Individual Assignment
Practice Modelling and Simulation
Authors
Mitul Saini, Sanket DuttaAishwarya Aswal
Module
Systems Modelling
Date
October 7, 2019
Deadline
October 28, 2019
1 Introduction
Mostly in the places with water bodies and with suicient rainfall water dams are of common practice. These structures not only serve the purpose of electricity generation and water distribution but also are a key aspect for the safety in case the water level rises above the safety limit because of excessive rainfall. In this assignment we will be focusing on the safety aspect of these structure. The simplified schematic of the system of a water dam is shown in the figure1.1:
Figure 1.1: Schematic of the water dam
The system consists of:
A gate with mass m on one side of the river storing the water for use in future
A reservoir with a height hr and length lr
A pulley with radius rp
A gearset with teeth N1 and N2
A DC motor with inertia J, Damping D, Inductance L, Resistance R and the supply voltageVs
As the water level rises on the left side of the gate and crosses the safety limitdue to excessive rainfall etc., the gate is lifted using a ropechain connected to the mass through a pulley which in turn is controlled by a DC motor. As the gate is lifted, the water flows into the reservoir and the water level of the river is brought below the danger level. As the water flows into the reservoir, it would be of interest to study how much the level of water increases when the gate is opened for a certain amount of time. The working schematic of the system is shown in the figure?? below.
i
RL Vs
rp
DC motor
J,D
River water
Ground hr
N1 N2
m
lr
Reservoir
Figure 1.2: Working of the water dam
2 Problem Definition
As a research engineer, it is your task to research whether the given DC motor with the given supplied input voltage will be able to lift the dam gate in case of extreme situations or not.
3 Simulink Modelling
The DC motor combination can be modeled using a mechanical and an electrical equation. The mechanical equation is:
and
The electrical equation is:
KtiJdD dt
VsLdiiRKbd dt dt
Further on, the torque of the motor can be calculated using the formula,
TmKti
The gearset can be modeled using simple constant amplification of the torque as follows:
TgearoutN2Tm N1
ii
RL Vs
rp
DC motor
Tm,m J,D
N1 N2
River water
Ground hr
m
ylift
Fma
Lwater
Reservoir
The pulley converts the rotational output of the motor to the vertical translation of the gate through a rope. The equation representing the conversion is as follows:
FropeTgearout rp
Using a simple free body diagram the equations of the lift of the gate can be represented as follows:
Fropemgmd2y dt2
Once the lift of the mass is known, the rise of water level in the reservoir can be easily represented through flow equationsflowrate balance between the reservoir and the area of the opening created through the lift of the mass. The equation are:
where,
ArdLwaterAopeningvwater dt
ArArea of the reservoir in metre sq.
LwaterLevel of the water in the reservoir in metres
AopeningArea of the opening created due to lift of mass in metre sq. vwaterExit velocity of water through the opening in msec
The area of the opening can be calculated using the dimensions of the dam gate and the lift of the gate. Figure1.1 shows the side view of the entire system. The 3D view of the dam gate with its dimensions is shown in the figure?? where,
lmLength of the gate in metres hmWidth of the gate in metres wmHeight of the gate in metres
hm
lm
Figure 3.1: Dimensions of the gate
Similarly, the area of the reservoir can be calculated using the dimensions of the reservoir, the 3D view
iii
wm
of the reservoir is shown in figure??.
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Model Verification
where,
hr
Figure 3.2: Dimensions of the reservoir
lrLength of the reservoir in metres hrWidth of the reservoir in metres wrHeight of the reservoir in metres
lr
Model verification is a step in which you run your system for different scenarios and observe whether the results you are getting are consistent with your knowledge of the system. Verification ensures that the model has been translated from differential equation into a simulink diagram correctly. The following model parameters should be chosen to verify the model:
R0.025 ohms Kt 2.47 Nm
A
Kb 0.33 Vsec rad
L0.23 103H J0.05 102Kgm2
D1.265 Nmsec rad
m3800 Kg N21250
N1125
rp0.375 m
iv
wr
5
lm2 m wm0.3 m hm12 m
lr500 m wr20 m hr20 m
vwater75 m sec
Run the following scenarios, show the simulation results and comment briefly on the results.
Give a step voltage input of 0 to 400 volts at 0.1 sec to the system. Run the simulation for 50 seconds and research the lift of the gatemass and the change in level of water in the reservoir and keep in mind that the gate can be lifted to the maximum vertical distance of 1.5 m.
Choose your own input400 V type and run the simulation for 50 seconds and comment on the response of the system. Choose the outputs you want to comment on and mention why you chose those outputs.
The following outputs plots should be generated from the simulation:
a figures displaying the voltage as input, mass lift and the water level as outputs.a figure displaying the torque vs current of the motor.
Model Validation
Validation of the model is most important thing within a project. How much do our model results comply with the test results? Does our modeled system behave like the actual physical system within a certain framework? These questions can only be answered through validation. We can validate our model using comparison to the test data but in many cases, the test data is not available to us. In that case, changing the parametersi.e sensitivity analysis can be used to validate our model. Use the following approaches to validate your model:
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Import the data file InputOutputData.xlsx of the test results and match them with the obtained model results, choose the vehicle parameters given above. In case you find deviationswhich is the most obvious case, comment on why could these deviations be present and because of what reasons. Use the input data from the imported data to run the simulation and compare the model results with the actual results.
Make a sensitivity analysis of 10 increase and decrease of the parametersone parameter at a time m, Arand Kt on the outputs of the system. Choose your outputs wisely and comment on why you chose the outputs.
State space
Create the state space for the systemHint: It would be wise to create a statespace for each subsystem separately. Find the A, B,C and D matrix for this system and model it in simulink to match the results
v
with the differential equation model. What do you observe?
Note: You might encounter some problems in the state space of the gatemass. It will be interesting to see how you tackle that hurdle.
7 Transfer Function
After you have achieved the state space, use matlab to convert the state space into the transfer functionor you can create a transfer function of the entire system from scratch as well. Match the results of the transfer function with the state space and the differential equation model and comment what you observe.Is it possible to obtain a single equivalent transfer function of the system?
Note: Similar to the state space you might encounter some problems with the transfer function of the mass. Hint: Can you consider it as a multiple input system?.
8 Bonus Question
As a systems engineer, you have been asked by your company to downsize your motori.e smaller voltage and different constants for the same system. That means you have to get the same system to produce similar outputs using a smaller motor. Hint: Keep in mind that it is neither feasible nor wise to reconstruct the dam and its components like the gate and the reservoir. Think as an engineer and bring interesting solutions on to the table.It would be interesting to know that as an engineer what kind of a solution you come up with. Explain your modified system architecture and back it up with solid arguments in your report. Consider following points for the required analysis:
Plot input and outputs of the new system and comment on the behavior of the system.Do you think is your proposed solution correct? is it feasible?
How close to the actual system response can you get using your proposed solution.
9 Deliverables
The simulation model created in simulink version r2017b or further.
One mfile containing all your preprocessing commands, your simulation commands and your postprocessing commands with proper comments and structure.
All the files required to run your model.
A PDFfile in which all graphs and a conclusion is given with respect to:
A validation of the simulation model
All graphs and figures created by the mfile for model verificationThe state space obtained the results
The transfer function for the system and the results
Analysis on the bonus partif attempted
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10 Assessment
Your individual assignment will be assessed only if it meets the following conditions:
The deliverables are handed in through softcopy before or on the day of the deadline October 28, 2019 with the responsible lecturer to their email IDs.
Mitul.Sainihan.nl
S.Duttahan.nl
Aishwarya.Aswalhan.nlHatim.Malahan.nl
All files are delivered in one zip file. Your assignment should be in pdf format and not longer than 8 pages including the cover page but excluding bonus question.
The report is properly structured and professionally formatted. Extra marks will be taken off for grammatical errors.
Copying other students Simulink model, Matlabcode, figures or conclusions is considered fraud and will be reported to the exam committee. The same accounts for the student sharing his individual work with others.
No print screens are used to visualize simulations.
11 Marking Scheme
Your deliverables are assessed according to the following criteria:Correct and orderly modeling in Simulink 15p
Correct and logical coding in matlab 15p
Correct and complete visualisation 10p
Correct verification 20p
Correct validation 20p
Correct State Space 10p
Correct Transfer function 10p
Correct Bonus question max 10p
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