PCM Distillation Column Project Change

PCM Distillation Column Project

Liu, Tongtong (MU-Student) Fan FengTongtong LiuSi Shen

ContentsExecutive Summary.....................................................................................................................................3

System Description......................................................................................................................................4

Module 6 Transient Response Analysis...................................................................................................6

Module 7 Steady State Feedback Control................................................................................................7

Proportional Control............................................................................................................................8

Proportional Control for a Disturbance...............................................................................................8

Proportional–Integral (PI) Control.......................................................................................................9

Proportional-Integral (PI) Control for a Disturbance.........................................................................11

Module 8 Controller Tuning..................................................................................................................12

Module 9 Feedforward Control.............................................................................................................14

Results.......................................................................................................................................................18

Module 6...............................................................................................................................................18

Module 7...............................................................................................................................................24

Proportional Control..........................................................................................................................24

Proportional Control for a Disturbance..............................................................................................27

Proportional Integral Control.............................................................................................................30

Proportional Integral Control for a Disturbance.................................................................................33

Module 8...............................................................................................................................................36

Cohen-Coon Tuning...........................................................................................................................36

Ziegler-Nichols Tuning.....................................................................................................................39

Auto Relay Tuning..............................................................................................................................41

Module 9...............................................................................................................................................44

Feed-forward Controller Only............................................................................................................44

Feedback Controller Only..................................................................................................................48

Feedfoward-feedback Controller.......................................................................................................50

Discussion and Conclusion.........................................................................................................................54

Discussion..............................................................................................................................................54

Conclusions............................................................................................................................................57

Recommendations.................................................................................................................................58

1

Appendix...................................................................................................................................................59

Module 6...............................................................................................................................................59

Module 7...............................................................................................................................................63

For the Proportional Control..............................................................................................................63

The proportional Control for a Disturbance.......................................................................................65

For the Proportional Integral Control.................................................................................................67

For Proportional-Integral (PI) Control for a Disturbance...................................................................68

Module 8...............................................................................................................................................68

Cohen-Coon tuning............................................................................................................................68

The Ziegler-Nichols tuning................................................................................................................72

Closed-Loop Auto Relay Tuning Method..........................................................................................76

Module 9...............................................................................................................................................78

2

Executive SummaryObjective

The CFLS team has conducted a transient response analysis which by using the process

control module simulation software. This process control simulation includes a Column

simulation model from MATLAB. The corresponding transient response data has been collected

which was used to obtain eight first-order-plus-delay transfer function models for two key

outputs (overhead concentration and bottoms composition) corresponding to two manipulated

inputs (vapor flow rate and reflux rate) and two disturbance inputs (feed flow rate and feed

composition). These transfer functions serve as the analysis basis for the following studies of

control method and testing. Based on these, several characteristics of various types of action and

influence on the performance were studied, especially the impact of controller gain and reset

time on offset between output and setpoint at steady state. Also, since the fine tuning is critical

for a well functioned control loop, we used several standard tuning algorithms to determine the

PID controller tuning constants (control gain, time constant and derivate time) instead of through

trial and error process. Finally, to overcome the disadvantage of the feedback control strategy,

which is that the control action is only taken after the controlled variable starts deviating from its

setpoint, a feedforward control strategy was implemented to reduce the effect of disturbances on

process outputs.

3

System Description

The schematic drawing in Figure 1 below represents the dynamic model of the distillation

column system. This system consists of a binary distillation column which separates a mixture of

methanol (MeOH) and ethanol. The distillation column has 27 trays, a reboiler on the bottom

tray, and a total condenser on the overhead stream. A 50%-50% mixture of methanol and ethanol

is fed at the fourteenth tray (counted from the bottom).

Figure 1. Schematic of the distillation column module

The operator interface for the column and the column process monitor of this process can be

found in Figure 2 and Figure 3. The column is modeled with component mass balances and

steady state energy balances which result in coupled nonlinear differential algebraic equations.

The column model has four inputs and four outputs as listed below.

4

Table 1. Column simulation variables

Manipulated Inputs Key Measured Output

Reflux Ratio (R) Overhead Methanol Composition (xD)

Vapor Flow Rate (V) Bottom Flow Rate (xB)

Disturbance Inputs Other Measured Output

Feed Methanol Composition (zF) Bottom Methanol Composition (B)

Feed Flow Rate (F) Overhead Flow Rate (D)

Figure 2. Operator Interface for the Column

5

Figure 3. Column Process Monitor

Module 6 Transient Response Analysis

In this module, transient response data will be collected which will be used to obtain a first-

order-plus-time-delay transfer function model of the distillation column. The required data for

obtaining a first-order-plus-time-delay transfer function model of the column was collected by

conducting the following runs:

1. Changed one of the input variables. For this project, four different cases were conducted:

Increased the value of the Feed Flow Rate by 2% (from 0.025 to 0.0255 m3/s); Decreased the

value of the Feed Methanol Composition by 4% (from 0.5 to 0.48 mol/mol total); Increased the

value of the Vapor Flow Rate by 3% (from 0.033 to 0.03399 mol/s); Increased the value of the

Reflux Ratio by 2% (from 1.75 to 1.785).

2. Record the time at which the input was changed.

6

3. Allowed the column to reach a new steady state.

4. Saved the four outputs to a data file.

5. Returned the input variables to their initial values.

6. Allowed the column to return to its initial steady state.

Module 7 Steady State Feedback Control

In this unit the characteristics of some of the various types of feedback control action and

their influence on the performance of the column will be studied. The two types of controllers

that will be studied in this section are proportional (P) and proportional-integral (PI) controllers.

The SIMULINK flowsheet of the column with control is shown in Figure 4.

Figure 4. SIMULINK Flowsheet of the Column with Control

7

Proportional Control

1. The controller parameters in the Figure 4 were set as the following values:

Table 3. Controller Parameters

Gain of the controller (Kc) 55 mol total

mol MeOH .

Reset time or the integral time constant (τI) 300 seconds

Rate time or the derivate time constant (τD) 0

Integral Action On 0

Derivative Action On 0

2. Changed the set point of the overhead MeOH composition to 0.83mol MeOH

totalmol . Record the

values when the system reaches steady state. Setting the Kc as the following values: 0,

55, 65, 75mol total

mol MeOH for four different run, turn on the overhead loop and run the

simulation. Record the steady state values for each run, respectively.

Proportional Control for a Disturbance

1. When the column back to its initial steady state, changed the overhead MeOH

composition setpoint back to 0.85 mol MeOH

totalmol . The tuning parameters of the controller

were set as the Table 3 mentioned above. The SIMULINK flowsheet of the column with

Proportional Control for a disturbance is shown below.

8

Figure 5. SIMULINK flowsheet of the column with Proportional Control for a Disturbance

2. When the overhead loop switch was opened, changed the feed MeOH composition from

0.5 mol MeOH

totalmol to 0.4 mol MeOHtotalmol . The final steady state values of the overhead MeOH

composition were record.

3. Bring the column to initial steady state, set the gain Kc as 55, 65, 75 mol total

mol MeOH ,

respectively and run the simulation. Step 2 was repeated and the final steady state values

were record for each run.

Proportional–Integral (PI) Control

1. When the column back to its initial steady state, changed controller parameters in Figure

6 as the Table 4 mentioned below:

9

Figure 6. SIMULINK flowsheet of the column with PI Control

Table 4. Controller Parameters

Gain of the controller (Kc) 55 mol total

mol MeOH .

Reset time or the integral time constant (τI) 300 seconds

Rate time or the derivate time constant (τD) 0



2. A step change from 0.85 mol MeOHtotalmol to 0.83

mol MeOHtotalmol was introduced in the overhead

MeOH composition setpoint. When steady state was reached, the final steady state values

of the overhead MeOH composition were record.

10

3. Bring the column to initial steady state, repeated the step 1, 2, and 3 for the following

values of the integral reset time: τI=350, 400, 450 (sec). The final steady state values were

record for each run.

Proportional-Integral (PI) Control for a Disturbance

1. When the column back to its initial steady state, changing the controller settings to the

values mentioned in Table 4 above. The SIMULINK flowsheet of the column with

Proportional-Integral Control for a disturbance is shown below.

11

Figure 7. SIMULINK flowsheet of the column with PI Control for a Disturbance

2. The overhead MeOH composition setpoint of 0.85 mol MeOHtotalmol was kept. When the

overhead loop switch was opened, changed the feed MeOH composition from 0.5

mol MeOHtotalmol to 0.4

mol MeOHtotalmol . The final steady state values of the overhead MeOH

composition were record.

3. Bring the column to initial steady state, repeated the step 1, 2, and 3 for the following

values of the integral reset time: τI=350, 400, 450 (sec). The final steady state values were

record for each run.

12

Module 8 Controller Tuning

The Proportional-Integral-Derivative (PID) controller was used in this module for the

column. A trial and error selection process for PID controller tuning constants required a lengthy

iterative procedure. Three methods: Ziegler Nichols, Cohen-Coon and Relay Tuning rules were

used to test the performance of the controllers in closed-loop for both setpoint and disturbance

changes. The inputs and outputs for the relay tuning method is shown in Figure 8. And the

SIMULINK flowsheet for this module is shown in Figure 9

Figure 8. Inputs and Outputs for the Relay Tuning Method

13

Figure 9. SIMULINK flowsheet for Controller Tuning.

1. The proportional-integral (PI) controller tuning constants calculated from the Cohen-

Coon tuning rules were tuned in the bottom MeOH composition controller. The integral

action was on and the derivative action was off. A new setpoint on the Bottom MeOH

Composition of 0.13 mol MeOH

totalmol was introduced. The decay ratio was calculated when

the system reached the 95% of the new steady state.

2. The system reached the initial steady state by changing the bottom MeOH composition to

its initial value, 0.15mol MeOH

totalmol . The controller parameters were changed to PID settings

which obtained with the Cohen-Coon tuning rules for the bottom MeOH composition. A

new setpoint on the bottom MeOH composition of 0.13 mol MeOHtotalmo l was introduced and

14

the integral action and derivative action were both on. The decay ratio was calculated

when the system reached the 95% of the new steady state.

3. The system reached the initial steady state by changing the bottom MeOH composition to

its initial value, 0.15mol MeOH

totalmol . The controller parameters were changed by using the

proportional gain obtained from the Ziegler-Nichols tuning rules for the bottom MeOH

composition. After turning off the integral action and derivation action, disturbed the

system by changing the feed MeOH composition from 0.5 mol MeOHtotalmol to 0.4

mol MeOHtotalmol .

The maximum derivation was calculated from the setpoint.

4. Assume that φm = 45 degrees and α = 4. The input oscillation amplitude for the

distillation column case study is d = 0.005. The ultimate gain was obtained by using the

relay tuning method. When the steady state was reached, the PID controller parameters

were calculated.

5. When the system was reset to reach the steady state, the controller was set by using the

PID parameters obtained from the relay tuning rules. A new setpoint in the bottom

concentration of 0.13 mol MeOH

totalmol was introduced and the decay ration was obtained

when a new steady state was reached.

Module 9 Feedforward Control

A feedforward controller for the feed MeOH composition disturbance based on the FOTD

models developed in Module 6 was derived in this module. Both setpoint and disturbance

changes were considered by implemented the feedforward controller both alone, and in

combination with a feedback controller. The feedforward control scheme was shown in the

Figure 10 below. And the SIMULINK flowsheet for the feedforward control is shown in Figure

11 below.

15

Figure 10 . Feedfoward Control Scheme

Figure11. SIMULINK flowsheet for the Feedforward Control

16

1. The loop between the overhead MeOH composition and reflux ration with the feed

MeOH composition as the disturbance was considered by running the simulation with the

values of Kp and Ƭp for the disturbances and the plant models that obtained in the

Transient Response Analysis Module. The feed concentration was changed to 0.47

mol MeOHtotalmol after 500 seconds simulation. The changes of the bottom MeOH composition

and the maximum deviation from setpoint were record at the final steady state.

2. When the system was reset to the initial steady state, the loop between the bottom MeOH

composition and the vapor flow rate with the feed flow rate as the disturbance was

considered. The feed flow rate was changed to 0.027 m3/s and the maximum deviation

from setpoint for the bottom MeOH composition and the change of the overhead MeOH

composition were record at the final steady state.

3. Reset the system to initial steady state. The values listed in the following table were

changed repeatedly and the corresponding results at steady state were record. The

maximum derivation from setpoint and the change of the overhead MeOH composition

were determined by the results.

Table 5 . Variables changed in the process

Variable Initial FinalCase A Overhead MeOH

Composition setpoint

0.85 mol MeOH

totalmol 0.86mol MeOH

totalmol

Case B Bottom MeOH Composition

Setpoint

0.15mol MeOH

totalmol 0.14 mol MeOH

totalmol

4. The feedfoward-feedback controller was implemented by entering the Cohen-Coon

Controller tuning constants calculated in the previous module for Proportional-Integral

control of the overhead MeOH composition loop. The quantitatively and qualitatively

like offsets, rise time, etc. were test at final steady state after changing the feed MeOH

composition to 0.35mol MeOH

totalmol .

17

5. After resetting to the initial steady state, the Cohen-Coon tuning constant calculated in

the previous unite for PI control of the bottom MeOH composition loop was entered to

the system. The quantitatively and qualitatively like offsets, rise time, etc. were test at

final steady state after changing the feed MeOH composition to 0.35mol MeOHtotalmol .

18

Results

Module 6 All the data collected in PCM MATLAB Simulink were analyzed in Excel software. The

following 12 graphs provide step changes made in inputs and response of output for step change.

The following 4 tables show the estimated parameters in process transfer functions based on

experimental data and the graphs. The process transfer functions are approximated by first-order-

plus-delay-time model.

Feed flow rate changed from 0.025 to 0.0255 m3/s at 2050 seconds.

Table 6. Key Parameters for FOPDT Model

Parameter Value for xD Value for xB

K(mol/ total mol

m3/sec) 0.1 27.22

τ (sec) 644.77 901.9θ (sec) 140.33 19.12

-2000 -1000 0 1000 2000 3000 4000 5000 6000 70000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

Feed Flow Rate Step Change

Time(sec)

Feed Flow(m^3/sec)

Figure 6.1. Step Change in Feed Flow Rate

19

-2000 -1000 0 1000 2000 3000 4000 5000 6000

-0.007

-0.005

-0.003

-0.001

0.001

0.003

0.005

0.007

Overhead Concentration VS Time

xD' Data

xD' Model

Time(sec)

xD'(mol/ total mol)

Figure 6.2. Bottom MeOH Concentration Response for Feed Flow Rate Step Change

-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000

-0.005

0

0.005

0.01

0.015

Bottom Concentration VS Time

xB' Data

xB' Model

Time(sec)

xB'(mol/total mol)

Figure 6.3. Overhead MeOH Concentration Response for Feed Flow Rate Step Change

Feed concentration changed from 0.5 to 0.48 mol/total mol at 2050 sec.


Parameter Value for xD Value for xB

K(mol/ total molmol/ total mol ) 0.97 1.082

τ (sec) 1257.67 1225.38θ(sec) 193.08 254.65

20

-2100 -1100 -100 900 1900 2900 3900 4900 59000.465

0.47

0.475

0.48

0.485

0.49

0.495

0.5

0.505

Feed Composition Step Change

Time(sec)

zF'(mol/total mol)

Figure 6.4. Step Change in Feed Concentration

-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005


xD' DataxD' Model

Time(sec)

xD'(mol/total mol)

Figure 6.5. Bottom MeOH Concentration Response for Feed Concentration Step Change

21

-2100 -1100 -100 900 1900 2900 3900 4900 5900 6900

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

Bottom Concentration Vs Time

xB' DataxB' Model

Time (sec)

xB'(mol/total mol)

Figure 6.6. Overhead MeOH Concentration Response for Feed Concentration Step Change

Vapor flow rate changed from 0.033 to 0.03399 mol/sec at 2050 second.


Parameter Value for xD Value xB

K(mol/ total mol

mol /sec ) -2.41 -22.13

τ(sec) 1196.74 810.05θ (sec) 984.33 29.78

-2000 -1000 0 1000 2000 3000 4000 5000 6000 70000

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

Vapor Flow Rate Step Change

Time(sec)

V'(mol/sec)

Figure 6.7. Step Change in Vapor Flow Rate

22

-2200 -1200 -200 800 1800 2800 3800 4800 5800 6800

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

Overhead Concentration Vs Time

xD Data

xB' Model

Time(sec)

xD'(mol/total mol)

Figure 6.8. Overhead MeOH Concentration Response for Vapor Flow Rate Step Change

-2200 -1200 -200 800 1800 2800 3800 4800 5800 6800

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

Bottom Concentration Vs Time

xB' Data

xB' Model

Time (sec)

xB'(mol/total mol)

Figure 6.9. Bottom MeOH Concentration Response for Vapor Flow Rate Step Change

Reflux ratio changed from 1.75 to 1.785 at 2100 second.


Parameter Value xD Value xBK 0.132 0.096

τ(sec) 796.81 1123.52

23

θ(sec) 71.33 200.75

-2200 -1200 -200 800 1800 2800 3800 4800 5800 68000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Reflux Ratio VS Time

Time(sec)

R'

Figure 6.10. Step Change in Reflux Ratio

-2200 -1200 -200 800 1800 2800 3800 4800 5800 6800

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012


xD' DataxD' Model

Time(sec)

xD'(mol/total mol)

Figure 6.11. Overhead MeOH Concentration Response for Reflux Ratio Step Change

24

-3000 -2000 -1000 0 1000 2000 3000 4000 5000 6000 7000

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

Bottom Concentration VS Time

xB'DataxB' Model

Time(sec)

xB'(mol/total mol)

Figure 6.12. Bottom MeOH Concentration Response for Reflux Ratio Step Change

Module 7

Proportional Control

First, the P control Servo Response in the Overhead MeOh Composition loop is operating in

the Simulink. A step change in the Overhead Composition is introduced and in order to compare

the effect of controller gain, different values of controller gain is using in the simulation. The

response of input and outputs in different controller gains are shown below.

25

Figure 7.1. Response of proportional-only controller when Kc=0


26



Recording from the MATLAB, the response data are obtained and the new steady state

values are shown in the table below.

27

Table 10. Overhead MeOH Composition- P Control Load Response

(For the step change of the Overhead MeOH Composition from 0.85mol MeOH

mol total to 0.83mol MeOH

mol total )

K c (mol total

mol MeOH) STEADY STATE

VALUESET POINT VALUE OFFSET

0(INITIAL) 0.8505 0.83 0.0205

55 0.8343 0.83 0.0043

65 0.8320 0.83 0.002

75 0.8316 0.83 0.0016

As it can been seen from the result, while the gain is increasing, usually the oscillatory

response will be shorter. And for the steady state, larger the gain is, the closer the steady state

value to the Set point Value.

Proportional Control for a Disturbance

The P control Load Response in the Overhead MeOH Composition loop is operating in the

Simulink. A step change in the Feed Composition is introduced and in order to compare the

effect of controller gain, different values of controller gain is using in the simulation. The

response of input and outputs in different controller gains are shown below.

28

Figure 7.5. Response of proportional-only controller for disturbance step change when Kc=0



29




Table 11. Overhead MeOH Composition- P Control Load Response

(For the step change of the Feed MeOH Composition from 0.5mol MeOH

mol total to 0.4

mol MeOHmol total )

K cmol total

mol MeOHSTEADY

STATE VALUE

SET POINT

VALUEOFFSET

0(INITIAL) 0.7460 0.85 0.104

55 0.8383 0.85 0.0117

65 0.8405 0.85 0.0095

75 0.8416 0.85 0.0084

30

During the observing in the module, the proportional controller response quiet slow to the

step change compared with the PI or PID controllers, which means it take more time for them to

have the system reached the final steady state.

Proportional Integral Control

First, the PI control Servo Response in the Overhead MeOh Composition loop is operating in

the Simulink. A step change in the Overhead Composition is introduced and in order to compare

the effect of integral time constant, different values of integral time constant is using in the

simulation. The response of input and outputs in different integral time constatns are shown

below.

Figure 7.9. Response of proportional-integral controller step change when τ I=300

31



32

Figure 7.12 . Response of proportional-integral controller step change when τ I=450



Table 12. Overhead MeOH Composition- PI Control Servo Response

(For the step change of the Overhead MeOH Composition from 0.85 to 0.83)

τ1(sec) STEADY

STATE VALUE

SET POINT

VALUEOFFSET

300(INITIAL) 0.8310 0.83 0.001

350 0.8298 0.83 0.0002

400 0.8288 0.83 0.0012

450 0.8296 0.83 0.0004

For the Proportional only controller, while the gain is increasing, the steady state value would

be getting closer to the Set point value. However, for the proportional-integral controllers, it does

not make any different for them while changing the time constant for the controllers. And also,

33

the Proportional-integral controllers are less oscillatory and response immediately to the step

response.

Proportional Integral Control for a Disturbance

First, the PI control Load Response in the Overhead MeOH Composition loop is operating in

the Simulink. A step change in the Feed Composition is introduced and in order to compare the

effect of integral time constant, different values of integral time constant is using in the

simulation. The response of input and outputs in different integral time constants are shown

below.

Figure 7.13. Response of PI controller for disturbance step change when τ I=300

34

Figure 7.14. Response of proportional-integral controller for disturbance step change when τ I=350

Figure7.15. Response of proportional-integral controller for disturbance step change when τ I=400

35

Figure 7.16. Response of proportional-integral controller for disturbance step change when τ I=450



Table 13. Overhead MeOH Composition- PI Control Servo Response

(For the step change of the Feed MeOH Composition from 0.5 to 0.4)

τ1(sec) STEADY STATE VALUE

SET POINT VALUE

OFFSET

300(INITIAL) 0.8501 0.85 0.0001350 0.8449 0.85 0.0001400 0.8512 0.85 0.0012450 0.8502 0.85 0.0002

Comparing with the Proportional only controller, in the step response of the feed MeOH

composition, the PI controller does not response very oscillatory and reach the steady state quiet

fast and the final value of the steady state is much closer to the set point value. However, the P

only controllers still have a very oscillatory response to this step change and the steady state

values are less closer to the set point value.

36

Module 8

Cohen-Coon Tuning

From the data obtained in the Module 6: 𝐾=−22.1, 𝜏=810.05, 𝜃= 29.78 ,=0.00099

Table 14. Parameters obtained from Cohen-Coon tuning Method

Proportional-Integral Control K c=−0.0196 τ I=1299.314

Proportional-Integral-Derivative Control K c=−0.03476 τ I=2939.549 τ D=515.5975

0 200 400 600 800 1000 1200 1400 16000

0.020.040.060.08

0.10.120.140.160.18

0.2

Self-Tuning DataxB

Time(sec)

xB(mol/total mol)

Figure 8.1. The Self-Tuning response

From the figure, the Pu is 1000 sec, and calculated Ku is -0.2134.

The response for the Bottom MeOH Composition controller with the PI controller tuning

constant in the Cohen-Coon tuning rules shows below in MATLAB SIMULINK and EXCEL.

Table 15. Key Value for PI ControlKc -0.0196

τI 1299.31

37

0 1000 2000 3000 4000 5000 6000 7000 80000.115

0.12

0.125

0.13

0.135

0.14

0.145

0.15

0.155

Bottom Compositon Response for PI Control

xB

Time (sec)

xB(mol/mol total)

Figure 8.2. Bottom Composition of Column Response for PI Control

Figure 8.3. Response of PI Control with Cohen-Coon Tuning from Simulation

Decay Ratio of PI control for bottom composition is 0.562.

The response for the Bottom MeOH Composition controller with the PID controller

tuning constant in the Cohen-Coon tuning rules shows below:

38

Table 16. Key Value for PID Control

Kc -0.0348

τI 2939.55

τD 515.60

0 1000 2000 3000 4000 5000 6000 7000 80000.12

0.125

0.13

0.135

0.14

0.145

0.15

Bottom Concentration Response For PID Controller

xB

Time(sec)

xB(mol/mol total)

Figure 8.4. Bottom Composition of Column Response for PID Control

Figure 8.5. Response of PID Control with Cohen-Coon Tuning from Simulation

39

Decay Ratio of PID control for bottom composition is 0.424.

Ziegler-Nichols Tuning

The response for the Bottom MeOH Composition controller with the PID controller tuning

constant in the Closed-loop Ziegler-Nichols shows below:

Table 17. Key Value for P-only Control

Kc -0.1067

τI -

τD -

0 1000 2000 3000 4000 5000 60000.1

0.11

0.12

0.13

0.14

0.15

0.16

Z-N Tuning P-Only Control

xBsetpoint

Time(sec)

xB(mol/total mol)

Figure 8.6. Bottom Composition of Column Response for Ziegler-Nichols Tuning P-only Control

40

Figure8.7. Response of PID Control with Ziegler-Nichols Tuning P-only Control from Simulation

The maximum deviation for the setpoint is 0.0327


Kc -0.1067

τI 250

τD 62.5

0 500 1000 1500 2000 2500 3000 3500 40000.125

0.13

0.135

0.14

0.145

0.15

0.155

Z-N Tuning PID Control

xB

setpoint

Time(sec)

xB (mol/total mol)

Figure 8.8. Bottom Composition of Column Response for Ziegler-Nichols Tuning PID Control

41

Figure 8.9. Response of PID Control with Ziegler-Nichols Tuning from Simulation

The maximum deviation for the setpoint is 0.0153.

Auto Relay Tuning The response for the Bottom MeOH Composition controller with the PID controller

tuning constant in the Closed-loop Auto relay tuning Method shows below:


Kc -0.1509

τI 450.159

τD 112.54

42

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.115

0.12

0.125

0.13

0.135

0.14

0.145

0.15

Auto Relay Tuning PID Control

xb

setpoint

time(sec)

xB(mol/total mol)

Figure 8.10. The Bottom composition response for PID controller

Figure 8.11. Response of PID Control with Auto Relay Tuning from Simulation

Decay Ratio for ART PID control is 0.32.

In order to find out the best tuning method in this module, the graph of output response in

Cohen-Coon tuning and Auto Relay tuning are shown below.

43

The result in the Cohen-coon tuning parameters is shown below:

0 1000 2000 3000 4000 5000 6000 7000 80000.12

0.125

0.13

0.135

0.14

0.145

0.15

Bottom Concentration Response For PID Controller

xB

Time(sec)

xB(mol/mol total)

Figure 8.12. The Bottom composition response for PID controller

Compared with the Auto relay tuning Method shown below:

0 100 200 300 400 500 600 7000.12

0.125

0.13

0.135

0.14

0.145

0.15

Auto Relay Tuning PID Control

xB

Time (sec)

xB(mol/total mol)

Figure 8.13. the Bottom composition response for PID controller

Seeing from the graph, It is easy to find out that it take more time for the controller

using the parameters from Cohen-Coon tuning methods to get the set point value and reach the

steady state. Therefore, the Auto Relay tuning method is preferred.

44

Module 9

Feed-forward Controller Only

The responses of Overhead MeOH Composition with feed MeOH composition as

disturbance and bottom MeOH Composition with no disturbance to the step change in feed

concentration are shown below.

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.846

0.848

0.85

0.852

0.854

0.856

0.858

Overhead MeOH Composition Response

xD

time(sec)

xD(mol/total mol)

Figure 9.1 Overhead Composition responses

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.1360.138

0.140.1420.1440.1460.148

0.150.1520.1540.156

Bottom MeOH Composition Response

xB

Time(sec)

xB(mol/total mol)

Figure 9.2 Bottom Composition Responses

45

Based on the figure 9.1, the maximum deviation is 0.005589.

0 500 1000 1500 2000 2500 3000 3500 4000 45000.8495

0.85

0.8505

0.851

0.8515

0.852

0.8525

0.853

Overhead Composition Response

xD

time(sec)

xD(mol/total mol)

Figure.9.3 Overhead Composition Response to the Step Change in Disturbance (Feed Flow Rate)

According to the graph above, the feed-forward only controller do not reject the disturbance

step change.

The responses of the bottom MeOH composition with the feed flow rate as disturbance and

overhead composition with no disturbance to the step change in feed flow rate are shown below.

The maximum deviation of bottom composition is 0.002707.

0 500 1000 1500 2000 2500 3000 3500 4000 45000.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Bottom Composition Response

xB

time(sec)

xB(mol/total mol)

Figure.9.4 Bottom Composition Response to the Step Change of Disturbance (Feed Flow Rate)

46

The responses of setpoint change for overhead composition and bottom composition are

shown below. The overhead composition setpoint changed from 0.85 to 0.86 (molMeOH/total

mol). The maximum deviation from the set point for the Overhead MeOH Composition is

0.000926.

10000 10500 11000 11500 12000 12500 13000 13500 140000.8502

0.8504

0.8506

0.8508

0.851

0.8512

0.8514

0.8516

0.8518


xD

Time(sec)

xD(mol/total mol)

Figure.9.5 Overhead Composition Response to the step change of Overhead composition set point

10000 10500 11000 11500 12000 12500 13000 13500 140000.146

0.148

0.15

0.152

0.154

0.156

0.158

0.16


xB

Time(sec)

xB(mol/total mol)

Figure.9.6 Bottom Composition response to the step change of Overhead composition set point

47

The responses of setpoint change for overhead composition and bottom composition are

shown below. The bottom composition setpoint changed from 0.15 to 0.14 (molMeOH/total

mol). The maximum deviation of bottom composition from the set point is 0.010658.

13500 14000 14500 15000 15500 160000.8507

0.850705

0.85071

0.850715

0.85072

0.850725

0.85073

0.850735


xD

Time(sec)

xD(mol/total mol)

Figure.9.7 Overhead Composition Response to the step change of Bottom Composition set point

13500 14000 14500 15000 15500 160000.150570.150580.15059

0.15060.150610.150620.150630.150640.150650.150660.15067


xB

Time(sec)

xB(mol/total mol)

Figure.9.8 Bottom Composition Response to the step change of Bottom Composition set point

48

Feedback Controller Only The responses of overhead composition with feed MeOH composition as disturbance and

bottom composition with no disturbance to the step change in feed composition are shown

below. The feed composition changed from 0.5 to 0.35 (mol MeOH/total mol). The offset of

bottom composition is 0.057, and the one of overhead composition is 0.0315.

16600 17600 18600 19600 20600 216000.79

0.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88


xD

Time(sec)

xD(mol/total mol)

Figure.9.9 Overhead Composition Response to the step change of Feed Composition

16600171001760018100186001910019600201002060021100216000.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

Bottom Composition response

xB

Time(sec)

xB(mol/total mol)

Figure.9.10 Bottom Composition Response to the step change of Feed Composition

49

Figure 9.11. The Response of Feed-forward only and Feedback only Controller from Simulation

Figure 9.12 . The Response of Feed-forward only and Feedback only Controller from Simulation (continued)

50

Feedfoward-feedback Controller

The responses of overhead composition with feed MeOH composition as disturbance and

bottom composition with feed flow rate as disturbance to the step change in feed MeOH

composition are listed below. The feed MeOH composition changed from 0.5 to 0.35 (mol

MeOH/total mol). The parameters of PI controller are from previous Conhen-Coon tuning

section.

The following two figures provide the response of bottom composition and overhead

composition when feedback PI controller turns on only for overhead MeOH composition loop.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17


xB

Time(sec)

xB(mol/total mol)

Figure 9.13 Bottom Composition Responses for the Step Change of Feed Composition

51

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88


xD

Time(sec)

xD(mol/total mol)

Figure 9.14 Overhead Composition Responses for the Step Change of Feed Composition

Figure 9.15. The Response of Feedforward-Feedback Controller from Simulation

52

The following two figures provide the response of bottom composition and overhead

composition when feedback PI controller turns on for two loops.

15000 20000 25000 30000 350000.8

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88


xD

Time(sec)

xD(mol/total mol)

Figure 9.16 Overhead Composition Responses for Step Change of Feed Composition

15000 20000 25000 30000 350000.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18


xB

Time(sec)

xB(mol/total mol)

Figure 9.17 Bottom Composition Responses for Step Change of Feed Composition

53

Figure 9.18. The Response of Feedforward-Feedback Controller from Simulation (continued)

54

Discussion and Conclusion

DiscussionSeveral observations are drawn from the experimental data from Module 6:

1. First, the time delay is not too large. The actual output response of an input change of the

manipulated variables should be much greater than these observed delay times, especially

for distillation columns since it will take even a whole day to respond a change in reality.

Also, it turns out that it’s difficult to determine the exact delay time of the system which

might draw some errors in the analysis.

2. Secondly, by looking at the controller gain, the bottom compositions will be influenced

more and have much larger “jump” changes in the response than the overhead

compositions when changing the four input variables. The reason behind this is due to the

number of trays of the column. By researching, a greater number of trays allows a greater

change in the “closer” output. In this case, it means that the larger change in stream

composition will likely occur in the bottoms.

3. Moreover, the bottoms stream reaches equilibrium quicker than the distillate. It is based

on the time constant and also the reflux drum on the top of column. The reflux drum will

result in a slower response since its characteristic will put lower pressure on the response.

Also, the time constant for the reflux drum is comparably smaller than the time constant

in the transfer functions. This means that when there is a change in reflux ratio, it allows

the distillate stream to respond much more quickly than bottoms.

Several observations are drawn from Module 7 simulation analysis,

1. It can be obviously noticed that there is an offset for each proportional control strategy of

different controller gain value. It is since there is no way for proportional control to

eliminate offset. Also, by increasing the controller gain, the value of offset is decreasing.

Moreover, as controller gain increases, the system comes more oscillatory and usually the

oscillatory response will be shorter. By looking at the plots on the process monitor, one

can find that the bottom composition is also influenced by the manipulation variable,

55

reflux ratio. During the observing in the module, the proportional controller response

quiet slow to the step change compared with the PI or PID controllers, which means it

take more time for them to have the system reached the final steady state.

2. Secondly, for the proportional only controller with increasing gain, the steady state value

would be getting closer to the Set point value. However, for the proportional-integral

controllers, it does not make any different for them while changing the time constant for

the controllers. And also, the proportional-integral controllers are less oscillatory and

response immediately to the step response.

3. Comparing with the proportional only controller, in the step response of the feed MeOH

composition, the PI controller does not response very oscillatory and reach the steady

state quiet fast and the final value of the steady state is much closer to the set point value.

However, the proportional only controllers still have a very oscillatory response to this

step change and the steady state values are less close to the set point value.

Several observations are drawn from Module 8 tuning analysis,

1. From the controller parameters obtained with Ziegler-Nichols and Cohen-Coon tuning

rules, one can easily find that the controller gain obtained by Ziegler-Nichols tuning is

negative and, on the other side, the one obtained by Cohen-Coon tuning rule is positive.

For time constant, the time constant in Cohen-Coon is much smaller than the one in

Ziegler-Nichols tuning which means that Cohen-Coon gives more conservative control

tuning method.

2. After adding on the derivative control, PID control strategy turns out to have shorter

period and less attentive oscillation compared to PI controller. This means that PID has

much more stable and desired control advantage.

3. From the figure of proportional control only Ziegler-Nichols tuning method, we can see a

really noisy and, obviously, there is a non-self-regulating process going on.

4. Compared to the performance of Ziegler-Nichols tuning proportional-only control, the

Ziegler-Nichols PID control has better performance. From the figure, we can see that the

process under Ziegler-Nichols PID control is well-tuned and well-self-regulating process,

with a reasonable downtrend and well-fitting to meet the desired controlled output value.

56

Overall, the results show that the Ziegler-Nichols PID control is a good choice for fine

tuning.

5. Compared with the parameters obtained for Ziegler-Nichols tuning, the value of

controller gain from the closed-loop auto relay tuning method is really similar. However,

the time constant is much different since both τ I and τ D in the Ziegler-Nichols method is

much smaller that the parameters obtained from the closed-loop auto relay tuning

method. From this point, we can conclude that the Ziegler-Nichols usually result in a

more aggressive response control method.

6. By comparing the responses diagrams from closed-loop auto relay tuning method and

Cohen-Coon tuning method, one can easily find that it takes much more time for the

system to go stable and reach set point by closed-loop auto relay tuning method.

Therefore, Cohen-Coon tuning method is preferred here, which because it gives a more

stable response and reach steady state more quickly.

Several observations are drawn from Module 9 analysis,

1. By looking at the control response diagram, we can see that by using feedforward control

loop, the overhead composition increased after just a short period time of time delay and

then reached back to the set point smoothly. It shows that the feedforward loop does have

a positive effect on control.

2. By only using feedforward control, the overhead composition response is completely not

regulating, which shows that the controller totally does not reject the disturbance step

change.

3. By only using feedback control, there is a big offset for overhead composition. The value

gradually decreased at the beginning and then reached steady state with an offset. Besides

that, the bottom composition also encountered an offset at its steady state. It shows that

the feedback-only control is not the desired control strategy.

4. Based on all the results and observations above, we can conclude that a

feedback/feedforward control strategy with Cohen-Coon tuning method results in a

perfect control system. The reason behind this is because for either feedback-only or

feedforward-only control, they have specific well-functional control range. And by

combining them together, the control system will meet the desired response. Moreover,

57

as we discussed before, the Cohen-Coon tuning method is the desired method for this

case which can improve the control parameter to achieve the best control decision.

ConclusionsThroughout the whole process control module simulation, the dynamic process reactions

curves were generated by the control monitor, which were related to four different types of input

changes. Based on the curves and data, the time delay, process gain and time constant were

calculated for those two key outputs, which are overhead concentration and bottoms

composition. According to the basis of first-order-time-delay transfer function, eight transfer

functions were determined as shown below.

Table 20. Final results

Feed Flow RateFeed Methanol

CompositionVapor Flow Rate Reflux Ratio

Bottom

Transfer

Function

xB(s)F (s)

= 27.215e−19 s

901.980 s+1xB(s)zF (s )

= 1.082 e−254 s

1225.38 s+1xB(s)v (s)

=−22.134 e−30 s

810.051 s+1xB(s)R(s)

= 0.126 e−200s

1123.517 s+1

Distillate

Transfer

Function

xD (s)F (s)

= 0.1 e−140 s

644.777 s+1xD (s)zF (s )

= 0.971 e−193s

1257.666 s+1xD (s)v (s)

= −2.41 e−984 s

1196.742 s+1xD (s)R(s)

= 0.132e−71 s

796.814 s+1

After that, by changing the value of control gain and time constant, we observed

characteristic relations about how the value of these affect control response, which deepens the

insight of different types of controllers. Also, by introducing different tuning methods, a series of

tuning test was conducted and a variety of comparison between different tuning methods was

carried out. Finally, by testing feedforward-only control, feedback-only control and

feedback/feedforward control, we have observed different responses under various situation and

determined the best choice for control strategy.

58

Recommendations

1. The 6000 s modeling time might not be long enough to make sure the system has reached

its new steady state. One can wait for a longer time and might get more stable results.

2. From the simulation scattered graph, it shows that the range of change of overhead

composition is really small which makes people hard to read the number and might result

in certain error for data analysis. We recommend having a larger scale of input change

which will make the response larger also.

3. A first-order-plus-dead-time assumption is made for the whole module analysis, which

might turns out that it is not the best model to use. In order to test what type of model we

need to use, we recommend that different types of modeling methods should be chosen

for comparison and then one can get the best fitting modeling function.

Appendix

59

Module 6 In this module, the main propose is to get the first-order-plus-time-delay transfer functions

for the different situation. The method to manage this is discussed below.

Insert the data from the MATLAB PCM into the EXCEL and then plot the diagram of

Overhead MeOH Composition Response and the Bottom MeOH Composition Response for four

different kinds of step changes, which are Feed Flow Rate, Feed MeOH Composition, Vapor

Flow Rate, and Reflux Ratio. Then fit first-order-plus-time-delay transfer function models to

each of the responses.

To obtain the original process data, the MATLAB PCM is used for simulation for process.

As an example the Overhead Concentration Response of Feed composition step change is

discussed below.

First, open the clock display to make sure that the clock display is completely visible. Then

start the simulation in the original state, then pause the simulation, record the time.

Figure.A-1 Display the time in the simulink

Double-click on the Feed Composition box, change the value from 0.5 to 0.48.

60

Figure.A-2 Change the value of Feed Composition

Then start simulation again, allow the column to reach a new steady state. Then return the

Feed composition to the value 0.5, allow the column to return to its initial steady state. Then

original data of the simulation is recorded in the MATLAB workspace windows. Save it for the

further use.

All first-order-plus-time-delay transfer function formula is shown below,

G (s )= k e−θs

τs+1 (A-1)

In this equation, there are 3 parameters, process gain K , time delay θ, and time constant τ , which are needed to be determined. The equation which describing relation between output y(t)

and time t could be established by inserting U (s )= Ms in the above equation:

y (t )=KM [1−e−(t−θ)

τ ] (A-2)

where M is the magnitude of input change.

61

First, insert the initial guess value of three parameters into the equation the get the initial ydata. Using the EXCEL SOLVER to adjust the value of these parameters in order to minimize the sum of deviations between data and model which is shown below.

∑(deviation)=∑ ( ydata− ymodel)2 (A-3)

As the example, data are collecting from the simulation, in which decreasing the value of the

Feed MeOH Composition from 0.5to 0.48 mol

mol total , then collecting the response of overhead

concentration and bottom concentration, inserting the data from the simulation into the excel to form the graph of concentration response to time, which is shown below.

2000 3000 4000 5000 6000 7000 80000.82

0.825

0.83

0.835

0.84

0.845

0.85

0.855

0.86

Overhead Concentration Response to Feed Composition step change

xD

Time(sec)

xD

Figure.A-3 Original data of Overhead Concentration Response to the step change of Feed Composition

It can been easily seen from the graph that these is no clear changing point, which means that

a very small time delay would be suited to the process. Assuming that the time delay would be

θ=1 s.As for the process gain, the assumption is shown below,

K=y ss ( t )− y (0)

M (A-3)

62

where y(t) stands for the new steady state value and y(0) refers to the steady state value before

the step change. Both of these values could be obtained from the data collecting in the MATLAB

simulation. For the case shown above, the probable guess of the process gain would be

K=y ss ( t )− y (0)

M=0.8524036−0.852023

0.0255−0.025=0.766

As it has been mentioned in the manual, the process get to the new steady state in

approximately 6000 simulation seconds. Then using the approximately method for time constant

τ , which is shown below,

τ=T ss

5=6000

5=1200 s

Using these data in the EXCEL SOLVER, in which changing parameters to minimize the

value of ∑ (deviation) in equation A-3. Then using the parameters for process gain, time constant

and time delay from the EXCEL SOLVER to graph the ymodel. Then compare the graph of ydata to

it to find out whether the transfer function would be fit to the original model.

The first-order-plus time delay transfer function for the example case and the graph

mentioned above are shown below.

xD(s)zF

=0.97 e−193 s

1257 s+1

63

1900 2900 3900 4900 5900 6900 79000.82

0.825

0.83

0.835

0.84

0.845

0.85

0.855

0.86

Curve fitting of Step Change for Overhead Composition

xDCalculated xD

Time(sec)

Ove

rhea

d Co

mpo

sition

(mol

/mol

tota

l)

Figure.A-4 Comparison between original data and calculated model data for Feed Composition step change in Overhead Composition.

It shows that our calculated values of the gain K, time constant τ , and time delayθ works for

this simulation module. Based on the figures, the calculated key outputs match the original data

from the experiment. The rest of situations are based on the same method shown above.

Module 7

In this module, the parameters of both P and P controllers for column are given. By

changing the controller gain and reset time to examine the effect on the dynamic closed-loop

response. And finally, characterize the impact of various controller tuning parameters on the

offset observed at steady state. Start the column with control, start MATLAB PCM Simulink on

the section Distillation Column Menu.

For the Proportional Control

For here the Overhead MeOH Composition- P Control Servo Response is shown as an example.

Double-click on the Overhead Composition Controller block and set the controller parameters to

the following values:

Table A-1 Given parameters for the Overhead Composition Controller

Gain of the controller(K c ¿¿ 55 mol totalmol MeOH

64

Reset time or the integral time constant (τ I ) 300 sec

Rate time or the derivative time constant (τD) 0



Figure A-5. Changing the Parameters of the Overhead Composition Controller

Then double-click on the overhead loop to change it to the value On and switch the bottom loop

switch to Off . Change the Setpoint of the Overhead MeOH Composition to 0.83 mol MeOHmol total .

When a steady state is reached, record the final values in the Tables. Then Change the controller

settings of gain to the different values which are list in the given form, turn on the overhead loop,

and repeat the exercise in the former steps. All the final values in steady state are recorded in the

previous section.(Result and Conclusion)

65

Figure A-6. Change the Overhead Composition Set Point

Table A-2 Overhead MeOH Composition- P Control Servo Response

K cmol total

mol MeOHSteady State

Value Set Point Value

0(Initial)556575

The proportional Control for a Disturbance

The Overhead MeOH Composition Setpoint should be returned to 0.85 mol MeOHmol total . Change the

Feed MeOH Composition from 0.5 mol MeOHmol total

¿0.4 mol MeOHmol total .

66

Figure A-7. Changing the Feed Composition.

The Simulink diagram should be like below.

Figure A-8. The block Diagram for the Proportional Control for a disturbance

67

Then Change the controller settings of gain to the different values which are list in the given

form, turn on the overhead loop, and repeat the exercise in the former steps. All the final values

in steady state are recorded in the previous section.(Result and Conclusion)

For the Proportional Integral Control

The controller parameters are given in the form. Insert these parameters in the controller block,

which is shown in the former step.

Table A-3. Given parameters for the PID controllers

Gain of the controller(K c ¿¿ 55 mol totalmol MeOH

Reset time or the integral time constant (τ I ) 300 secRate time or the derivative time constant (τD) 0

Integral Action On 1Derivative Action On 0

Then introduce a step change in the Set Point from 0.85 mol MeOHmol total to 0.83 mol MeOH

mol total , the

Simulink bloack diagram should be like below.

Figure A-9. The block diagram for PI controller in a step change

68

Then Change the controller settings of integral time constant to the different values which are list

in the given form, turn on the overhead loop, and repeat the exercise in the former steps. All the

final values in steady state are recorded in the previous section.(Result and Conclusion)

Table A-4 Overhead MeOH Composition- PI Control Servo Response

τ I (sec) Steady State Value Set Point Value

300(Initial)

350

400

450

For Proportional-Integral (PI) Control for a Disturbance

The Overhead MeOH Composition Setpoint should be returned to 0.85 mol MeOHmol total . Change the

Feed MeOH Composition from 0.5 mol MeOHmol total

¿0.4 mol MeOHmol total .

Then Change the controller settings of integral time constant to the different values which are list

in the given form, turn on the overhead loop, and repeat the exercise in the former steps. All the

final values in steady state are recorded in the previous section (Result and Conclusion).

Module 8

In this module, design PID controllers for the Vapor Flow Rate−Bottom MeOH Composition

loop using: (i) Ziegler Nichols (ii) Cohen-Coon, and (iii) Relay Tuning Rules. Test the

performance of the controllers in the closed-loop for both Set point and disturbance changes.

Cohen-Coon tuning

Calculate the controller parameters using the Cohen-Coon tuning method for the first-order-plus-

time delay transfer functions obtained in the Transient Response Module (Module 6) for the

following variable pairings. The data are shown below.

69

Vapor Flow Rate →Bottom MeOH Composition

Table A-5 The parameters for tuning calculationK=−22.134 τ=810.0511 θ=2079.784 M=0.00099

From the identified effective gain, time constant and dead time (K P , τP , θ ¿ ,which are listed

above, one can tune the controller using the rules which are summarized below:

Table A-6. The Method of Calculating the Cohen-Coon tuning Parameters

Controller Type Controller Gain Reset Time Derivative Time Constant

P K c=( 1K P

)(τP

θ)(1+ θ

3 τ P)

PI K c=( 1K P

)(τP

θ)( 9

10+ θ

12 τ P) τ I=θ (

30+3θτP

9+20 θτ p

)

PID K c=( 1K P

)(τP

θ)( 4

3+ θ

4 τ P) τ I=θ (

32+ 6 θτP

13+ 8 θτ p

) τ D=θ 411+2θ /τP

Using the Formula given in the form above:

Vapor Flow Rate →Bottom MeOH Composition

Table A-7. Parameters obtained from Cohen-Coon tuning MethodProportional-Integral Control K c=−0.0196 τ I=1299.314

Proportional-Integral-Derivative Control K c=−0.03476 τ I=2939.549 τ D=515.5975

Then open the MATLAB Simulink PCM, Distillation Column, tune the Bottom MeOH

Composition controller with the proportional-integral (PI) controller tuning constant calculated

from the Cohen-Coon tuning rules. Make sure that the integral action is ON and the derivative

action is OFF. Introduce a new setpoint on the Bottom MeOH Composition of 0.13mol MeOH

mol total

The Simulink block diagram should be like below.

70

Figure A-10 The block diagram for PI Controller using the Cohen-Coon tuning

Then the response of the outputs would be shown in the MATLAB simulation windows, which

would be shown in the result section.

Decay Ratio is calculated by following equation. Where, a presents height of the first peak, and c

stands for height of the second peak.

Decay Ratio for PI control= ca=0.13−0.1290

0.13−0.1282=0.562

After the PI controller tuning, reset the Bottom MeOH Composition to its initial value, 0.15

mol MeOHmol total . Once the system has returned to steady state, change the controller parameters to the

PID settings in the former calculations. Make sure that both integral action and derivative action

are both ON. Introduce a new Set Point on the Bottom MeoH Composition of 0.13mol MeOH

mol total

71


Figure A-11 The block diagram for PID Controller using the Cohen-Coon tuning



Decay Ratio is calculated by following equation. Where, a present’s height of the first peak,

and c stands for height of the second peak.

Decay Ratio for PID control= ca=0.13−0.1290

0.13−0.1276=0.424

72

The Ziegler-Nichols tuning

The Ziegler-Nichols tuning method requires two key process parameters: the ultimate period (

Pu ¿, and the ultimate gain (Ku ¿. These parameters can be obtained from the Simulink closed-

loop test with a proportional controller. The Simulink Block diagram is shown below.

Figure A-12 Tuning for finding the ultimate gain and ultimate period

With Self-Tuning Loop Switch ON, the following response could be obtained.

Figure A-13 Self tuning graph for obtaining the ultimate gain and ultimate period

73

Then specify the amplitude of the input oscillation (Vapor Flow Rate diagram on the left hand

side) d . From the observed magnitude (a) and period (Pu ¿ of the oscillation in the output

(Bottoms Composiiton diagram on the right hand side), the ultimate gain could be obtained,

K u=4dπa

where:

a=¿ Amplitude of output oscillations

d=¿ Amplitude of input oscillations

The data collecting from the graph is shown below.

0 200 400 600 800 1000 1200 1400 16000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Self-Tuning Data

time(sec)

Botto

m C

ompo

sition

Figure A-14. The Self-Tuning response

Calculating the parameter by using the given equations:

Pu=1000 s , 2d=0.01

a=0.120272−0.1786382

=−0.029183

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K cu=4 dπa

= 2 ×0.01−0.029183 × π

=−0.2134

The rules of controller using Ziegler-Nichols tuning are summarized below.

Table A-8. Rules to calculate Ziegler-Nichols tuning parametersController Type Controller Gain Reset Time Derivative Time Constant

P K c=0.5 Ku

PI K c=0.45 Ku τ I=Pu

1.2

PID K c=0.6 K u τ I=Pu

2τ D=

Pu

8

Using the rules and calculated data to calculate controller parameters

,Table A-9. Parameters obtained from Ziegler-Nichols tuning MethodProportional Control K c=−0.107

Proportional-Integral Control K c=−0.096 τ I=833.333

Proportional-Integral-Derivative

ControlK c=−0.128 τ I=250 τ D=62.5

Return the system to steady state by resetting the Bottom MeOH Composition to its initial

value, 0.15mol MeOHmol total . Once the system has returned to steady state, change the controller

parameters to the PI settings in the former calculations. Make sure that both integral action and

derivative action are both ON. Introduce a new Set Point on the Feed MeOH Composition of

0.50mol MeOHmol total to 0.40

mol MeOHmol total

The Simulink Block Diagram is shown below.

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Figure A-15 The block diagram for PI Controller using the Ziegler-Nichols tuning



The maximum deviation for the setpoint is calculated by following equation.

maximum deviati on=0.15−0.1173=0.0327

After the PI controller tuning, reset the Bottom MeOH Composition to its initial value, 0.15

mol MeOHmol total . Once the system has returned to steady state, change the controller parameters to the

PID settings in the former calculations. Make sure that both integral action and derivative action

are both ON. Introduce a new Set Point on the Feed MeOH Composition of 0.50mol MeOH

mol total to

0.40mol MeOHmol total


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Figure A-16. The block diagram for PID Controller using the Ziegler-Nichols tuning



The maximum deviation for the setpoint is calculated by following equation.

maximum deviation=0.15−0.1347=0.0153

Closed-Loop Auto Relay Tuning Method

Using the parameters in the former section,

Pu=1000 s , 2d=0.01

K cu=4 dπa

= 2 ×0.01−0.029183 × π

=−0.2134

And the other parameters are given below,

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Table A-10 The given parameter for Auto Relay tuning methodα=4 ∅m=45

Given the parameters above, a PID controller can be calculated as follow:

K c=Ku cos (∅m )

ωc=2πPu

τ D=tan∅m √ 4

α+tan∅m

2ω

τ I=α τ D

For the case in this section, the tuning parameters could be obtained as follows.

K c=Ku cos (∅m )=−0.2134 × cos (45 )=−0.1509

ωc=2 πPu

= 2π1000

=6.28× 10−3

τ D=tan∅m√ 4

α+tan∅m

2ω= tan 45√1+tan 45

2 ×6.28 × 10−3 =112.540

τ I=α τ D=4 × 112.540=450.159

Then start the system by setting the controller with the PID parameters obtained above. Introduce

a new Set Point in the bottom concentration 0.13 mol MeOH

mol total .The Simulink block diagram

should like figure below.

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Figure A-17 The Simulink diagram for the Auto Relay tuning Method

Then the response of the outputs would be shown in the MATLAB simulation windows,

which would be shown in the result section.

Decay Ratio is calculated by following equation. Where, a present’s height of the first peak,

and c stands for height of the second peak.

Decay Ratio for PID control= ca=0.13−0.1291

0.13−0.1272=0.32

Module 9

In this module, a feedforward controller for Feed MeOH Composition (column) disturbance

based upon the FOTD models developed in Module 6 is obtained. Then implement the

feedforward controller both alone, and in combination with a feedback controller.

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As discussed in previous modules, the manipulated variables for the column are Vapor Flow

Rate and Reflux Ratio. The load variables for the Column are the Feed Flow Rate and Feed

MeOH Composition.

The models are obtained from the first-order-plus-time-delay system models in Module 6.Given

the following process model and disturbance model.

G p (s )=K p

τ p s+1e−θ p s,Gd ( s)=

Kd

τd s+1e−θd s

Then a perfect feedforward controller is given by

Gf =−Gd

G p=

−K d

K p×

τ p s+1τ d s+1

e (θ p−θd ) s

For the case here, the approximate dynamic compensation is used based on a lead-lag element as

shown below,

Gf =−Gd

Gp=

−Kd

K p×

τ p s+1τ d s+1

Consider the loop between the Overhead MeOH Composition and reflux Ratio with the Feed

MeOH Composition as the disturbance. Then the process model and disturbance model would be

G p (s )= 0.132796 s+1

e−71 sGd (s )= 0.971257 s+1

e−193 s

Consider the loop between the Bottom MeOH Composition and the Vapor Flow Rate with the

Feed Flow Rate as the disturbance. Then the process model and disturbance model would be

Gp (s )= −22.13810 s+1

e−29 s Gd (s )= 27901 s+1

e−19 s

Open the MATLAB PCM Simulink in the distillation column, feedforward section. First, insert

the values of Overhead MeOh Composition models into the controller and start the simulation.

Make sure that the value of feedback controller is Off since the feedback controller is not

supposed to use in this section. The Simulink block diagram is shown below.

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Figure A-18. The block diagram process with feedforward controllerThe Feedforward Controller parameters should be inserted in the simulation like below.

Figure A-19 The Feedforward controller parameters in Overhead Composition Loop.

81

Start the simulation and after 500 simulation seconds, change the feed concentration to 0.47

mol MeOHmol total . After the new steady state is reached, change the Feed MeoH Composition back to

0.5mol MeOH

mol total . Let the system return to its initial steady state. Then insert the value of the

feedforward controller in Bottom Composition section to enable the feedforward controller for

feed flow rate. Then change the Feed flow rate to 0.02 m3

sec7.After it reach a new steady state,

change the value of Feed Flow Rate back to 0.025 m3

sec, let the system return to its initial steady

state.

Figure A-20. The Feedforward controller parameters in Bottom Composition Loop.

Without changing any parameters in the process, a change in the overhead MeOH

Composition Set Point (0.85mol MeOH

mol total to 0.86mol MeOHmol total ) and Bottom MeOH Composition

Set Point ( 0.15mol MeOH

mol total to 0.14mol MeOHmol total ) is introduced separately into the process after the

initial steady state reached.

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All the response graphs and data are given in the result section.

In case of a large magnitude disturbance, a feedback controller could be used in conjunction with

the feedforward to get improved disturbance rejection. Enable the feedback controller in the

feedforward controller block. Change the feed MeOH composition to 0.35mol MeOHmol total . After it

reach a new steady state, return the Feed MeOh Composition to the normal steady value.

Then response of the above in the MATLAB windows is shown below

Figure A-21.The input and output response for the above process.

83

Then implement the Feedforward-feedback controller by entering the Cohen-Coon Controller

tuning constant calculated in the previous module for Proportional-Integral Control of the

Overhead MeOH Composition Loop, which is given below.

Table A-11.Cohen-Coon tuning parameters for the controller in Overhead Composition LoopParameter Overhead MeOH Composition Loop

K c 3.1268τ I 1305.359

Figure A-12.The Feedback controller parameters in Overhead Composition Loop.

Make sure the switch value is set to ON. Again, change the Feed MeOH Composition to 0.35

mol MeOHmol total .

The inputs and outputs responses figure would be like below.

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Figure A-13. The response of Cohen-Coon tuning Feedforward-feedback Controller.

Then return the feed MeOH Composition to its initial steady state value 0.50mol MeOH

mol total and

let the system return to steady state.

While the feedback controller is still operating on the Overhead MeOh Composition Loop,

entering the Cohen-Coon tuning constant calculated in the previous unit for PI Control of the

Bottom MeOh Composition Loop, which is given below.

Table A-12.Cohen-Coon tuning parameters for the controller in Overhead Composition LoopParameter Bottom MeOH Composition Loop

K c -0.0196τ I 1299.314

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Figure A-14. The Feedback controller parameters in Bottom Composition Loop.

Make sure the switch value is set to ON. Again, change the Feed MeOH Composition to 0.35

mol MeOHmol total . The inputs and outputs responses figure would be like below.

Figure A-15. The response of Cohen-Coon tuning Feedforward-feedback Controller.

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PCM Distillation Column Project Change