full project and a report

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1) Submit your report via the Turnitin link on Moodle on or before the due date.
2) The date you upload to Moodle is considered as the ‘Date of Submission’ when
calculating the late submission.
3) Any late submission will result in the application of the late submission rule.
4) The deadline for this project is Tuesday the 31stof May 2022
Learning outcomes

The tasks within this assignment satisfy the Learning Outcomes of the course:
1) Demonstrate advanced knowledge of core principles of control and
2) Critically analyse and evaluate transient response characteristics of first and
second order systems.
3) Apply and demonstrate instrumentation and control strategies for a feedback
control system.
4) Formulate, apply and present tuning methods for finding suitable PID controller
parameters to meet an industry standard requirement for a defined control
design problem
This project is worth 30% of your final grade and uses MATLAB/SIMULINK to design a
controller for a pH neutralization plant. The time scale of the project will be announced
y your tutor.

The following deliverables must be submitted by the project deadline:
1) Your MATLAB/SIMULINK code that designs your proposed controller.
2) The simulation model of the control system in MATLAB/SIMULINK.
3) A project report explaining how you calculated the controller and the reasoning
ehind your design choices.
Project: Control design of a pH neutralization plant for Sustainable
Wastewater Treatment.

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Project Report

Write a project report outlining all the tasks below. You need to justify the reasoning
ehind the controller choice and how they have met the criteria for the transient response
design specifications. Make the report as clear and transparent as possible. You need to
ensure the following:
• Demonstrate your results with suitable MATLAB/SIMULINK plots & code (very,
very strict rule).
• All m-files (editable text, no pictures) and SIMULINK block diagrams may be
included in the appendix section of your report (not-so-strict rule).
• Label the axes of each graph. This includes attaching a figure legend when
appropriate. Include the unit with the label itself (“speed m/s” versus “time in
milliseconds” or "time [ms]") so that we know what’s being measured and that it is
not an a
itrary variable (very, very strict rule).
• Instead of sending many figures, you can use subplot () to group relevant figures
(not-so-strict rule).
• Every m-file code must contain some comments describing the function of the
MATLAB code/command (very, very strict rule).
• Every graph must have a descriptive Title. Label and scale all axes accurately.
(very, very strict rule).
• If a plot contains multiple lines, you must add a legend explaining each curve.
(very, very strict rule).
• Do not paste SIMULINK ‘Scope’ images into the report, since they do not contain
proper labeling (very, very strict rule).
• For SIMULINK block diagrams, avoid overlapping and crossing lines as much as
possible. Re-a
ange the icons so that a clear path from left to right is visible (very,
very strict rule).
• Number your plots and graphs sequentially, e.g. Fig.1, 2 etc. (very, very strict rule).
Sustainable Wastewater Treatment Systems
An important part of the environmental degradation suffered by the planet is caused by
the discharge of untreated or poorly treated wastewater. Industrial, u
an, and
agricultural wastewater contain many different types of pollutants such as biodegradable
and nonbiodegradable organic matter, suspended solids, tu
idity, nutrients, heavy
metals, pesticides, pathogens, etc. All of these pose a threat to the environment and
human health, so the selected treatment techniques must be adapted to their nature to
optimize their removal. In addition to efficiency, wastewater treatment methods must be
sustainable, not only from an environmental point of view, but also economically and
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The pH of industrial and municipal wastewater streams tends to drift toward an acidic
value, due mostly to wate
orne anaerobic microorganisms that generate acidic by-
products. These acids, such as hydrogen sulfide (H2S) and small organic acids, emit
strong odors that are simultaneously unpleasant for neighboring businesses and
esidents and highly co
osive to the wastewater collection system infrastructure.
Wastewater system
Figure 1. Neutralization tank with pH control
Parameters Description Unit Value
? Tank volume Meters3 10
??(?) Base volumetric flow rate Meters
3/Second 5 × 10−3
??(?) Acid volumetric flow rate Meters
3/Second 5 × 10−3
????? Maximum base volumetric flow rate Meters
3/Second 5 × 10−3
????? Maximum acid volumetric flow rate Meters
3/Second 25 × 10−4
∗ Steady State base volumetric flow
Meters3/Second 5 × 10−3
∗ Steady state acid volumetric flow
Meters3/Second 5 × 10−3
?∗ Steady state output volumetric flow
Meters3/Second 10−2
∗ Maximum Steady State base
volumetric flow rate
Meters3/Second 5 × 10−3
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∗ Maximum Steady State acid
volumetric flow rate
Meters3/Second 25 × 10−4
∗ Steady state base feed
Moles/Liter -10
∗ Steady state acid feed
Moles/Liter 10
?(?) Excess acid concentration Moles/Liter
???? Maximum excess acid
Moles/Liter 10−6
Derivation of model
According to the A
henius theory of acids and bases, when an acid is added to water, it
contributes an ?+ ion to water to form the molar concentration of hydronium ion
+ (often represented by ?+ ). The higher the concentration of ?3?
+ (or ?+ ) in a
solution, the more acidic the solution is. An A
henius base is a substance that generates
hydroxide ions, ??−, in water. The higher the concentration of ??− in a solution, the more
asic the solution is, i.e.
?2? ⇌ ?
+ + ??−
pH is defined as the negative of the base-ten logarithm of the molar concentration of
hydronium ions present in the solution. The unit for the concentration of hydrogen ions
is Moles/Liter. ?? can be determined as follows:
?? = −log(?+)
Consider the wastewater system outlined in Figure 1 that contains one single tank with
volume ?. Let ??(?) (Moles/Liter) and ???(?) (Moles/Liter) denote the concentration of
?+ and ??− ions, respectively. ?(?) denotes flow rate. Let further subscript ? denote
acid, subscript ? denote base and no subscript denote the outlet stream. Material
alances for ?+ and ??−yields
{??(?)} = ??(?)??,? + ??(?)??,? − ?(?)?? + ??
{???(?)} = ??(?)???,? + ??(?)???,? − ?(?)??? + ??
where ?(moles/second . m3) is the rate for the reaction ?2? ⇌ ?
+ + ??− which for
completely dissociated ("strong") acids and bases is the only reaction in which ?+ and
??− participate. We may eliminate ? from the equations by taking the difference to get a
differential equation in terms of the excess of acid
?(?) = ??(?) − ???(?)
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{?(?)} = ??(?)?? + ??(?)?? − ?(?)?(?) (1)
?? = ??,? − ???,? XXXXXXXXXXand ?? = ??,? − ???,?
This is the material balance for mixing tank without reaction. The overall model is bilinear
due to the product of flow rate and concentration ?(?)?(?). Note that ?(?) will take on
negative values when pH is above 7. The acid and base feed concentrations ?? and ??
for both ?+ and ??−are assumed to be constants. Linearising equation (1) around a
steady-state nominal point (denoted with an asterisk)
{?(?)} + ?∗?(?) = ??(?)(??
∗ − ?∗) + ??(?)(??
∗ − ?∗)
* is used to denote steady-state values, and
?∗ = ??
∗ + ??
∗ ?∗ = 10−?? − 10−14+??
∗ = ??,? − ???,? ??? ??
∗ = ??,? − ???,?
Scaled variables for the input are introduced for the input, output and the distu
ance as
?(?) =
; ?(?) =
; ?(?) =

1) Explain how the performance of pH level control system can be compliant with
environmental regulations and the treatment of wastewater. Provide two
examples to explain the importance of a stable pH and its role in minimizing
pollution in our ecosystem. [5 Marks]
2) For a neutral pH = 7 , using Laplace transforms and assuming zero initial
conditions, show that
�̅�(?) =
?? + 1
∗ − ?∗

�̅�(?) +
∗ − ?∗

where the time constant is ? = ?/?∗. [7 Marks]
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3) Construct a block diagram depicting an open loop a
angement for the signals
and transfer functions defined in 2). [3 Marks]
4) Assume zero initial conditions and a step input with magnitudes ? and ? for each
of �̅�(?) and �̅�(?) respectively. Find the concentration output ?(?). [10 marks]

5) Using MATLAB, produce a unit step response for the output ?(?) and verify the
esult by comparing it with the analytical result derived in 4). Select the time scales
so that both the transients and the steady state output are visible. [10 marks]
6) Assuming �̅�(?) = 0, specify the parameter values that needs to be changed for
the speed of the response to increase. Explain and justify your reasoning using
appropriate mathematical functions and step response plots? [5 marks]
7) Assuming a unity negative feedback loop, derive the following transfer functions

a. ???(?)
. ???(?)
c. ???(?)
d. ???(?)
[8 marks]
May 15, 2022

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