CHEMICAL ENGINEERING LABORATORY CHE 4137W/4139W

Liquid Level Control

Objective: In this experiment, you are to gain hands-on experience with the real world instrumentation and software used in industrial process control installations. You will be exploring the liquid level control of two gravity-drained tanks in series. Your specific objective is to investigate and mathematically describe the dynamic behavior of this process. You are then to design, implement and test the level control performance of a P-Only, PI and PID controller. Major Topics Covered: Level control, P, PI, PID control, fluid mechanics. Theory: Information on the theory behind this experiment can be found in the references. Specifically, the website www.controlguru.com is on on-line textbook developed by Prof. Doug Cooper, professor of chemical engineering at UConn, and provides an excellent overview of the topics needed for this experiment. Safety Precautions:

1. Water and electrical equipment are used in close proximity in this experiment. Use care to not spill water on the equipment or the surrounding floor area.

Available Variables: Controller tuning parameters (gain, integral time constant, derivative time constant), control type (proportional-only, proportional-integral, proportional-integral-derivative). Procedure: See the Control System Operational Checklist. Analysis: Your analysis must include:

1. A demonstration of the linear or non-linear behavior of the process, together with a justification for you choice.

2. The objectives and design criteria for controller performance.

3. A study of the capabilities of the different controller algorithms, and the impact of different tuning values on the performance of the system.

4. A demonstration of the controller’s ability to reject different disturbances to the system.

5. Comparison of at least one set of software-computed parameters to hand-calculated

parameters obtained via graphical analysis for determination of the FOPDT (first-order

plus dead time) model parameters,

6. An empirical model that shows the influence of controller settings on one important response of the system such as settling time, overshoot, or offset for either the PI or the PID controller.

7. A judgment as to the ‘best’ controller and support your decision with quantitative data.

Report: Describe the design of your experiments and the results obtained, including an error analysis. Provide thoughtful and quantitative discussion of results, explain trends using physical principles and relate your experimental observations to predicted results (optimal feed plate location, minimum number of trays, minimum reflux ratio, etc). Express any discrepancies between observed and predicted results in terms of quantified experimental uncertainties or limitations of the correlations or computational software used. Pro Tips:

1. Make sure you are entering the correct tuning parameters in the Loop-Pro software, including the appropriate units.

2. Do not run the pump at output levels that could cause the tanks to overflow. If there is imminent danger of overflow, immediately shut down the pump.

References:

1. Seborg, D., Edgar, T., Mellichamp, D., Doyle, F., Process Dynamics and Control, 3rd Edition, Wiley, New Jersey, 2010.

2. www.controlguru.com by Cooper

Start Up Procedure: See Appendix 1 for Start Up Procedure. Be sure to read the ENTIRE Start Up Procedure before beginning the experiment. PRECAUTIONS:

1. Keep an eye on the liquid level in the top tank. If it reads over 20 inches, put the loop in manual (open) and reduce the pump output (LI102), or turn off the pump. 2. Use common sense: Do NOT touch electronic equipment with wet hands! 3. When switching between P-Only, PI and PID control, be sure that appropriate tuning values are entered. Note that P-Only and PI should have a Derivative term of zero.

Experimental:

1. Data will be collected using Loop-Pro OPC Inbox and analyzed using the Loop-Pro Design Tools module. A description of using these software tools can be found in Appendix 2 at the end of this procedure. 2. Be sure to copy and save appropriate plots to Word or PowerPoint as you work through your investigation so you have them for future reference and reports. You will need a USB thumb drive to retrieve these files after you are done. 3. As the plot layout cannot be changed outside of the program, be sure they look presentable before copying and saving them. As an alternative, save raw data files and create your plots later using Microsoft Excel. 4. Before you begin following the analysis below, be sure to spend a few minutes examining the working set-up and record any observations you may find.

Non-linearity check:

• With the control loop open (Manual), put the controller output at 20% and let the process reach steady state. Step the output from 20% to 30% and after the response is complete, from 30% to 40%. Repeat from 40% to 50%. Record the average in-line rotameter reading for each setting of controller output. • Warning: Do not set the controller output below 20% or above 55%! • Compare the process gain, time constant, and dead time for each step response. The values can be obtained using Loop-Pro Design Tools to analyze data collected with OPC Inbox. Keep in mind any differences observed between the controller output setting and the actual manipulated variable.

Preliminary Controller Tuning:

• With the controller in Manual (open loop), perform a doublet bump test around a design level of operation (DLO) of 10” in the lower tank. Determine a first order plus dead time (FOPDT) model that describes the dynamic process data. Be sure to print or export any plots required to defend your model. • Use your FOPDT model to calculate preliminary tuning parameter values for a P- only, PI, and PID controller. Record moderately aggressive tuning values based on the IMC (internal model control) design method as a base case for your study.

Set Point Tracking Performance: P-Only, PI and PID Controllers:

• Put the controller in Auto (closed loop). Using the tuning values calculated from step 2b, test a P-only, a PI and then a PID controller for tracking set-point steps of several inches in each direction away from the DLO. • Repeat the set-point-tracking experiment by changing (as appropriate) the controller gain, reset time and derivative time according to an efficient experimental design. Comment on performance using quantitative terms such as offset, peak overshoot, decay ratio and settling time. Include plots to defend your observations and conclusions.

• Compare and contrast the three control algorithms for set point tracking. Disturbance Rejection Performance: PI Controller:

• Put the controller in Auto (closed loop). Using your base case PI tuning values calculated from step 2b, put the set point at 10” and allow it to reach steady state. • Using the pitcher or a large cup, collect a measure of water from the storage tank and add it to the lower (level controlled) tank. Establish the controller’s performance in correcting for this unmeasured disturbance. • Compare disturbance rejection performance for a moderate and aggressive PI controller. Establish and defend your choice as to the “best” tuning. • Using the pitcher or a large cup, collect the same measure of water from the storage tank and add it to the upper tank while using your “best” PI controller tuning values. Comment on whether the disturbance rejection performance is the same for the two disturbances and provide an explanation based on the physics of the process.

Shut Down Procedure: See Appendix 1 for Shut Down Procedure.

Appendix 1: Operating Procedure Start Up: 1. Turn on the computer and log-in as administrator. There is no password. 2. Prime the pump (LY 102)

a. Person A will hold the hose feeding the pump so the blue foot valve is above the level of the rotameter (the foot valve is a blue plastic check valve on the end of the suction line to LY102). They will unscrew the two blue pieces that make up the valve (the filter cone and the foot valve itself).

b. Person B will use the Iced Tea Pitcher to gather water from the storage tank

below the apparatus. They will use it to prime the pump through the hose Person A is holding. Pour in enough water to see a level in the rotameter.

c. Re-fasten the filter cone to the foot valve, re-fasten the foot valve to the hose,

and return it to the storage tank.

d. The Allen-Bradley PanelView Plus 600 monitor, located on the wall next to the tanks, will act as your controller for the experiment. It is a touch screen and should respond as such. Go to LIC102. Set the system to Manual (Loop Open) and enter an output of 50%. (Press ENTER OUT, type in “50,” and then press the arrow in the bottom right hand corner.)

e. Turn on the power strip the pump is plugged into.

Shut Down: (must be completed before lab notebook can be signed) 1. Turn off the power strip the pump is plugged into. 2. Drain the pump.

a. Unscrew the filter cone and the blue foot valve and lower the hose into the empty Iced Tea Pitcher placed on the floor. Wait until water stops flowing into the pitcher and air can be seen in the tubing below the pump.

3. Close the software programs on the computer

a. When prompted to save changes for KEPServerEx, select “NO”

4. Log off the computer.

Appendix 2: Using Loop-Pro

Launching: 1. Open Loop-Pro. 2. Click the “OPC Inbox” button. This will launch OPC Inbox 3. File -> Load OPC Workspace... 4. Select “Workspace1.ows” [Path: C:\Program Files\Control Station\OPC Inbox]

• Note: another window titled “KEPServerEX” will pop up after opening “Workspace1.ows”. DO NOT CLOSE IT, or no data will be collected. Minimize it instead.

Collecting Data: 1. After Launching, click the “Create Trend” button at the top, but be sure to wait for

values to appear on the Data View window. If you go too fast the system will not yet have fully launched.

2. Click “Next” 3. Specify the axis.

a. While Axis 1 is the heading check off: Ch_test_1.PLC_offline.Global.L102_PV

Ch_test_1.PLC_offline.Global.L102_SP Click on the heading and find Axis 2, then check: Ch_test_1.PLC_offline.Global.L102_CVOut ...and click “Next”

4. Label Axis: Y-Axis 1 Label: Process Variable Y-Axis 2 Label: Controller Output ...and click “Finish”. You can now collect experimental data. Storing Data: 1. Once a trial is finished, click the pause button ( | | ) 2. Click the “Save Data” button next to the pause button (the small floppy disk) 3. Click and drag around the data you wish to store (the Good Stuff) 4. Save the file in the CHEG 4137W, Fall 2010 folder on the desktop. You may want to

make a separate folder for your group within this folder. Deriving Tuning Parameters: 1. From Loop-Pro’s main screen, select “Design Tools” (Note that the OPC Inbox taking

the data is a separate program, and that Loop-Pro is separate) 2. Open your saved data file containing your experimental data 3. Click and drag the “Manipulated Variable” column heading so it is above the column

describing the controller output. Make sure the “Process Variable” is over the column that describes tank level (the other column is set point, which is identical to PV when the loop is open). Click “OK”.

4. Select “Select Model”. Make sure the first FOPDT model is selected 5. Select “Start Fitting”. The gain, time constant, and dead time can be found above and

below the chart. Click “Accept and Close”. 6. Click “Set Controller Spans”. Change the PVmax to 20. (Why 20? Hint: What is the PV

measuring?) 7. Set the aggressiveness of the tuning values. 8. The IMC Tuning correlations can now be copied from this screen. 9. When exiting the programs DO NOT save changes to KEPserverEX when prompted.

A P P E N D I X T

Controller Tuning

Contents

x� To present the theory of controller tuning.

x� To present and apply current tuning correlations.

T.1 THEORY

PID controllers are used in the majority of feedback controllers because of their ef-fectiveness and simplicity. All of these controllers focus on controlling a single output vari-able using a single manipulated input variable. Hence they are known as SISO control sys-tems. The ideal form of the three-model controller is

� � � � »¼

º«¬

ª�� ³ dt

dedteteKtm D

Ic 1 W

W (1)

1

2 Controller Tuning Appendix T

where Kc is the controller gain, WI is the integral time constant and WD is the derivative time constant. . The transfer function of the ideal PID controller is given by

)(11)( sess

Ksm DI

c ¸̧¹

·¨̈©

§�� W

W (2)

Because of the difficulty with differentiating noisy signals, actual industrial controller im-plementations vary from the ideal form given above. Usually a noise filter is added to the derivative term as follows:

)()1(

111)( sesss

Ksm DI

c ¸̧¹

·¨̈©

§�

�� WDW

This adds another parameter D, called the filter time constant. Increasing D has the effect of smoothing the signal at the expense of slowing down the response time of the derivative action. Usually D is chosen to be about 0.1WD. Derivative action is not used if the signal is very noisy or if the delay time is small. Controller tuning refers to determining the appropriate values of DWW andK DIc ,, in the controller transfer function. There is no 'right' way to do this. The primary reason is the uncertainty associated with the model. Rarely do we have an accurate model of the process and even so, the process is subject to variability and so the process characteristics will change due to nonlinearities present in most process systems. Often, we may have a model but not know how accurate it is and the range of applicability of the model may be un-known. What exactly do we mean by a well-tuned controller? Again there are no set answers. Vari-ous criteria are used depending on the application, the past experience of the engineer and the operators’ personal preferences. These include: (i) Fast response to set point changes, with minimal overshoot and fast settling times

(This is particularly important for servo control problems where the set point is con-stantly changing).

(ii) Fast recovery from disturbances. Most disturbances are random in nature. This in-

troduces another level of uncertainty in the design because the tuning for one set of disturbances may be quite different than another set. Fast recovery may be character-ized in the form of an integral squared error, decay ratio, settling times or a combina-tion of these.

Figure 1 shows the typical response expected from a controller for a step change in set point (servo control) or disturbance (regulatory control) along with some of the characterizing parameters.

T.1 Theory 3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6

New set point

Overshoot, A Rise time, Tr

B

e(t), Error in control

ISE e dt

Decay Ratio B A

³ 2

/

Figure 1a Response of a control system to a step change in setpoint

time, t

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

Figure 1b Response of a control system to a step change in the load

(disturbance) variable

4 Controller Tuning Appendix T

T.2 TUNING CORRELATIONS

A number of authors have published correlations for tuning PID controllers based on the selected performance criteria, and assumed process model structure. The FOPDT model is used most often. Generally correlations are provided in terms of the process gain, the time constant and time delay in the FOPDT model. Separate correlations are provided for servo control and regulatory control. Different criteria are used to evaluate the perform-ance including: (i) Integral Squared Error (ISE) (1) ³

f

odteISE 2

(ii) Integral Absolute Error (IAE) ³

f

odteIAE (2)

(iii) Integral Time Average Error (ITAE) ³

f

otdteITAE (3)

The well-known correlations are due to: (i) Ziegler-Nichols (1943) (Z-N tuning) For a system modeled using a first order plus dead time (FOPDT) transfer function,

G s �� �� � Ke ��T� s

W�s �� 1

the Z-N tuning constants are

T.2 Tuning Correlations 5

� �

� �

� � TTTW

TTWTW

WW

5.000.22.1

33.39.0

1

Derivative-Integral-Prop.

Integral alProportion

alProportion

¸¹·

¨©§

�¸¹·

¨©§

��¸¹·

¨©§

KPID

KPI

KP

k DII

(ii) Cohen-Coon (19xx) (C-C Tuning) These tuning rules are shown below

¸̧¹

·¨̈©

§�¸̧

¹

·¨̈©

§��

¸¹·

¨©§ �¸

¹·

¨©§

���

¸¹·

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¹·

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¹·

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WTT

WTWTT

WT

TW

WTWTT

WT

TW

WT

TW

WW

3

.9

2114

813632

41

341

20930

12101

3111

KPID

KPI

KP

K Dcc

(iii) IMC (Brosilow) Tuning These tuning rules are more recently established based on the Internal Model Control algo-rithm (Zarfirou and Morari, 1990). Chien and Fruehauf (1990) and Brosilow (1996) pub-lished PID tuning rules based on a single tuning parameter WCL for the closed-loop response time of the process.

� �TWTW

TW

2

1

2

�

¸̧¹

·¨̈©

§�

�

CL

CLc K

K

� �TWTWW

2

2

��

CLI

� � ¸̧¹

·¨̈©

§�

�

ICLD W

TTW

TW3

1 2

2

WCL is a secondary tuning parameter, called the closed loop time constant. This de-

termines how fast the closed loop will respond. Smaller values of WCL will give aggressive

6 Controller Tuning Appendix T

control with a significant overshoot. Generally WCL is chosen to give a stable controller even if the plant parameters change. The literature recommends a value

TW 80.0 !CL and

WW 1.0 !CL It is suggested that you use the larger of these two initially and then fine tune if necessary to yield faster or slower control.

T.3 PID TUNING OF 1ST ORDER PROCESSES

If the time delay estimated in a process is substantially smaller than the time con-stant then, it may be treated as a pure first order process. Consider the first order process

1)(

�

sK

sGp W

If we use a PI controller with transfer function

¸̧¹

·¨̈©

§�

sKsG

Icc W

11)(

We get the closed loop transfer function as (see Figure):

6

yset +

+ � �SG p y � �SGc

� �

1

11

2set�¸

¸¹

·¨¨©

§��¸

¸¹

·¨¨©

§�

�

scKK

IscKKI

sGG

GGyy

I

I

pc

pc

WWWW

W

T.3 PID Tuning Of 1ST Order Processes 7

Thus, the closed loop behaves like a second order system and is stable for all values of Kc and WI ! 0. (In practice, instability will result for high values of Kc or low values of WI from the constraints imposed on the manipulated variable and from small delays present.) The damping coefficient [ of the second order system is given by

cI

I

KKcKK

/2

11

WW

W

[¸¸¹

·¨¨©

§�

The loop gain KKc is usually kept below about 10 to prevent amplification of noise in the measurement. Choosing

KKc = 10 Yields

WW

[ I

210

choosing [ = ½ to yield an overshoot of about 25% results in

WI = W/10 Some fine-tuning may be needed if this control tuning constants are too aggressive or oscil-lating.

EXAMPLE:

A first order process has a time constant of 10 sec and a gain of 5 %/%. (All % re-fer to a full scale of 100%). Tune a PI controller.

Solution: The controller gain is Kc= 10/K = 10/5 = 2 %/%. This implies that a 1% change in measurement would cause a 2% change in controller out-put from the proportional action. A 25% change in measurement would be needed to cause the controller output to saturate (assuming the normal controller output is 50% of full scale). The recommended time constant would be:

WI = W/10 = 1 sec.

Thus a 1% change in measurement will cause the output to change by 2 %/sec. In 25 seconds the valve will saturate if the error does not decrease.