gonzales_wesley_ENGR3406_FINAL_PROJECT

ENGR3406
Process Control Systems
Project: Level Control of a Twin Tank System
Wesley Gonzales
4/21/2014

ENGR3406 Final Project: Two Tank Level Control Wesley Gonzales
Page 1 of 18
Executive Summary
The purpose of this project is to develop a model of level control for a two tank system in which
an electric pump controls flow into the first tank, which subsequently affects by its own unique
process dynamics the level in the second tank. The manipulated variable will be the voltage
supplied to the pump, the controlled variable is the inlet flow to the first tank and the process
variable is the level in the secondary tank. Additionally, the outflow from the second tank will
flow into an overflow reservoir in which the pump shall draw and subsequently pump water back
into the first tank. The process is capable of being controlled in two modes: manual, in which the
voltage supplied to the pump is manipulated by an operator in open-loop mode, and automatic,
in which the process shall be controlled in a closed feedback configuration based on PID
parameters. Initially, a model shall be developed in order to numerically estimate the process
dynamics and response of tank 2 level based on voltage supplied to the pump. An empirical
model shall be devised based on actual data from the tank, utilizing PAS TuneWizard software,
which shall provide the process gain and time constant as well as provide recommendations for
PID tuning parameters. Different tuning methods shall be employed and compared for optimal
performance until finally an operational test shall be employed using the PID tuning parameters
with the best response by conducting closed loop performance tests. This project shall illustrate
the key takeaways from the process control curriculum: numerical modelling, controller tuning,
operational testing.
Main Contributions/Results
This project demonstrated the six-step procedure for developing a model for a two tank level
control system. It involved analytical modeling, empirical modeling, experimental tuning and
validation of results. The application of level control has many industrial applications, and this
project demonstrated achieving level control with rather unsophisticated equipment and
feedback control using a PID algorithm programmed into National Instruments LabVIEW
software. This project revealed the functionality of the PAS TuneWizard software that enables
process control technicians (or students) to accurately develop numerical models and provide
tuning parameters for optimal performance. By the end of this project, analytical and empirical
models were developed using different methods, all of which successfully contributed to the
achievement of controlling fluid level in a second order system.

Page 2 of 18
Table of Contents
I. Introduction
A. Literature Review 3
B. Project Objective and Description 4
C. Project Significance and Impact 4
II. Methods and Materials
A. Alternative Approaches Considered
to Solve the Problem
5
B. Selected Approach to Solve the
Problem
6
1. Materials 6
2. Data 6
3. Assumptions 7
4. Problem Formulation 7
5. Calculations 8
6. Experiments 14
III. Results
A. Presentation of Results 15
B. Discussion/Interpretation 15
IV. Conclusions
A. Contributions of Project 17
B. Significance of Work 17
V. Future Work 17
VI. Appendices
VII. References 18

Page 3 of 18
Literature Review
‘Process Control, Designing and Processes and Control Systems for Dynamic Performance’ by
Thomas E. Marlin provided the fundamental theories and practices that made this project possible.
It established the modeling procedure that was adopted for this project and even included some
handy tables that were often utilized for reference. One of the examples of level control in the text
was indispensable and particularly valuable for the analytical modeling developed in this
experiment.
‘Applied Fluid Mechanics’ by Robert L. Mott provided insight into the conservation of energy of
incompressible fluids through Bernoulli’s equation. One of the essential aspects of this project
entailed understanding the dynamics of the change in flow rate with respect to elevation changes.

Page 4 of 18
Project Objective and Description
The purpose of this endeavor is to develop analytical and empirical models for a two tank level
control system. The numerical models shall attempt to capture the process dynamics in which the
voltage applied shall control the inlet flow into the first tank, and the contents of the first tank shall
freely flow into the second tank based on the hydrostatic pressure based on the level differential
between the two tanks. Additionally, the second tank will have an outflow that will empty into a
system return reservoir that continuously provides the pump flow into the first tank. The analytical
model will reflect the theoretical process dynamics and furthermore the empirical model shall be
developed using proprietary software that shall utilize actual process data from the ultrasonic level
transducers in both tanks. The analytical model and empirical models shall be conducted
simultaneously, independently in order to provide a comparison of the reliability of the two
different modeling methods. Based on the process dynamics of the models, numerous tuning
methods shall be employed, including IMC and Ziegler-Nichols in order to find the optimal set point
response. This project shall demonstrate the general six-step modeling procedure and fulfill some
of the essential skills in the study of process control systems.
The physical layout of the project entails the two tanks and system reservoir, the ultrasonic sensors
and the PC which functions as the controller based on a National Instruments LabVIEW software
algorithm. The LabVIEW program is capable of functioning in manual (open loop) mode or
automatic mode (closed feedback loop). In the manual mode, the operator can freely manipulate
the voltage to the pump and the subsequent inlet flow into the first tank. In the automatic mode, the
LabVIEW software shall increase and decrease the voltage and pump flow into the first tank based
on PID tuning parameters entered by the operator. The manual mode shall be necessary for the
development of the empirical model in which the operator shall conduct open loop test(s) in order
to capture the output response due to a change in the input at steady state. The automatic mode
shall be used as model and tuning parameter validation at the conclusion of the project analysis.
Project Significance and Impact
Level control has applications in many processes such as distillation systems, coolant return
reservoirs for reactors and ballast control. The variable control demonstrated in this project is a
mere component in what could otherwise be a complex system that involves multi-variable control
such as pressure, flow, concentration and temperature. This system process involves a master and
slave configuration in which the tank 2 controller determines the set point of tank 1. This cascaded
control loop within a control loop can even be utilized between different variables as long as the
slave directly influences the process variable of the master. The interface between the controls of
different variables enables a process to reach higher levels of optimization and efficiency, and after
further analysis, provides an opportunity for identification of diminished levels of performance and
degraded system components. The capability to analyze and control at different levels empowers
managers and supervisors of process systems to make better decisions and provide flexibility
under budgetary and resource constraints.

Page 5 of 18
Alternate Approaches Considered to Solve Problem
For this modelling problem, we used the six step modeling procedure as a baseline to guide our
analysis.
The six steps and their associated considerations are as follows:
1. Define goals – what variable are we measuring?
2. Prepare information – collect static data, define assumptions, draw block diagram
3. Formulate the model – conduct material / energy balance, conduct degree of freedom
analysis, develop differential equation(s), non-linear, linear models
4. Determine the solution – determine input / output response process dynamics and
parameters: process gain, time constant, time delay
5. Analyze the results – assess accuracy of process response with predicted, compare process
response with empirical (if possible)
6. Validate the model – conduct data collection that supports modelling results and present
post-analysis
Generally, this six step procedure can apply exclusively to theoretical models, however, this
exercise was intended to represent the process dynamics of an actual physical process, so we were
presented with the luxury of developing a theoretical analytical model, and an empirical model. We
would be able to carry out the theoretical modeling procedure and simultaneously collect empirical
data using open loop testing and utilize PAS TuneWizard software to evaluate the process dynamics
and recommend tuning parameters.
One of the different approaches we considered was to conduct the empirical analysis first, and let
the process dynamics and tuning parameters guide our analytical modelling process analysis.
However, we wanted the analytical modelling to proceed independent of the empirical modelling in
order to get a more theoretical ‘second opinion’ and allow the empirical results reinforce and
validate our theoretical model.
Due to the cascaded configuration of this process, we were also faced with the decision to pursue
tuning parameters for the process dynamics of tank one first and then implement tuning for tank 2
or develop second order tuning for the integrated process, with the voltage input to the pump as
the manipulated variable and tank 2 level as the controlled variable. A theoretical tuning
spreadsheet had been developed as a class exercise that could be implemented to simulate manual
tuning.

Page 6 of 18
Selected Approach to Solve Problem
Materials
Other than the physical components associated with this experiment, this project extensively
utilized various software platforms, notably MS Excel to develop the analytical modeling, as well as
PAS TuneWizard software that facilitated the empirical modeling of this process. PAS TuneWizard
is used in order to conduct an analysis of the process dynamics and transient response of a
particular process. It has been utilized in industrial applications for process tuning and
performance assessment.
Figure 1. Physical layout of twin tank system
Data
The physical dimensions of the plant determined the model parameters, and additionally, steady
state data was available. The height of tank 1 and tank 2 are 37cm, however, the ultrasonic flow
transmitters are calibrated such that the level is 100% at 30cm.
Table 1. Physical Dimensions and Equipment Specifications
Length (cm) 14.2
Width (cm) 12.8
Height (cm) 30
Pipe diameter (in.) 0.5
Pump Rating (gpm) 1200
Ultrasonic level sensor range (mA) 4 - 20
Pump voltage operating range (V) 0-12
Pulse Width Modulation range (V) 0-5

Page 7 of 18
Table 2. Steady State Values
Variable Value Units
Vps 2.75 V DC
F1s 48.45 cm3/s
F2s 6.5 cm
L2s 3.5 cm
Assumptions
Most of the assumptions we shall make will be based on the equipment we shall be using for this
experiment. The LabVIEW program that contains the PID algorithm has been pre-conceived by
another individual, so we shall assume that the algorithm operates with a reasonable level of
satisfactory performance. We do not have a flowmeter available to measure the flow rate of this
experiment, so we shall have to rely on empirical methods to estimate the flow rates that increase
with voltage input and extrapolate flow rates from minimum values to maximum. The level sensors
that we shall be using have been calibrated such that the level sensors will read 100% at 30cm
(when the top of the tank is actually 37cm). One last caveat is that for every possible session in
which open loop testing, closed loop tuning and performance verification occurred, every possible
effort was made to ensure that operating conditions were the same as the previous sessions and
that no alterations or equipment configuration changes were made.
Problem Formulation
To approach this problem, we decided to apply the six step modeling procedure as closely as
possible, which entailed us developing an analytical model, an empirical model and developing
tuning parameters based on the process dynamics of each model. The analytical and empirical
models would be done in parallel, as independent as possible, in order to get independent
verification and confirmation of the results. For the analytical model, the process gain and time
constant will be found by numerical manipulation as well as importing the simulated transient
response created in Excel into the PAS TuneWizard software. For the empirical model, the process
gain and time constant will be found by conducting open loop testing from steady state and
importing the csv file data into TuneWizard in order to get the process gain and time constant and
recommended tuning parameters. In TuneWizard, one can select tuning parameters based on
different applications, for disturbance rejection or setpoint response. For the purposes of this
project, the tuning parameters shall be selected based on setpoint response using IMC tuning
parameters.
Figure 2. Block diagram representation of two tank level control system

Page 8 of 18
Figure 3. Flowchart for Procedural Methodology
Calculations
The development of the non-linear model started by developing a mass balance regarding the level
as a function of inlet and outlet flow. The cross sectional area of the tank multiplied by the
derivative of tank level with respect to time would give the volumetric displacement as a function of
time. At any given time, the volumetric displacement would be function of the inlet flow minus the
outlet flow.
𝑑𝐿1
𝑑𝑡
=
𝐹0
𝐴
−
𝑘 𝑓1√ 𝐿1 − 𝐿2
𝐴
The outlet flow is determined by Bernoulli’s equation, in this case, the cross sectional diameter of
the pipe does not change from tank 1 to tank 2, so there is no change in kinetic energy. There is no
differential pressure from tank 1 to tank 2 since both are at atmospheric pressure, so the outlet
flow from tank 1 to tank 2 is determined by the height differential, with the level of tank 1 utilized
as the datum. The value of the drain coefficient kf1 was found by determining the outlet flow rate of
tank 1 to tank 2 at steady state which was measured using empirical data and solving for kf1.

Page 9 of 18
𝐹0 = 𝑘 𝑓1√ 𝐿1 − 𝐿2
The differential equation for the non-linear model of tank 2 was completed similarly by measuring
the flow rate by volumetric displacement for a given unit of time at a steady state tank level L2. In
the case for the differential equation for tank 2, the inlet flow to tank 2 is the same as the outlet flow
from tank 1.
𝑑𝐿2
𝑑𝑡
=
𝑘 𝑓1√ 𝐿1 − 𝐿2
𝐴
−
𝑘 𝑓2√ 𝐿2
𝐴
Figure 4. Non-linear model in MS Excel, voltage input step change and flow response
Figure 5. Non-linear model transient response from steady state 2.75V to 3.5V SS
0
20
40
60
80
100
120
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
Flow(cm^3/s)
Voltage(V)
Time(s)
Manipulated Variable Step Δ
V
F
0
5
10
15
20
25
30
35
0 200 400 600 800
Level(cm)
Time (s)
Controlled Variable (PV)
Tank 1
Tank 2

Page 10 of 18
The linear model was developed by defining the non-linear term to linearize, which was the (L1 –
L2)-0.5.
[(𝐿1 − 𝐿2)]′ =
0.5𝑘 𝑓1(𝐿1 − 𝐿2)−0.5
[(𝐿1 − 𝐿2) − (𝐿1𝑆 − 𝐿2𝑆)]
𝐴
𝑑𝐿1
𝑑𝑡
=
𝐹0
𝐴
−
𝑘 𝑓1√ 𝐿1 − 𝐿2
𝐴
−
0.5𝑘𝑓1(𝐿1 − 𝐿2)−0.5
[(𝐿1 − 𝐿2) − (𝐿1𝑆 − 𝐿2𝑆)]
𝐴
0 =
𝐹0
𝐴
−
𝑘 𝑓1√ 𝐿1𝑆 − 𝐿2𝑆
𝐴
−
0.5𝑘 𝑓1(𝐿1𝑆 − 𝐿2𝑆)−0.5
[(𝐿1𝑆 − 𝐿2𝑆) − (𝐿1𝑆 − 𝐿2𝑆)]
𝐴
𝑑𝐿1′
𝑑𝑡
=
𝐹0
𝐴
−
0.5𝑘 𝑓1(𝐿1 − 𝐿2)−0.5
𝐴
𝐿1′
𝑑𝐿′
𝑑𝑡
=
1
𝐴
𝐹0 − (
0.5𝑘 𝑓(𝐿1 − 𝐿2)−0.5
𝐴
)𝐿′
𝜏 𝑝
𝑑𝐿′
𝑑𝑡
= 𝑘 𝑝 𝐹0 − 𝐿′
𝜏 =
𝐴
0.5𝑘 𝑓(𝐿1 − 𝐿2)−0.5
𝑘 𝑝 =
1
0.5𝑘𝑓(𝐿1 − 𝐿2)−0.5
Figure 6. Linearized Model transient response from steady state 2.75V to new steady state value 3.5V
0
5
10
15
20
25
0 50 100 150 200
Level(cm)
Time (s)
Controlled Variable (PV)
Tank 1
Tank 2

Page 11 of 18
IMC Tuning Parameters (Analytical model)
𝑘 𝑝 𝐾𝑐 =
𝜏 +
𝛩
2
𝜏 +
𝛩
2
𝐾𝑐1 =
1
𝑘 𝑝1
=
1
0.012
= 83.3
𝐾𝑐2 =
1
𝑘 𝑝2
=
1
0.016
= 62.5
𝜏𝐼 = 𝜏 +
𝛩
2
𝜏𝐼1 = 𝜏 +
𝛩
2
= 22.19 +
0
2
= 22.19𝑠
𝜏𝐼2 = 𝜏 +
𝛩
2
= 29.74 +
0
2
= 29.74𝑠
𝜏 𝐷 =
𝜏 ⋅ 𝛩
2𝜏 + 𝛩
𝜏 𝐷1 =
𝜏 ⋅ 𝛩
2𝜏 + 𝛩
=
(22.19) ⋅ 0
2(22.19) + 0
= 0
𝜏 𝐷2 =
𝜏 ⋅ 𝛩
2𝜏 + 𝛩
=
(29.74) ⋅ 0
2(29.74) + 0
= 0
Figure 7. Analytical Model parameters and recommended tuning in PAS TuneWizard software for Tank 1

Page 12 of 18
Figure 8. Analytical Model parameters and recommended tuning in PAS TuneWizard software for Tank 2
Figure 9. Empirical model parameters and tuning in PAS TuneWizard for Tank 1
The tuning parameters from the analytical and empirical models were imported into a MS Excel
spreadsheet that simulated the closed loop transient impulse response for tank 1 and tank 2, which
can be seen in Fig. 11-12. The independent confirmation of the tuning parameters in PAS
TuneWizard and the MS Excel spreadsheet with the PID algorithm inspired our confidence in the
tuning parameters generated by TuneWizard, and gave us at least some initial tuning parameters to
implement into the two tank level controller. No conversion would be necessary because
TuneWizard time constant and dead time was already in minutes as was the LabVIEW program for
the two tank controller. There was an issue to consider when assessing performance: the LabVIEW
program gave values of level in percentages, instead of actual data in centimeters, which
necessitated some intermediary calculations for steady state values and step changes. However,
this should not have affected the tuning parameters or process dynamics.

Page 13 of 18
Figure 10. Empirical model parameters and tuning in PAS TuneWizard for Tank 1
𝒌 𝒑 𝝉 𝜣 P I D
Analytical TuneWizard Recommended Tuning
Tank 1 52.8 2.45 0 0.01 2.5 0
Tank 2 33.2 2.97 0.0875 0.029 3.0 0
Empirical TuneWizard Recommended Tuning
Tank 1 16.5 68.2 5.47 0.056 68 0
Tank 2 9.92 63.5 15.6 0.081 63 0
Figure 11. PID Simulation of closed loop empirical model in MS Excel using PAS tuning parameters
0
0.2
0.4
0.6
0.8
1
1.2
-50 50 150 250 350 450 550
Level(cm)
Time (s)
Tank 1
PV
Setpoint

Page 14 of 18
Figure 12. PID Simulation of closed loop empirical model in MS Excel using PAS tuning parameters
Experiments
For the final tuning, the LabVIEW interface has two possible configurations: cascaded and non-
cascaded. In cascaded, the operator must tune each tank individually and enter PID parameters that
ultimately affect the set point response and offset. In the non-cascaded, the PID parameters that the
operator enters only affects the tank one controller, bypassing the tank 2 controller but using the
error inputs from the tank 2 ultrasonic level transmitter. For the cascaded configuration, tank 1 was
tuned first, and followed by optimal
tuning for tank 2 set point response.
Under close observation, the final
results reveal that the non-cascaded
tuning had better performance.
Additionally, the non-cascaded
configuration is obviously easier to
tune considering that the operator
only had to tune one set of tuning
parameters and did not have to worry
that optimal tuning parameters for
tank 1 would create a conflict with the
parameters for tank 2. One might
wonder why even bother have
separate tuning for tank 1 at all.
With the non-cascaded configuration, for large set point increases, the transient response for tank 1
could potentially have an unstable response. For example, if a large set point change from 10% was
increased to 80%, it would excessively cycle the pump and increase the flow rate to tank 1 in such a
manner that the flow into tank 2 could not handle the increased volumetric flow into tank 1 and
tank 1 could overflow. The cascaded configuration could be safer and more stable and offers more
control in more sensitive processes. In the non-cascaded configuration, the operator is not too
concerned what is going on in tank 1. Notice that the process response is slower due to the tank 1
controller basing its algorithm on the tank 2 level, which has a higher time constant. The cascaded
configuration will be more responsive, due to the tight restrictions of PID tuning parameters being
placed on both tanks.
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
Level(cm)
Time (s)
Tank 2
PV
Setpoint
Figure 13. Experimental evaluation of closed loop response

Page 15 of 18
Results
The results from this experiment revealed tuning parameters that were close to the ones
recommended by TuneWizard PAS. They were close enough to reveal baseline values in which to
fine tune by conventional methods. The method that is employed is to first set kp such that a set
point change will provoke a slight overshoot (ensure no oscillatory behavior) and increase the
integral term to get rid of the offset. The PAS TuneWizard did not recommend a derivative term,
and one can see the satisfactory results one gets with PI tuning. One can see a slight offset in the
cascaded configuration, which was acceptable in the LabVIEW front panel interface initially,
however, importing the data into MS Excel and plotting the trend in a graph revealed disappointing
level of offset in retrospect, which could have been eliminated in further tuning by increasing the
integral term. However, the process response and settling time were impressive, reaching 2%
steady state value in 3.38 minutes.
Figure 14. Closed Loop performance of cascaded PID tuning parameters
The initial analytical modeling revealed some deficiencies, particularly the steady state values
following a step change. The low process gain was attributed to the fact that the voltage-inlet flow
relationship had not been taken into account in the differential equation that was developed, and
thus a process gain <1 was realized. When the data simulating a steady state value step change from
2.75V to 3.5V using the analytical method was imported into PAS, the voltage-inlet flow was taken
into account, and the model parameters reflected numbers closer to the empirical model. The
empirical model proved to be a reliable source of modeling parameters and yielded solid tuning,
which guided the eventual final tuning parameters and revealed the deficiencies of the initial
analytical model.
0
5
10
15
20
25
560 660 760 860 960 1060 1160
Level(%)
Time (s)
Cascaded
PV
Setpoint

Page 16 of 18
Figure 15. Closed loop performance of non-cascaded PID tuning parameters
Final Closed Loop Tuning Parameters
P I D
Cascaded
PID Controller Tank 1 0.15 5.13 0
Non-cascaded
0
5
10
15
20
25
30
35
7121 7321 7521 7721
Level(%)
Time (s)
Non-Cascaded
PV
Setpoint

Page 17 of 18
Conclusions
Contributions of Project
The contributions of this project reinforce the ability of a feedback control loop utilizing a PI
algorithm to control fluid level using rather unsophisticated equipment. The ability to control fluid
level has much significance in industrial applications and control processes. It can be utilized in
conjunction which other controlled variables, such as temperature, if the fluid is utilized as cooling
water. For this application, the two would be utilized in a cascaded configuration, such that the
temperature determines the set point of the cooling water fluid level, in a master-slave
configuration. This project proved the functionality of the PAS TuneWizard software, which
accurately developed modeling parameters and recommended fairly reliable tuning, which could
potentially save much engineering man-hours and increase productivity if it replaced more
conventional methods.
Future Work
This project by no means explores the full range and capabilities of level control, and a more
exhaustive study is possible. This project could have explored the possibility of multivariable
control by controlling temperature and fluid level. This project could have further evaluated the
disturbance rejection of the tuning parameters from the PAS TuneWizard software. It is highly
probable that many students shall utilize level control as their capstone senior project, possibly by
using more sophisticated control interfaces and measurement devices.

Page 18 of 18
References
Marlin, Thomas, E. “Process Control, Designing Processes and Control Systems for Dynamic
Performance”, 2nd Edition, McGraw-Hill, 2000.
Mott, Robert L. “Applied fluid mechanics”. 6th Edition,. Upper Saddle River, N.J.: Prentice Hall, 2005.
Print.

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