which in effect cancels out or reduces the impact of disturbance on system response.

As disturbance can be effectively removed, perfect control is theoretically possible for

feedforward control.

Figure 2. A general block diagram for Feedforward Control

However, feedforward control is usually used together with feedback control, as a process is

subjected to known and unknown disturbances. Feedforward control serves to enhance the

control performance by eliminating known disturbance while feedback corrects unknown

disturbances.

2.2.3.

Cascade Control

Cascade control consists of two or more nested feedback loops with the secondary loop(s) is

placed within the primary loop. The primary loop is often called the master loop as it controls

the output as well as the set point of the secondary loop. The secondary loop, on the other

hand, is named slave loop. The use of slave loop(s) is to enhance a system performance by

fast correction of unknown disturbances presented in the system. Therefore, slave loop(s)

responds faster than master loop

Disturbance

Sensor

ProcessActuator

Feedforward

Controller

Manipulated

variable

Controlled

Variable

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Figure 3below shows a simplified block diagram of cascade control. As can be seen in the

figure, output from process 1 serves as the controlled variable of slave loop while output from

process 2 serves as the controlled variable of master loop. Note that the deviation of the

master loop is the set point for process 2. Any disturbances introduced into the system will be

quickly corrected by slave controller and hence the output is less disturbed.

Figure 3. A simplified block diagram of Cascade control

2.3.

Transfer function of control strategy

2.3.1. Transfer function of feedforward-feedback control

FromFigure 4below, the transfer function for feedforward-feedback control can be

developed. Firstly, the closed loop transfer function for disturbance change, sDsY

, is derived

as follow:

mpvc

pvftd

GGGG

GGGGG

sD

sY

1 Equation (1)

Since perfect control is desired in feedforward control, i.e. controlled variable remains at set

point regardless of any upsets in the system. Hence, the deviation of output Y(s) is zero for

perfect control. D(s) is not 0 because it presents in the system and therefore the following

conclusion is reached by substituting Y=0 into equation 1:

0 pvftd GGGGG

Disturbance 2Disturbance 1

Master

Controller

Process

2

Set Point 1

OutputSlave

Controller

Process

1

Primary Loop

Secondary Loop

Sensor 2

Sensor 1

Actuator

++-

-+

Set

Point

2

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Rearranging,

pvt

df

GGG

GG Equation (2)

Usually, lead-lag units (Equation (3)). are used to provide reasonable approximations to

ideal feedforward controllers Feedforward gain, Kfand the controllers time constants, 1and

2,are parameters that can be tuned. Note that a feedforward gain of 0 will simply bring the

control system back to simple feedback control.

1

1

2

1

s

s

KG ff

Equation (3)

Figure 4. A block diagram for a feedforward-feedback control system (Adapted from Process

Dynamics and Control by Seborg et al)

2.3.2. Design of cascade control

The closed loop transfer function for disturbance changes are derived based on the block

diagram shown inFigure 5:

12121222

21

2

1

1 mppvccmpvc

dp

GGGGGGGGGG

GG

sD

sY

Equation (4)

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12121222

2221

1

1

1

1

mppvccmpvc

mpvcd

GGGGGGGGGG

GGGGG

sD

sY

Equation (5)

The characteristic equation is therefore:

01 12121222 mppvccmpvc GGGGGGGGGG Equation (6)

If the secondary loop is removed, i.e. Gc2=1 and Gm2=0, the characteristic equation reduces to

simple feedback control.

Figure 5. A block diagram for a cascade control system (Adapted from Process Dynamics

and Control by Seborg et al)

2.4.

Methods for the Evaluation of System Response

There are different types of methods that can be exploited to examine the performance of

system. This involves basic studying of the response curve such as time to reach the steady

state and overshoot of the system response, or using integral error criteria that analyzes the

magnitude of error that is introduced to the system.

2.4.1.

Characteristics of system response curve

Km1 Gc1

MasterController

Gc2

SlaveController

Gv

ControlValve

Gp2 Gp1

Gd2 Gd1

Gm2

Gm1

+-

++

+-

++

Ysp1 1~spY 2

~spY E1 E2

Ym2

Ym1

P Y2 Y1

D2 D1

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A controller performance can be examined by looking at a few obvious criteria from a system

performance curve. These characteristics include time to reach first maximum, overshoot,

decay ratio, rise time and settling time.

First characteristic is the time to reach first maximum which is labeled as tpinFigure 6.The

second characteristic is overshoot, which is the ratio of a and b, as labeled in Figure 6.

Thirdly, decay ratio which shows how fast the fluctuation of the system settles is defined as

the ratio of c and a. These three concepts are prominent for oscillatory response.

Another two important concepts that are used to characterize the performance of the control

system are rise time and settling time, denotes trand tsrespectively in figure below. Rise time

is the time where the system response reaches the set point if the system whereas settling time

is the time required for the response to settle down within a fixed percentage (for e.g. 5% as

shown in the figure below).

Figure 6. Basic characteristics of a system performance curve.

2.4.2. Integral error criteria

To achieve the best tuning of the controller, it can be difficult just to judge based on the

abovementioned characteristics of the response curve. In such case, integral error criteria can

be used to determine the best tuning of the controller. There are a few types of criteria that

can be utilized which include integral of the absolute value of error (IAE), Integral of time

weighted absolute error (ITAE), integral of squared error (ISE) and integral of time weighted

squared error. Their definitions are as follow:

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The four integral error methods described above penalize the error differently. The first

criterion IAE simply integrates the overall error in the system without any penalization of

error. It gives response in between ISE and ITAE, with reasonable intial response and smaller

amplitude oscillation.

In ITAE, however, the error is penalized by a factor of length of time. The time factor ensures

that the error will not persist for a long time in the system. The system settles quicker but

with sluggish initial response which is good to avoid sustain oscillation

On the other hand, ISE penalizes errors that are large, since the errors are squared. In such

case, tuning from ISE ensures small fluctuation of the system but it might result in sustained

low amplitude oscillation.

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3. Experiment

3.1.Apparatus List

1 x CE117 process trainer ()

1 x CRT monitor

Stirrer, fan and heater were not used throughout the whole process of this experiment

Figure 7. Picture of CE117 Process Trainer - (Top) Miniaturized plant set up (Bottom) Mimic

control panel.

3.2.

Experimental Procedures

3.2.1. Feedforward Control

Figure 8. Schematic layout of connections made for feedforward control experiment.

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1. The computer connected to the system was turned on.

2. Folder CE117 was opened and C3 Feedfoward Control.ict was loaded

3.

The connections of the mimic panel were made as shown inFigure 8.All miscellaneous

switches were placed to manual.

4. Pump 2 was set to external, and drain valve was opened while bypass valve closed.

5.

Feedforward gain was left at 0, PID block was set as follows:

Proportional = 5, Integral = 0.2. Derivative = 0

N.B. For the whole experiment, controller has no derivative action.

6. Start the process and allow the system to stabilize for about 5 minutes.

7. A disturbance was introduced by increasing the pump voltage to 10 V. The reaction of

the system was observed as it stabilized

8.

Increase the pump voltage back to 7 V. The system was allowed to stabilize.

9. Repeat step 6 - 8 were repeated for feedfoward gains of 0.2 0.4, 0.6, 0.8 and 1.

Figure 9. Flowchart for feedforward control experiment.

Open the PID controller block. Set proportional gain to 5, integral to 0.2,

leaving derivative at 0

Set level setpoint and pump voltage at 7 V. Start the process and allow itto run till stabilization is reached (typically in about 5 minutes).

Increase pump voltage to 10V. Observe the changes in controller action

and response curve. Wait for system to stabilize again.

Decrease the voltage back to 7 V and observe the response again. Allow

the s stem to settle.

Repeat this process for feedfoward gains of 0, 0.2, 0.4, 0.6, 0.8 and 1.0.

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3.2.2. Cascade Control

Figure 10. Schematic layout of connections made for cascade control experiment.

1. From the same CE117 folder, C3 Cascade Control.ict was loaded and the mimic panel

was readjusted as shown inFigure 10.

2. The proportional valve was set to 10 V (fully open), while the reference level was set at 7

V.

3. The 2 PID blocks were set as follows:

Master Slave

P 20 1

I 1 1

D 0 0

4. The software was started after opening the drain valve fully and switching pump 2 to

External. The system was left to stabilize.To investigate the effect of change in level set point,

5. The level set point was increased by 1 V and the system was allowed to stabilize.

6. The level set point was returned to 7 V and the system was allowed to stabilize.

To investigate the effect of change in inflow rate,

7. The system was started again and allowed to reach steady state at 10 V

8 The valve was changed to 8 V and the system was allowed to stabilize.

9. The valve was changed back to 10 V and the system was allowed to stabilize.

10. Repeat Step 7-9 for 4.0V, 6.V0 and 8.0V step change.

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To investigate the effect of change in outflow rate,

11. The drain valve was 1/3 closed. Allow the system to stabilize.

12. The drain valve was reopened fully and the system was allowed to stabilize again.

13. Repeat Step 1112 for the case when drain valve is 2/3 closed.

Load C3 Cascade Control.ict from folder CE117

Set the proportional valve block to 10 V. Set the reference level to 7V.

Go to the 2 PID blocks. For the master controller set P to 20 and I to

1; for the slave, P=I=1. For both blocks leave D at 0.

Start the process. Allow the system to settle (within a few seconds).

Increase reference level by 1 V and observe the response. Allow

about 30s for system to settle.

Reduce the level back to 7 V and observe the change in response curve.

Adjust the valve settings for 2.0V, 4.0V, 6.0V, 8.0V.Observe

systems response to changes in inflow rate.

Manually adjust the drain valve (1/3 and 2/3 closed). Observe

systems response to changes in outflow rate.

Figure 11. Flowchart for cascade control experiment.

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3.3. Safety Analysis

1) Many electrical connections are involved in this experiment. It is therefore important to

keep the workspace dry especially where the power points are to avoid electric shocks.

Within the design of the experiment, set appropriate flow rates to ensure that the water in the

vessel does not overflow. Open the drain valves in the process vessel to prevent incident

whereby the pump is accidentally switched on without setting the control system in place. In

the event that water spillage did occur, switch off all electric points and inform laboratory

safety officer immediately.

2) Ensure air vent of vessel is opened to prevent pressure build up in system, which could

potentially rupture the vessel.

3) Switch off the heater control which is not required for this experiment, but could

potentially pose thermal hazard if kept running.

4) Ensure that water is circulating in the system while the pump is switched on, otherwise the

pump could overheat and spoil, posing mechanical hazard.

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4. Results and Calculations

4.1.Feedforward Control

In the first part of the experiment, responses of the system to disturbance were investigated inthe feedforward control. Feedforward gains were set to 0, 0.2, 0.4, 0.6, 0.8 and 1.0. For each

feedforward gain, the system was allowed to reach steady state before disturbance was

introduced into the system. The pump voltage, which was the disturbance in this experiment,

was increased from 7V to 10V and back to 7V again. The responses of how the controller

reacts to disturbance and makes corrective action to the actuator signal were observed.

4.1.1. Feedforward Control with Feedforward Gain = 0

Initially, the tank was being filled up to the desired set-point of 7V. As shown in Figure 12,

there was a gradual increase in water level until it overshot which peaked at about 70.3s.

Between 70.3s till 181.5s, the system was approaching the desired set point by decreasing the

water level. At this point, the controller reacted to the correct the action and hence explained

the increase in the controller voltage. At about 181.5s, the system stabilized.

Figure 12. Response graph for feedforward control with gain = 0.

-5

0

5

10

15

20

25

30

35

40

45

0 200 400 600 800 1000 1200 1400V

olt(V)

Time (s)

Setpoint Control Level

Start up - for

system toreach steady

state

Pump voltage

increased

from 7V to

10V

Pump voltage

decreasedfrom 10V to

7V

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Figure 13. Response Graph for Feedforward Control with feedforward gain 0 (400s till

1247.9s)

Pump voltage increased from 7V to 10V at 426s

The increase in pump voltage caused greater flow of water into the vessel and hence

deviation of water level from the set point as shown in Figure 13. The PI feedforward

controller reacted by sending signal to the valve to reduce the inflow of water into the vessel.

The drop in the control voltage was due to the controller action to eliminate the offset.

Pump voltage decreased from 10V to 7V at 804.7s

The decrease in pump voltage, which meant decrease in pump speed, resulted in drop in the

water level. The deviation of water level from the set point causes the PI controller to

increase the valve voltage and hence bring the water level back to the set point level of 7.0V.

As shown inFigure 13,an overshoot in the control voltage from 3.38V to 4.504V explained

the oscillatory mode as the controller tried to bring the water level back to the set point.

0

1

2

3

4

5

6

7

8

400 600 800 1000 1200 1400

Volt(V)

Time (s)


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4.1.2. Feedforward Control with Feedforward Gain = 0.2

Figure 14. Response Graph for Feedforward Control with feedforward gain 0.2

Figure 15. Response Graph for Feedforward Control with feedforward gain 0.2 (400s till

799.2s)

Pump voltage increased from 7V to 10V at 416s


-5

0

5

10

15

20

25

30

35

40

0 200 400 600 800

Volt(V)

Time (s)


Start up - forsystem to reach

steady state

Pump voltage

increasedfrom 7V to

10V

Pump

voltage

decreased

from 10V

to 7V

0

1

2

3

4

56

7

8

400 500 600 700 800

Volt(V)

Time (s)


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Figure 16. Response Graph for Feedforward Control with feedforward gain 0.4.


729.5s)

Pump voltage increased from 7V to 10V at 230.5s


-5

0

5

10

15

20

25

30

35

40

0 200 400 600 800

Volt(V)

Time (s)


Start up -

for systemto reach

steady state

Pump voltage

increased from7V to 10V

Pump voltage

decreased from10V to 7V

0

1

2

34

5

6

7

8

200 300 400 500 600 700 800

Vol

t(V)

Time (s)


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729.5s)



-5

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800

Volt(V)

Time (s)


Start up - for

system to reach

steady state

Pump voltage

increased from7V to 10V

Pump voltage

decreased from10V to 7V

0

1

2

3

4

5

6

7

8

200 300 400 500 600 700 800

Volt(V)

Time (s)


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Figure 21. Response Graph for Feedforward Control with feedforward gain 0.8 (200s till729.5s)



-5

0

5

10

15

20

25

30

35

0 100 200 300 400 500 600 700 800

Volt(V)

Time (s)


Start up - for

system to reach

steady state

Pump voltage

increased

from 7V to10V

Pump voltage

decreased from

10V to 7V

0

1

2

3

4

5

6

7

8

200 300 400 500 600 700 800

Volt(V)

Time (s)


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725.9s)



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4.1.7. Summary of Parameters Used to Evaluate Control System Performance

The control system performance was evaluated based on three criteria, i.e. time taken for

stabilization, maximum deviation from set point and the integral of absolute error (IAE).

Time taken for stabilization is the time required for the system to return to the set point value,

7.0V. It measures how efficient the system reacts and takes corrective action. By analyzing

maximum deviation from set point and the integral of absolute error (IAE), the accuracy of

corrective actions taken can be observed. The parameters used to evaluate the first two

criteria are summarized inTable 1.

Table 1. Comparison of the various feed forward gains 0, 0.2, 0.4, 0.6and 0.8

Feed

forwardgain= 0

Feed

forwardgain= 0.2

Feed

forwardgain= 0.4

Feed

forwardgain= 0.6

Feed

forwardgain= 0.8

Feed

forwardgain=1.0

Pump Voltage Increased from 7V to 10V

Time at which

change took

place (s)426.0 416.0 230.5 291.8 319.8 295.3

Time when

level stabilized

back to

setpoint (s)

488.3 493.0 286.8 347.9 374.7 347.8

Time taken forstabilization (s)

62.3 77.0 56.3 56.1 54.9 52.5

Maximum

deviation of

level from

setpoint (V)

+0.117 +0.031 +0.061 +0.139 -0.246 -0.334

Pump Voltage Decreased from 10V to 7V

Time at which

change took

place (s)

804.7 712.1 484.2 545.5 542.8 513.6

Time whenlevel stabilized

back to

setpoint (s)

863.0 792.4 561.2 616.3 600.3 572.6

Time taken for

stabilization (s)58.3 80.3 77.0 70.8 57.5 59.0

Maximum

deviation of

level from

setpoint (V)

-0.130 -0.032 +0.058 +0.114 +0.218 +0.313

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As observed from Figure 15 (system with feedback gain 0.2) and Figure 17 (system with

feedback gain 0.4), the response obtained was apparently better with less fluctuation in the

water level. The maximum deviation is relatively smaller compared to other systems with

greater feedforward gains value as shown in Table 1.The results suggested that the control

was under compensating for the disturbance.

For systems with feedforward gain 0, 0.2, 0.4, 0.6, water level increased when a step up of

the pump voltage from 7.0V to 10.0V as shown in Table 1. However, for system with

feedforward gains 0.8 and 1.0, it was found that the water level decreased despite the step up

of pump voltage. The observation could be due to an over compensation of increased pump

voltage by the feedforward controller whereby it over reduced the valve voltage for greater

feedforward gains of 0.8 and 1.0. It also showed that feedback control will bring the water

level back to the desired set point level regardless of the extent or source of disturbance.

When the feedback gain increased from 0.2 to 1.0, it was observed that maximum deviation

of level from the setpoint increased. The feedforward controller was changing from under

compensating to overcompensating the disturbance by adding too much of the disturbance

signal to the actuation signal.

It was also observed that the controller for feedforward gain 0 took corrective action onlyafter deviation in water level had taken place. It is because the controller is a feedback

controller which will only take corrective action after the disturbance had been introduced. In

contrast, for systems with feedforward gain of 0.2, 0.4, 0.6, 0.8 and 1.0, the controller took

immediate corrective action when there was step up and step down of pump voltage. This

was evident by the sharp drop in control in Figure 14,Figure 16,Figure 18,Figure 20and

Figure 22.This illustrate that feedforward control reacts more effectively in arresting

disturbance.

Generally, the time taken for system stabilization decreased from system with feedforward

gain 0.2 to 1.0 for both disturbances introduced from step up and step down of pump voltage

as displayed inTable 1.

To calculate integral of the absolute value of the error (IAE), the area of square under the

curve are summed using excel since data point were collected at small time interval of 0.1s,

rendering the approximation to integral of curve a valid estimation. IAE value is the

difference area between the level curve and setpoint curve.

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Table 2. Summary of IAE at respective feedforward gain value

Gain Total Run Time e(t) IAE

0 1247.8 2325.845 232.5845

0.2 799.2 2050.563 205.0563

0.4 725.9 2031.896 203.1896

0.6 725.9 2221.697 222.1697

0.8 725.9 2207.177 220.7177

1.0 725.9 2141.617 214.1617

As shown in

To calculate integral of the absolute value of the error (IAE), the area of square under the

curve are summed using excel since data point were collected at small time interval of 0.1s,

rendering the approximation to integral of curve a valid estimation. IAE value is the

difference area between the level curve and setpoint curve.

Table 2,system with feedforward gain 0.2 has the smallest integral of the absolute value of

the error. Although it took longer time to reach setpoint after disturbances, it has least

deviation from the setpoint overall. As discussed in the previous section that the time taken

for stabilization decreased from feedforward gain 0.2 to 1.0, however, the maximum

deviation from setpoint after disturbances introduced increased. From the analysis, it could be

concluded system with feedback gain 0.2 is the optimum in this experiment.

4.2.Cascade Control

In the second part of the experiment, the system is subjected to 3 types of manipulation, i.e.set point change, disturbance in the form of inflow rate and disturbance on the form of

outflow rate. The master controller adjusts the vessel level and provides the setpoint for the

slave controller which then adjusts the flow of water in the process loop.

4.2.1. Set point Change Perturbation

In the first part of the cascade control experiment, the response of the system to level setpoint

changes was observed.Figure 24 (a) and (b) shows the initial startup response and the

response to level setpoint changes after it achieved steady state respectively. During the

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25

startup, the master controller output (F2-ref) suddenly jumped to a high value because there

was a large error in the system. However, FT2 maintained at the maximum value of about

4.6V because the pump was already operating at its maximum speed. As the water level

approached the setpoint, master controller output gradually decreased, and fell below 4.6V.

Finally, when the system reached steady state (within 99% of the setpoint), FT2 matched the

value of the master controller output at around 2.5V.

After the steady state, when the setpoint was changed from 7V to 8V, the master controller

started to correct the error by giving higher output. Similar but opposite action was observed

when the setpoint was changed back to 7V. However, there was oscillation in the water level

as well as the controller output. This is probably due to inadequate tuning in the controller

parameters. Furthermore, the asymmetric response to step changes in opposite directions also

implies that there is nonlinearity in the system. In addition, fromFigure 24 (b), FT2 seems to

lag behind F2-ref for both setpoint changes. This is because the master controller detected the

deviation from the setpoint and kicked in first. Subsequently, the master controller output was

fed into the slave controller as a new setpoint, therefore its reponse tailed that of master

controller.

(a)

-20

0

20

40

60

80

100

120

140

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70 80 90

Volt(V)

Volt(V)

Time (s)

Setpoint Level FT2 (secondary axis) F2-ref (secondary axis)

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26

(b)

Figure 24. Response graph for (a) initial start and (b) level set point changes (From 7V to 8V

and back to 7V).

The maximum offset, rise time, and settling time for water level were calculated and

tabulated inTable 3.It can be seen that the water level has a larger maximum error when the

setpoint was reduced from 8V to 7V. In addition, although the rise time for the setpoint

change from 8V to 7V is shorter, the settling time is longer. This means that the controller is

more aggressive to negative offset, but it caused oscillation and therefore gave longer settling

time.

Table 3. Output variable (water level) response to setpoint changes

Maximum erro after

rise time (V)

Rise time

(s)

Settling time within 99%

of level setpoint (s)

Setpoint change 7V

to 8V-0.101 10.8 22.6

Setpoint change 8V

to 7V+0.705 6.2 36

-20

-10

0

10

20

30

40

50

0

1

2

3

4

5

6

7

8

9

75 95 115 135 155 175 195 215 235 255 275

Volt(V)

Volt(V)

Time (s)

Setpoint Level FT2 (secondary axis) F2-ref (secondary axis)

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4.2.2. Disturbance to SystemChange in Inflow Rate

In the next part of the experiment, secondary disturbance in the form of inflow rate was

introduced to the system. FromFigure 25,when the proportional valve voltage was changed

from 10V to 8V and from 8V back to 10V, there was no significant change in the water level

This means that the slave controller was able to give additional corrective action to counteract

the secondary disturbance caused by the change in the inflow rate. Together with the master

controller action, the response was fast thus the water level was not affected much. Similarly

inFigure 26,no significant offset was observed when there was a 4V change in the inflow

rate. However, the controller action was larger compared to 2V change in the inflow rate.

Figure 25. Response graph for inflow rate change 10V8V10V


0

0.5

1

1.5

2

2.5

3

6.8

6.85

6.9

6.95

7

7.05

7.1

7.15

7.2

100 200 300 400 500 600

Volt(V)

Volt(V)

Time (s)Setpoint Level 10V to 8V

8V to 10V FT2 (secondary axis) F2-ref (secondary axis)

0

0.5

1

1.5

2

2.5

3

6.8

6.85

6.9

6.95

7

7.05

7.1

7.15

7.2

450 550 650 750 850 950 1050

Volt(

V)

Volt(

V)

Time (s)

Setpoint Level 10V to 6V


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When the inflow rate was changed from 10V to 4V, there was a much larger offset in the

water level as seen inFigure 27.This suggests that the disturbance was too large for the slave

controller to handle, and therefore caused an offset in the water level. Consequently, master

controller countered this offset by increasing its output. However, it was observed that the

water level increased very slowly back to the setpoint. This indicates that the flow rate into

the vessel was limited regardless of the pump speed because the valve was closed

significantly. Furthermore, this level offset also caused the master controller output to

decrease very slowly and was unable to return to its previous steady state value.

Subsequently, when the inflow rate was changed back to 10V, the water level shot up beyond

the setpoint. This is because there was a delay in the controller response caused by the

integral action of the controller, making it unable to change its output fast enough from the

high value, and eventually causing a large volume of water being pumped into the vessel.

This is referred to as reset windup of the integral action. Nevertheless, the water level was

able to return to the setpoint relatively fast after that, and the controller output could go back

to its previous steady state value as well.


0

1

2

3

4

5

6

7

8

9

6.5

6.6

6.7

6.8

6.9

7

7.1

7.2

7.3

7.4

7.5

1000 1100 1200 1300 1400 1500 1600 1700

Volt(V)

Volt(V)

Time (s)



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When the inflow rate was further reduced by changing the proportional valve voltage from

10V to 2V, the flow into the vessel was so small that the level kept dropping despite

increasing controller output, as shown inFigure 28.This is because the pump was already

operating at its maximum speed, however, because the valve opening was too small, the flow

into the vessel was limited. Finally, the level dropped to almost zero, and the controller

output reached a maximum value, because the integral action of the controller was put out of

action to prevent the controller output to increase excessively.


4.2.3. Disturbance to System Change in Outflow Rate

In the last part of the experiment, primary disturbance in the form of outflow rate wasintroduced to the system. This disturbance directly affects the water level and is outside the

direct control of the slave controller. Here, the master controller corrects for the deviation and

provides a new set point value for the slave controller which subsequently corrects the pump

voltage accordingly to restore the water level to that of set point.

FromFigure 29,the water level and controller output did not change significantly when the

drain valve was 1/3 closed. However, when the valve was opened back fully, there was a

notable deviation of water level from the setpoint. Consequently, the master controller output

0

20

40

60

80

100

120

140

160

0

1

2

3

4

5

6

7

8

1550 1600 1650 1700 1750 1800 1850 1900 1950

Volt(V)

Time (s)


FT2 (secondary axis) F2-ref (secondary axis)

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30

also increased in order to pump more water into the vessel to counteract the increased

outflow rate. It is also noted that FT2 lagged behind FT-ref, this is because the slave

controller had to wait for the master controller to detect the error first and then feed the

output into the slave controller.

Figure 29. Response graph for outflow rate change (drain valve fully open1/3 closed

fully open)

FromFigure 30,when the drain valve was 2/3 closed, the water level increased significantly

and there were some oscillations before it finally reached the setpoint. The water level

increased because the outflow rate decreased when the drain valve was closed. This primary

disturbance affected the water level directly, causing it to increase. Subsequently, the mastercontroller responded to this deviation by decreasing its output to deliver less amount of water

into the vessel. However, there was some oscillation in the controller output. This is probably

due to inappropriate tuning of the controllers. Again FT2 lagged behind FT-ref because the

slave controller had to depend on the master controller to detect the error first and then feed

the output into the slave controller. When the drain valve was opened back fully, the water

level dropped suddenly because of the increased outflow rate, causing a large deviation from

the setpoint. Therefore, the master controller gave greater corrective action to pump more

water into the vessel. Although no apparent oscillation was observed, the offset was larger

0

0.5

1

1.5

2

2.5

3

3.5

6.8

6.85

6.9

6.95

7

7.05

7.1

7.15

7.2

50 100 150 200 250 300 350 400 450 500

Volt(V)

Volt(V)

Time (s)

Setpoint Level Fully open to 1/3 closed

1/3 closed to fully open FT2 (secondary axis) F2-ref (secondary axis)

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31

compared to offset obtained when closing the valve. Finally, the water level increased slowly

back to the setpoint.

Figure 30. Response graph for outflow rate change (drain valve fully open2/3 closed

fully open)

From the response graphs for change in inflow and outflow rates, it can be concluded that for

regulatory control, the cascade controller was able to perform well to correct both primary

and secondary disturbances with small magnitude. However, as the disturbance magnitude

increases, the controller was unable to give satisfactory control probably due to the physical

limitation of the actuator and insufficient fine tuning of the controller.

0

1

2

3

4

5

6

7

8

6.5

6.6

6.7

6.8

6.9

7

7.1

7.2

425 525 625 725 825 925

Volt(V)

Volt(V)

Time (s)

Setpoint Level Fully open to 2/3 closed

2/3 closed to fully open FT2 (secondary axis) F2-ref (secondary axis)

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5. Discussion and Analysis

5.1.

Feedforward Control

5.1.1.

Block Diagram of Feedforward Control

Discussion Question 2: In what circumstances would you recommend a feedforward control

system rather than a cascade or a single loop feedback control system? Point out any

limitation of the feedforward control system.

In order to answer to this question, an understanding of limitations of feedback control or

cascade control must be first developed. This is followed by discussing how feedforward

control can help to overcome the stated limitation for achieving a better control. Lastly,

limitations of feedforward control will be discussed as well.

5.1.2.

Limitations of Simple Feedback Control

Simple feedback loop has its own advantage such as it can handle both known and unknown

disturbances, it is easier to implement, it requires less understanding of the process and it

ensures the controlled variable returns to desired set point eventually. Despite the advantages

of feedback control, there are a few intrinsic limitations that restrain the use of feedback

control.

Firstly, feedback controller only reacts when deviation of controlled variables occurred. This

means that the output has already been affected before the feedback controller can take

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action. If this limitation is coupled with large process dead time or large process time

constant, the action from feedback controller is usually not satisfactory which results in

transient behavior in the system.

The second problem of feedback controller is the presence of closed-loop instability. When

an open loop stable process is controlled by feedback control, the transfer function change to

a complex one and yields different poles and zeros. If there happens to have positive poles,

the system will become unstable and therefore inoperable. The controller in this case has to

be carefully designed to prevent instability.

Thirdly, feedback controller is usually more costly to operate. This is because larger control

action has to be taken and this translates to more power consumption which eventually drives

up the operational cost of the plant.

5.1.3. Limitations of Cascade Control

Cascade controller can improve the performance of feedback control, since it applies multiple

feedback controls in the systems, with the slave system(s) having a faster response as

compared to master control loop. However, cascade control also has its own limitation.

First of all, sometimes it is difficult to identify a measurable secondary controlled variable in

the system that has faster response than the primary controlled variable. In such case, cascade

control cannot be implemented.

Secondly, cascade control requires tuning of two controllers to achieve good control. The

process of tuning might be difficult. Also, the introduction of multiple feedback loops

increases the complexity of the characteristic equation, which is shown as the denominator of

equation 4 in theoretical background session. Again, closed loop stability remains to be a

problem.

Thirdly, from economics point of view, feedback control is generally more expensive in

operation as frequent control actions are taken to curb deviation. This applies to cascade

control as well since it uses more sensors, controllers and actuators.

5.1.4. Circumstances that feedforward control is recommended

Since limitations of feedback and cascade control are known, the circumstances where

feedforward control should kick in can be discussed.

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The first circumstance is when perfect control is necessary. Feedforward control measure the

known disturbances of the system and compensate or react to the disturbances before they

can affect the system. Thus, the system essential ensure the output is steady and this is

essentially a perfect control.

On top of that, perfect control has sound performance if the known disturbances have large

impacts on controlled variable. This can be seen in the feedforward experiment above. Pump

voltage, which translates to pump speed, is an important disturbance that affects the level of

the process vessel (controlled variable). Comparison of single feedback loop(Kf=0) and

feedforward control (Kf>0) showed that the level was well maintained in the case of

feedforward control while in feedback control large changes occurred before controller can

react to the deviation, i.e. level increased when step change of pump voltage occurred and

returned to set point sluggishly.

Moreover, feedforward control should be used if the system is large in size or slow in process

and therefore has large time delay and time constant which system response would be in

general slowly corrected if feedback control or cascade control is used.

Lastly, one of the significant advantages that feedforward control is that it does not affect the

system stability. As can be seen in section 2.3.1, inclusion of feedforward control to thefeedback control system does not affect the characteristic equation of the transfer function.

As such, feedforward control implementation is easier for its minimum impact on the system.

5.1.5. Limitations of Feedforward Controller

Having said that feedforward control is a theoretical perfect control system, the system is

usually affects by unknown and immeasurable disturbances which in effect make perfect

control hard to achieve. In addition, physical realizability as shown in the theoretical

background is another factor that restricts the feedforward control performance.

Furthermore, known or measurement disturbances might not account for large deviation of

controlled variable. If unknown or immeasurable disturbances contribute to major deviation

of the controlled variables, feedforward control installation would be less effective as

compared to feedback control and cascade control.

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Finally, an accurate process model is needed for implementation of feedforward control to avoid over compensation or under compensation with

respect to the size of disturbance. The understanding of dynamics of process might be difficult which limits the use of feedforward control.

5.2.Cascade control

5.2.1. Block Diagram of Cascade Control

Electrical signal [V]

Electrical signal, FT2 [V]

Flow sensor-transmitter (Analyzer)

Flow Control Loop

Inner Loop

Level Control Loop

Primary Loop

Level sensor-transmitter (Analyzer)

Process

vessel level

Set point

for slave

controller,

F2-Ref [V]

Pump 2 Proportional valve Flow

Electrical

signal,

Level sp

[V]

Process

vessel level

set-point

Level

sensor-

transmitter

(Analyzer)

(PI)(PI)

Electrical signal, Level [V]

Km1 Gc1

Master

Controller

Gc2

Slave

Controller

GvPr

oces

Control

ValveD

Gp2 Gp1

Gd2 Gd1

Gm2

Gm1

+-

++

+-

++

Ysp11

~

spY 2~

spY E1 E2

Ym2

Ym1

P Y2 Y1

D2 D1

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Discussion Question 2: What is the advantage of cascade control compared with single loop

feedback control? Point out the limitation of cascade control system.

Cascade control is a general improvement of single feedback control system if feedback

control performance is not acceptable and if feedforward control is not able to put into action

for reasons such as disturbances are not measurable. In this case, cascade control exploits a

secondary measurement point which can better and faster reflects the deviation of the system

and takes the corresponding corrections.

5.2.2. Advantages of Cascade control compared with single loop feedback control

Firstly, as slave control always has faster response control compared to the master control,

the performance of control on system response would generally be better. From our

experiment, we can observe that level fluctuation in single feedback loop was larger

compared to cascade control. This can be partly explained by the increase value in master

loop controller gain too. Generally, as pointed by Seborg et al, if the slave controller has

faster response than master controller, the stability of the system will be enhanced and thus

lead to a Kc value and a more robust response.

Others advantages are relatively minor compared to the abovementioned, but they are worth

mentioning. For instance, cascade control is widely accepted in industry and the tuning ofcontroller is similar to single feedback loop which utilizes PID controller. Also, cascade

control is also good for final control element that is nonlinear in nature since it utilizes

deviation of controlled variables.

5.2.3. Limitations of Cascade Control

The major limitations of cascade control have been discussed in Discussion question 2 in

feedforward control and are briefly summarized below.

1. Secondary measurement point, i.e. second controlled variable, might be difficult to

identify;

2.

Tuning of two controllers which is generally more complex to tune;

3. Closed loop instability remains a problem; and

4. Cascade control is more economically expensive than feedback loop.

Discussion Question 3: Look carefully at a single loop feedback control system and explain

why, when the valve is considered, it can be considered as a cascade control?

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5.2.4. Classification of Feedforward Control as Cascade Control

Firstly, in order for a control system to be consider as a cascade control system, the following

criteria are necessary:

1.

They are at least two feedback loops;

2.

One of the feedback loop must be placed inside of the other feedback loop;

3. There are two controllers, two controlled variables and one manipulated variable

A general proportional valve is shown inFigure 31below. It shows that the valve has a

feedback control loop that is built into the valve for controlling the valve stem position. Thus

in this case, the master control loop controls the level (first controlled variable), the

proportional valve controls the valve stem position to control flow.

For feedforward control case, the manipulated variables are both the valve stem position,

therefore in this case the single feedback loop can be considered as a cascade control system.

The speed of action of master loop and slave loop should be about the same for proportional

valve does not improve the loop response as compare to the case where the flow rate was the

slave controller process output.

For cascade control, since the manipulated variable is not the same in this case which the

master loops manipulated variables is pump speed while valve built-in controller control

valve stem position, as such, the system can only be loosely classified as a cascade system.

Figure 31. A control amplifier connected to proportional valve

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5.3. Error Analysis

1. Immeasurable disturbances are not taken into account to the study of the results in this

experiment. For example, bubbling in the water may cause water level readings to be

inaccurate and mistaken to be the system response towards the input disturbances.

2. Assumption of ideal flow within pipes and valve may not be valid and hence

contribute to the inaccuracy of the results.

3. Assumption of steady state was attained after 5 minutes of observation might not be

valid due to presence of unaccounted disturbances in the system. This can be seen

from the oscillatory behavior in the graphs. Therefore, discretion had to be exercised

in determining whether the steady state is reached.

4. For the second part of the cascade control experiment, the degree of opening for the

proportional valve and drain valve was not recorded automatically. Group members

must coordinate accordingly to note down the time when the valves were opened or

closed. Therefore, there might be some inaccuracies between the noted timing and

actual timing.

5. The change in outflow rate was controlled by closing the drain valve manually. As a

result, the disturbance introduced might be different for each person operating the

drain valve due to different degrees and speeds of closing. Therefore, the analysis for

the response to change in outflow rate is only in qualitative terms.

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6. Conclusion

In conclusion, the feedforward and cascade control system was successfully studied by

observing the response curve and the corresponding controller action profile in response toset point changes and disturbances introduced to the system.

In the first part of the experiment, the performance of the feedforward control was evaluated.

The optimum feedforward gain used to maintain the vessel level at set point value was

determined to be 0.2. At this setting, the maximum deviation from set point value and IAE

was the smallest, implying that the best control was achieved out of the other gain values

used in this experiment. It was observed experimentally that feedforward control tends to

under- or over-compensate the disturbances depending on the feedforward gain value used

which is one of the limitations of using feedforward control.

In the second part of the experiment, the cascade control system gave rise to rapid corrective

action thereby improving the control of level. This can be attributed to the presence of

slave controller nested within the master controller loop which action kicks in rapidly

should the disturbance manifests in the secondary variable under the control of secondary

loop. This arrests the disturbance quickly and allows the system to stabilize within a shorter

period of time.

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References

1. Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp. (2004) Process Dynamics and

Control. 2nd Edition, John Wiley & Sons, Inc.2. Chiu, M.S. & Lee, D.Y. (2010). Process Dynamics and Control: CN3121 [Lecture Notes].

Singapore: National University of Singapore, Department of Chemical and Biomolecular

Engineering.

3. Industrial Electronics. (n.d.) Types of Control from a Proportional Control Valve.

Retrieved September 9, 2011 from http://www.industrial-

electronics.com/output_devices_amplifiers_valves_relays_variable-

frequency_drives_stepper_motors_servomotors/Types_Control_Proportional_Control_Va

lve.html.

Table of Notation

Alphabetical List

Symbol Meaning

D Load Disturbance

e(t) Error, i.e. deviation from set point

E ErrorG Transfer function

K Gain

P Controller output signal

U Manipulated variable

Y Controlled variable

Subscript Meaning

c Feedback controller

d Disturbance

f Feedforward controller

m Feedback transmitter

p Process

sp Set point

t Feedforward transmitter

v Valve

1 First

2 Second

Greek Symbol List

Symbol Meaning

Time constant

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