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# Assessed Matlab Practical 1-Modelling a Fuel Tank Aim: To use Simulink to analyse the performance of a first order system and control the performance by adjustment of a controlling variable. A classic example of a first order system is a tank that contains liquid (see example 1.1 in chapter I of Introduction to Systems Modelling notes available on StudyNet.) The physical dimensions of the tank (i.e. the height, $\mathrm{h}_{\text {mas }}$ and the cross-sectional area, $\mathrm{A}$.) aro generated from your identity number on your ID card. (Type in your SRN number into "AMP__ results_sheet.xlsx" and the data will appear). As you complete cach of the following tasks type your answers in the white cells on the Results Sheet. When you have completed all the tasks, or as much as you feel you can do, submit the Results Sheet using the assignments facility on Studynet. Develop a Simulink Model The differential equation that models the beight of liquid in a tank of uniform cross sectional area is: $q_{i}=\frac{1}{R} h+A \frac{d h}{d t}$ Using the procedure given on the Introductory Simulink Instruction sheet (available an StudyNet) draw an analogue diagram and hence develop a Simulink model assuming the flow rate in (qi) is the input and the height of liquid in the tank, $\mathrm{h}$, is the output. 1. Filling the tank ( $30 \%)$ a) If the tap on the output pipe is closed $($ i., $\mathrm{R}-\infty)$ determine how loag it will take the tank to fill up assuming qi $=0.001 \mathrm{~m}^{3} / \mathrm{s}$. The physical dimensions of the tank (i.e. the height, $\mathrm{h}_{\max }$ and the cross-sectional area, A.) are generated from your identity number on your ID card. (Type in your SRN number into "AMP___results_sheet.xlsx" and the data will appear). As you complete each of the following tasks type your answers in the white cells on the Results Sheet. When you have completed all the tasks, or as much as you feel you can do, submit the Results Sheet using the assignments facility on Studynet. Develop a Simulink Model The differential equation that models the height of liquid in a tank of uniform cross sectional area is: $q_{i}=\frac{1}{R} h+A \frac{d h}{d t}$ Using the procedure given on the Introductory Simulink Instruction sheet (available on StudyNet), draw an analogue diagram and hence develop a Simulink model assuming the flow rate in (qi) is the input and the height of liquid in the tank, $\mathrm{h}$, is the output. 1. Filling the tank $(30 \%)$ a) If the tap on the output pipe is closed (i.e. $R-\infty$ ) determine how long it will take the tank to fill up assuming $q \mathrm{i}=0.001 \mathrm{~m}^{3 / \mathrm{s}}$. b) If the tap on the output is open liquid will be coming out at the same time as liquid is going in. If the flow rate in is bigger than flow rate out the height of the liquid in the tank will rise. Using the $\mathrm{R}$ value given on the Results Sheet, determine the steady state beight of liquid in the tank assuming $q \mathrm{i}=0.001 \mathrm{~m}^{3} / \mathrm{s}$. c) In theory it will take an infinite amount of time to achieve steady state so in practice we define the time to respond as the $95 \%$ settling time (i.e. the time taken to get to within $5 \%$ of the steady state output.) Measure the $95 \%$ settling time from your simulation in Q1b). Dimensions: A = 1.92m^2 hmax = 0.548m Civn answen to atlesur 3 signifcant fgures. 1. Fring the tak [row) Teme 8 til the tatk * ne: $\operatorname{tin}=\text { asc }$ Assessed Matlab Practical 1 - Modelling a Fuel Tank Aim: To use Simulink to analyse the performance of a first order system and control the performance by adjustment of a controlling variable. A classic example of a first order system is a tank that contains liquid (see example 1.1 in chapter 1 of Introduction to Systems Modelling notes available on StudyNet.) The physical dimensions of the tank (i.e. the height, $\mathrm{h}_{\max }$ and the cross-sectional area, A.) are generated from your identity number on your ID card. (Type in your SRN number into "AMP_ I results sheet $x$ Isx" and the data will appear). As you complete each of the following tasks type your answers in the white cells on the Results Sheet. When you have completed all the tasks, or as much as you feel you can do, submit the Results Sheet using the assignments facility on Studynet. Develop a Simulink Model The differential equation that models the height of liquid in a tank of uniform cross sectional area is: $q_{i}=\frac{1}{R} h+A \frac{d h}{d t}$ Using the procedure given on the Introductory Simulink Instruction sheet (available on StudyNet), draw an analogue diagram and hence develop a Simulink model assuming the flow rate in (qi) is the input and the height Develop a Simulink Model The differential equation that models the height of liquid in a tank of uniform cross sectional area is: $\mathrm{q}_{\mathrm{i}}=\frac{1}{\mathrm{R}} \mathrm{h}+\mathrm{A} \frac{\mathrm{dh}}{\mathrm{dt}}$ Using the procedure given on the Introductory Simulink Instruction sheet (available on StudyNet), draw an analogue diagram and hence develop a Simulink model assuming the flow rate in (qi) is the input and the height of liquid in the tank, $h$, is the output. 1. Filling the $\operatorname{tank}(30 \%)$ a) If the tap on the output pipe is closed (i.e, $\mathrm{R}=\infty$ ) determine how long it will take the tank to fill up assuming $q i=0.001 \mathrm{~m}^{3} / \mathrm{s}$. b) If the tap on the output is open liquid will be coming out at the same time as liquid is going in. If the flow rate in is bigger than flow rate out the height of the liquid in the tank will rise. Using the $R$ value given on the Results Sheet, determine the steady state height of liquid in the tank assuming $\mathrm{qi}=0.001 \mathrm{~m}^{3 / / \mathrm{s}}$. c) In theory it will take an infinite amount of time to achieve steady state so in practice we define the time to respond as the $95 \%$ settling time (i.e, the time taken to get to within $5 \%$ of the steady state output.) Measure the $95 \%$ settling time from your simulation in Q1b).  