Unit 24 Assignment 2

P4 – Describe how data can be represented in control systems  

Coding  

Binary  

Picture reference: https://www.erindorpress.com/2019/06/to-1-or-to-0-translating-binary-in-fiction/ 

Computer systems use the counting system named ‘Binary’. The binary counting system is of the base 2 allowing you to choose either the number 0 or 1. These individual numbers in binary are known as ‘bits’ which are the smallest unit of data in computing, and they are combined together to form a binary number commonly of eight bits which is equivalent to one byte. For example, the binary number 01010101 is equal to 64 + 16 + 4 + 1 which is 85 in our denary counting system. Computers use binary as their counting system due to their architecture being composed of billions of transistors. Transistors are very small switches which switch off and on by the electronic signals they receive which means that the numbers 0 and 1 can be used to reflect the state of a transistor, with 0 being off and 1 being on. (Bits and binary – Introducing binary – GCSE Computer Science Revision – BBC Bitesize, n.d.)  

Hexadecimal  

Picture reference: http://string-functions.com/string-hex.aspx 

In computing we often also use the counting system called ‘hexadecimal’ sometimes shortened to ‘hex’. It is a base 16 counting system which is often used as an alternative to representing binary as it much easier to use. Hexadecimal is composed of the following 16 digits: 0 1 2 3 4 5 6 7 8 9 10 A B C D E F. Each individual hex digit will correspond to a 4 bit binary number. For example, the hexadecimal F corresponds to the 4 bit binary number 1111. Therefore, this enables us to be able to store an 8 bit binary number aka a byte by just using two hex digits which saves up a lot more space and is easier to read and understand especially for programmers. This is why hexadecimal numbers are commonly used in different aspects of computing such as colour codes, error logs and assembly instructions. For example, in an assembly editor it will use hexadecimal numbers to refer to where instructions are being stored in memory, and in webpages inside the CSS you can refer to very specific colours by using a hex code. (Using hexadecimal – Hexadecimal and character sets – GCSE Computer Science Revision – BBC Bitesize, n.d.)  

Decimal  

Picture reference: https://en.wikibooks.org/wiki/GCSE_Computer_Science/Binary_representation 

Decimal which is also commonly referred to as ‘denary’ is a counting system of base 10 that us humans use in our everyday lives. It is a lot easier for us humans to understand and use and since we have been taught it from a young age it is also the most natural for us. The counting system of base 10 consists of the numbers: 0 1 2 3 4 5 6 7 8 9. The word decimal comes from the latin word ‘decimus’ which means tenth, which is how it got its name from our counting system of base 10 containing ten numbers. Decimal numbers work by multiplying their values by their position. For example, if you have the number 11 it would be 101 * 1 + 100 * 1 which equals 11 and for decimal numbers like 0.1, since the position of 1 is -1 then it would be 10-1 * 1 which is equal to 1/10 which is 0.1. (Denary Definition, 2015) 

ASCII 

ASCII which is short for American Standard Code for Information Interchange is a code that uses characters to be represented by numbers. A number between 0 and 127 is given to each letter. A separate value is given to the upper and lower case characters. For example, A is given a decimal number of 65, while a is given the decimal number of 97. Here is an ASCII table picture which shows you the different letters and their corresponding ASCII values. 

Picture reference: https://computersciencewiki.org/index.php/ASCII 

On a keyboard the keys that you press or the text that you receive are received as a bunch of decimal numbers. They work like this since microprocessors are only able to understand bits of information as 0s and 1s which form up to 8 bits which is known as a byte so they must be stored in this way in order for the microprocessor to communicate and understand the information they are dealing with and present it to the user. (Beal, n.d.) 

Logical operators 

For representing logical expressions, Boolean algebra or truth tables may be used in order to display the logical output from the input of these expressions. The most familiar operators when it comes to logical operators are Boolean are AND, OR, and NOT and they were always written in capital letters, there is also XOR which is exclusive or which I will also talk about later. When drawing logic gate circuits, each logical operator has a specific symbol which can be used to represent it. (Boolean algebra – Boolean logic – GCSE Computer Science Revision – BBC Bitesize, n.d.) 

Here is a NOT gate:  

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

A NOT gate only takes in one input. The output of a not gate will be the opposite of its input, so for example if you input 0 it will output 1 and if you input 1 it will output 0. Here is what the inputs and outputs would look like in a truth table: (Boolean algebra – Boolean logic – GCSE Computer Science Revision – BBC Bitesize, n.d.) 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

Here is an AND gate: 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

An AND gate takes in two inputs. The output of an AND gate will depend on the inputs provided. In order to output a 1, it must require both inputs to be 1. So for example, if you input 0 1, 1 0 or 0 0 it will output 0 but if you input 1 1 then it will output 1. Here is what the inputs and outputs would look like in a truth table: (Boolean algebra – Boolean logic – GCSE Computer Science Revision – BBC Bitesize, n.d.) 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

Here is an OR gate: 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

An OR gate takes in two inputs. The output of the OR gate will depend on the inputs provided. In order to input a 1, it must require at least one of the inputs to be a 1. So for example, if you input 0 1, 1 0, or 1 1 then the OR gate will output a 1 but if you input 0 0 then it will output a 0. Here is what the inputs and outputs would look like in a truth table: (Boolean algebra – Boolean logic – GCSE Computer Science Revision – BBC Bitesize, n.d.) 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

Here is an exclusive OR gate referred to as ‘XOR’: 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

An XOR gate takes in two inputs. The output of the XOR gate will depend on the inputs provided. In order to input a 1, it must require for only one of the inputs to be a 1. So for example, if you input 0 1 or 1 0 then the XOR gate will output a 1 but if you input 0 0 or 1 1 then it will output a 0. Here is what the inputs and outputs would look like in a truth table: (Boolean algebra – Boolean logic – GCSE Computer Science Revision – BBC Bitesize, n.d.) 

Picture source: https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2 

Numbers 

To reference specific types of numbers we give them a specific name which allows us to be more precise about what numbers we are referring to. The three types of numbers that I will be talking about are integers, fixed-point numbers, and floating-point numbers. I will also speak about when we use each of these types. 

Integer 

Picture reference: https://www.onlinemathlearning.com/integer-number-line.html 

An integer is simply a number that contains no decimal point/ fractional part. This just means that the number must be a whole number so it can be either positive or negative. This includes numbers such as: 1 2 3, -1 2 3 and 0 as zero is also classified as an integer. In mathematics integers are commonly written as in a set with the notation of curly braces { } such as this set: { 6, 28, 496, 8128, -2, -96, 0, -3598}. It is named integer as the word integer comes from the 16th century Latin word which is a meaning of ‘whole’ which is exactly what an integer is, a whole number. (Integer Definition (Illustrated Mathematics Dictionary), n.d.) 

Fixed-point  

Picture reference: https://www.sciencedirect.com/topics/computer-science/fixed-point-number 

A fixed-point number type is an option we can use in order to represent the data in computing for a number that has a set amount of digits after or even before the radix mark. This includes numbers such as: 6.1, -0.34, 509.1, 22.56 

When the microprocessor that is executing and handling the data does not contain a floating point unit to store these fractional numbers as a floating point type which is quite common for older or low price embedded microprocessors and microcontrollers, then a fixed-point storage system will be helpful for expressing these fractional values, typically for numbers that are in base 2 or base 10. Fixed point numbers are also used if they offer improved efficiency or precision for the application at hand, or if their usage is more suited for the issue such as for the representation of angles. 

Floating-point 

A floating-point number type is another option we have in order to represent the data in computing for a number that has a set amount of digits after or even before the radix mark. This includes numbers such as: 3.4, 3.14567, 1000.8, -13.23. 

Floating point numbers work by using a using formulaic real number representation as an approximation to facilitate a trade-off between range and accuracy. As a result, systems which contain very small and very large real numbers which require quick processing times, floating-point computing is mostly used. A floating-point value is represented roughly by a fixed number of significant digits which is known as the ‘significand’ and is scaled on a fixed base using an exponent, the scaling base which is typically used is most commonly a two, ten, or sixteen. 

They typically take this form: 

Picture reference: https://en.wikipedia.org/wiki/Floating-point_arithmetic 

When we use each type 

Depending on certain circumstances we will tend to use on type over the other. For instance, we would use an integer data type if we were just storing whole numbers that were positive or negative as opposed to using a float/fixed point type as integers use up less space as they only take up 4 bytes as opposed to float/fixed point type which usually take up 8 bytes if it referred to as a double in modern programming languages but can be just 4 bytes if referred to as float it also depends on the architecture of your computer so it is tricky to tell so you can sometimes. However, you cannot do vice versa and store float/fixed point values in an integer number type as it will just get truncated at the decimal point. 

For fixed point values and float point values the one you decide to use will depend on factors such as the system you are using, the performance and accuracy required and other ones, so for an older system you may be forced to use a fixed point type whereas when accuracy and performance is a priority you may consider using a floating point type instead. 

Control operations 

Open loop control 

Picture source: https://www.electrical4u.com/control-system-closed-loop-open-loop-control-system/#Open-Loop-Control-System 

An open loop control system is a control system where the control operation is completely independent of the device’s output. Therefore, this makes an open-loop control system a manual control system as it requires a user to manually interact with it giving it input of what instructions to follow and it will follow it as so not caring about the output/performance and just doing what it was told to do. Examples of open loop control systems that we see in our everyday life are: toaster, light switch, electric hand drier, volume on stereo system, time based tumble dryer and more. 

The advantages of an open loop control system are that they are usually quite stable not breaking down or having faults often which also makes them economical, they are simple in construction and design and are easy to use when the performance is hard to estimate.  

However, the disadvantages are that they can be quite inaccurate in some cases, for example in the example mentioned earlier of a toaster it will toast your bread depending on the timer you set it which means it will toast it for the set amount of time irrespective of whether the bread has been properly toasted or not meaning that the bread may be under toasted or become burnt this makes them unreliable as well. Another disadvantage is that the output any adjustment in output cannot be automatically fixed. (What is a Control System? (Open Loop & Closed Loop Control Systems Explained) | Electrical4U, 2020) 

Closed Loop Control System 

Picture source: https://www.electrical4u.com/control-system-closed-loop-open-loop-control-system/#Closed-Loop-Control-System 

A closed loop control system is a control system where the control operation is dependent on the output that it receives, this output will have an impact on the input quantity so that the input quantity adjusts itself in response to the output produced. This makes a closed loop control system and automatic control system due to it responding and adjusting based on the feedback provided as part of the input. 

Therefore, technically you can convert an open loop control system into a closed loop control system just by giving it feedback.  

Examples of closed loop control systems we see in everyday life are: air conditioners, cooling systems in cars and computers, automatic electric iron, a thermostat and many more. 

The advantages of closed loop control systems are that they are more accurate even if left alone as they utilize feedback in order to correct themselves to reach the desired outcome/output, they are highly accurate due to any error being fixed as a result of the feedback system, it is automatic meaning there is no need for a user to manually interact with it. 

However, the disadvantages of a closed loop control system are that they cost much more money in comparison to an open loop control system, they are much more trickier and complex to design and construct, they require more maintenance from the user, it has a major issue with stability and it requires more attention and care in order for a stable closed loop system to be designed. (Open Loop & Closed Loop Control Systems Explained) | Electrical4U, 2020) 

Feedback 

Picture source: https://x-engineer.org/graduate-engineering/signals-systems/control-systems/open-loop-vs-closed-loop-control-systems-xcos/ 

Feedback in a control system is a part of the output that is used as a part of the system input in order to improve the performance of the control system and control the output measurement using the feedback signal. This feedback signal is compared with the reference signal to produce an error signal, which will then be filtered by a controller to generate the control input for the device. There are two types of feedback: positive feedback and negative feedback.  

(Control Systems – Feedback – Tutorialspoint, n.d.) 

(Introduction to Feedback Control Systems, n.d.) 

Loop stability 

Picture source: https://www.tutorialspoint.com/control_systems/control_systems_stability.htm 

Loop stability is the ability of a control loop to minimize errors between the measured process variable and its expected value or set point. A stable control loop will influence the procedure to get the process variable closer to the set point value, while an unstable control loop will keep the distance between the two the same or even expand it. Feedback loops are typically created to be stable allowing the process variable to gradually reach a constant steady state when the set point value is shifted or if there is an external disturbance to the process. 

There are three types of systems that are used in order to identify which type of stability system it is: An absolutely stable system is a system in which it is stable for all range of the system component values. A conditionally stable system is a system in which it is stable for a specific set range of the system component values. Lastly, a marginally stable system is a system in which it is stable by generating an output signal with fixed amplitude and frequency of oscillations for constrained input. (Control Systems – Stability – Tutorialspoint, n.d.) 

PID 

Picture source: https://www.researchgate.net/figure/Structure-of-a-proportional-integral-derivative-PID-Controller-The-output-of-a-PID_fig24_224982597 

A PID short for proportional integral derivative controller is a device that regulates process variables in a system such as the: temperature, flow, pressure, speed, and other process variables. PID controllers are the most reliable and robust controllers since they use a control loop feedback system to control process variables. 

A PID works by first receiving output from the feedback controller. A feedback controller is programmed to provide an output that allows some corrective action to be done to the process in order to move a measurable process variable like one of the ones mentioned before towards the desired value which is formally known as the set point. The feedback controller affects the process with an actuator and measures the outcome with a sensor. 

Then the PID will look at the current value of the error which was provided by the feedback control system, the integral of the error over a recent time interval, and lastly the current derivative of the error signal to evaluate not only the amount of correction it needs to make but for how long of a period as well. These three values mentioned will then each be multiplied by a tuning constant and summed together to generate the current controller output. 

(PID Controller: Types, What It Is & How It Works | Omega, n.d.) 

(Control Engineering | Basics of Proportional-Integral-Derivative Control, 1998) 

Proportional Control 

Picture source: https://en.wikipedia.org/wiki/Proportional_control 

Proportional control is a control system that works by receiving a response from the feedback control system and making an adjustment to the measured process variable to make it closer to the set point value. This adjustment made to the measure process variable is proportional to the difference between the system’s measured process variable and the set point value.  

The proportional control principle is more complicated than an on–off control system such as a thermostat, but it is much less complicated than a proportional integral derivative controller control system that is utilized in a machine such as an automobile cruise control.  

An on-off control system is more effective in the case of the system having a fairly long response time, however the problem is that this can produce instability if the system generates responses rapidly. This is where proportional control shines as it solves this issue by modulating the output to the controlling unit, such as a control valve, at an extent that prevents instability while still applying adjustment as quickly as possible using the optimal amount of proportional gain. 

An example of where this advantage is clearly demonstrated can be seen in car speed control. An on-off system for controlling car speed would work by applying either full power to the car when turned on and no power when it is turned off. It’s easy to see how this will lead to poor control and massive speed variations. The stronger the engine or heavier the vehicle, the greater the instability.  

However, with proportional control the power output is proportional to the error at all times. If the vehicle is travelling at target speed and the speed changes slightly due to a decreasing gradient, the power is decreased slightly, or in proportion to the difference in error, so that the car slows down steadily and hits the new target point with little to no overshoot which is much better and smoother than on–off control. (Proportional control, n.d.) 

Sensor signal conditioning 

Analogue signals sampling 

Picture source: https://cnx.org/contents/BvMn_Fr1@29.4:ZeNNhvxI@3/Introduction-to-Sampling 

The definition of sampling is “the method of calculating the instantaneous values of continuous-time signal in a discrete form.”. When a source produces an analogue signal that needs to be digitized, the signal must be discretized in time, with 1s and 0s. Therefore by the definition provided earlier, analogue signals sampling is the process of discretizing an analogue signal. 

In order to discretize the signals, an equal suitable gap must be selected for the sample and must be kept constant. This gap is known as the sampling period.  

The inverse of the sampling period is referred to as the sampling frequency. The sampling frequency is also commonly known as the sampling rate as well. The sampling frequency refers to the amount of samples taken per second. 

The sampling frequency must be taken into account when reconstructing an analogue signal from a digitised signal. The sampling frequency should be such that neither the data in the message signal is missing nor is it overlapped. As a result, a standard was developed for this, known as the Nyquist rate. (Pulse Code Modulation – Tutorialspoint, n.d.) 

Digital filtering 

Picture source: https://www.slideshare.net/element14/digital-filters-part-1 

A digital filter is a device that includes an analog-to-digital converter (ADC) that samples the input signal, a microprocessor, and other components to store filter coefficients and data. A digital-to-analog converter exists as well and is used just before sending output. The software that the microprocessor executes comes with a digital filter and it performs several different mathematical operations in order to product different effects like amplification and delay on the sample signal.  

Digital filters are pricier in comparison to analog filters, however the big advantage is that digital filters are able to change impractical or impossible designs into being capable of being performing.  We see digital filters being used in everyday life devices like mobile phones, radios and audio/video receivers and more. (What is a Digital Filter? – Definition from Techopedia, n.d.) 

Output 

Pulse modulation 

Picture source: https://www.elprocus.com/pulse-amplitude-modulation/ 

Pulse width modulation (PWM) is a modulation technique for reducing the average energy provided by an electrical signal by breaking it down into isolated bits. The idea is that these isolated bits formally known as pulses can represent the amplitude of an analogue input signal. The average value of voltage/current that is provided to the load is managed by rapidly turning the switch between supply and load on/off. 

Based on the workload and operation, the speed at which the power supply must turn can differ considerably. For example, an electric stove must turn multiple times a minute whereas a light dimmer must turn at 120 Hz, a motor drive would normally turn from a few kilohertz (kHz) up to tens of kHz; and audio amplifiers and computer power supplies must turn far between the tens or hundreds of kilohertz. (Pulse-width modulation, 2021) 

Operator Displays 

Picture source: https://www.questertangent.com/products/train-crew-displays/ 

An Operator display which is more commonly referred to as an HMI short for ‘Human Machine Interface’, is a user interface touch screen or dashboard which connects an individual to a machine, device or some sort of system. Operator displays are important as in industrial environments they are utilized in order to: view machine input and output, graphically display data, monitor trends, production time, display the key performance indicator and many more. 

For example, in your house you may an air conditioner system which will most likely come with an operator display that will you let monitor the temperature in the room and allow you to fiddle around with buttons like adjusting the air temperature to something more suitable for you and much more. 

To obtain and interpret information for consumers, operator displays communicate with the programmable Logic controllers and input/output sensors. Through digitising and centralising data for the consumer, operator displays allow easier access and simplification an industrial operation. Operators can access critical data in the format of graphs, charts, or other diagrams, they can also view and control alerts, and communicate with SCADA and MES devices all from a single console using the operator display. (What is HMI?, 2018) 

Simulation 

Simulating control system operation 

Picture source: https://www.controleng.com/articles/process-control-simulation-benefits/ 

There are many different types of simulations in the world right now for different things such as video game simulations, amusement park rides, animated toys, manufacturing products. When it comes to control systems there is also a simulation function which plays an important role.  

This simulation function allows you to simulate and test a control system to see how it would respond and operate in the real world, with this simulation you can then identify any keys flaws or faults in the control system which could be catastrophic such as: what would the control system do if the power failed? How would it respond if there was a temperature change in the environment? What it would do if there was interference with radio frequencies leading to a lack of communication issues and many more. This is where simulation plays its big role of allowing you to simulate these sorts of events instead of putting the control system into the real world and having to waste time and money if these things do happen and monitoring how the control system reacts and amending it so it learns to react appropriately. (Vandoren, 2003) 

Converting the control model 

Picture source: https://www.mathworks.com/help/physmod/simscape/ug/creating-and-simulating-a-simple-model.html 

When creating models for different simulations of control systems they will have different file formats. For example, there are file formats of .mdl files for models created in the software The MathsWork MATLAB, .slx files for models created in Simulink software and etc. A simulation model converted will allow you to convert your models of these file formats into a file format suitable to be used by the LabVIEW VI software.  

The LabVIEW VI software provides many different functions that are used through the simulation diagram. To perform the conversion operation, the simulation model converted will utilize the MATLAB program and the Simulink program to compile the model file and any other files that were specified as dependencies before the procedure. It should be taken into account that the conversion may not provide accurate results if the MATLAB program or Simulink program is not presently installed on the computer that is performing the conversion.  (Using the Simulation Model Converter (Control Design and Simulation Module) – LabVIEW 2018 Control Design and Simulation Module Help – National Instruments, 2018) 

Bibliography  

BBC Bitesize. n.d. Bits and binary – Introducing binary – GCSE Computer Science Revision – BBC Bitesize. [online] Available at: <https://www.bbc.co.uk/bitesize/guides/zwsbwmn/revision/1&gt; [Accessed 23 February 2021].  

BBC Bitesize. n.d. Using hexadecimal – Hexadecimal and character sets – GCSE Computer Science Revision – BBC Bitesize. [online] Available at: <https://www.bbc.co.uk/bitesize/guides/zp73wmn/revision/2&gt; [Accessed 23 February 2021].  

Techterms.com. 2015. Denary Definition. [online] Available at: <https://techterms.com/definition/denary&gt; [Accessed 23 February 2021]. 

Beal, V., n.d. ASCII Definition & Meaning | What is ASCII Code?. [online] Webopedia. Available at: <https://www.webopedia.com/definitions/ascii/&gt; [Accessed 23 February 2021]. 

 BBC Bitesize. n.d. Boolean algebra – Boolean logic – GCSE Computer Science Revision – BBC Bitesize. [online] Available at: <https://www.bbc.co.uk/bitesize/guides/zc4bb9q/revision/2&gt; [Accessed 23 February 2021]. 

Mathsisfun.com. n.d. Integer Definition (Illustrated Mathematics Dictionary). [online] Available at: <https://www.mathsisfun.com/definitions/integer.html&gt; [Accessed 23 February 2021]. 

En.wikipedia.org. 2021. Pulse-width modulation. [online] Available at: <https://en.wikipedia.org/wiki/Pulse-width_modulation&gt; [Accessed 5 March 2021]. 

Inductive Automation. 2018. What is HMI?. [online] Available at: <https://www.inductiveautomation.com/resources/article/what-is-hmi&gt; [Accessed 5 March 2021]. 

 
Tutorialspoint.com. n.d. Pulse Code Modulation – Tutorialspoint. [online] Available at: <https://www.tutorialspoint.com/digital_communication/digital_communication_pulse_code_modulation.htm&gt; [Accessed 6 March 2021]. 

Techopedia.com. n.d. What is a Digital Filter? – Definition from Techopedia. [online] Available at: <https://www.techopedia.com/definition/6840/digital-filter&gt; [Accessed 6 March 2021]. 

Vandoren, V., 2003. Control Engineering | Test Your Control System with Simulation. [online] Control Engineering. Available at: <https://www.controleng.com/articles/test-your-control-system-with-simulation/&gt; [Accessed 6 March 2021]. 

Zone.ni.com. 2018. Using the Simulation Model Converter (Control Design and Simulation Module) – LabVIEW 2018 Control Design and Simulation Module Help – National Instruments. [online] Available at: <https://zone.ni.com/reference/en-XX/help/371894J-01/lvsimconcepts/sim_c_translator/&gt; [Accessed 6 March 2021]. 

Electrical4U. 2020. What is a Control System? (Open Loop & Closed Loop Control Systems Explained) | Electrical4U. [online] Available at: <https://www.electrical4u.com/control-system-closed-loop-open-loop-control-system/#Open-Loop-Control-System&gt; [Accessed 6 March 2021]. 

Tutorialspoint.com. n.d. Control Systems – Feedback – Tutorialspoint. [online] Available at: <https://www.tutorialspoint.com/control_systems/control_systems_feedback.htm#:~:text=Advertisements,performance%20of%20the%20control%20systems.&gt; [Accessed 6 March 2021]. 

n.d. Introduction to Feedback Control Systems. [ebook] p.5. Available at: <http://www.cim.mcgill.ca/~ialab/ev/Intro_control1.pdf&gt; [Accessed 6 March 2021]. 

Tutorialspoint.com. n.d. Control Systems – Stability – Tutorialspoint. [online] Available at: <https://www.tutorialspoint.com/control_systems/control_systems_stability.htm&gt; [Accessed 6 March 2021]. 

Omega.co.uk. n.d. PID Controller: Types, What It Is & How It Works | Omega. [online] Available at: <https://www.omega.co.uk/prodinfo/pid-controllers.html&gt; [Accessed 6 March 2021]. 

Control Engineering. 1998. Control Engineering | Basics of Proportional-Integral-Derivative Control. [online] Available at: <https://www.controleng.com/articles/basics-of-proportional-integral-derivative-control/&gt; [Accessed 6 March 2021]. 

En.wikipedia.org. n.d. Proportional control. [online] Available at: <https://en.wikipedia.org/wiki/Proportional_control&gt; [Accessed 7 March 2021]. 

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