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###### 日期：2019-10-11 11:06

Individual Assignment

Practice Modelling and Simulation

1 Introduction

Mostly in the places with water bodies and with sufficient 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 figure(1.1):

Reservoir Ground River water DC motor R L

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’ and the supply voltage‘Vs’

As the water level rises on the left side of the gate and crosses the safety limit(due to excessive rainfall

etc.), the gate is lifted using a rope(chain) 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.

Reservoir Ground River water DC motor R L

Lwater ylif t F = ma Tm, θm

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.

The DC motor combination can be modeled using a mechanical and an electrical equation.

The mechanical equation is:

The electrical equation is:

Further on, the torque of the motor can be calculated using the formula,

Tm = Kt· i

The gearset can be modeled using simple constant amplification of the torque as follows:

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:

Using a simple free body diagram the equations of the lift of the gate can be represented as follows:

Once the lift of the mass is known, the rise of water level in the reservoir can be easily represented

through flow equations(flow-rate balance) between the reservoir and the area of the opening created

through the lift of the mass. The equation are:

Ar·dLwater

dt = Aopening · vwater

where,

Ar = Area of the reservoir in metre sq.

Lwater = Level of the water in the reservoir in metres

Aopening = Area of the opening created due to lift of mass in metre sq.

vwater = Exit velocity of water through the opening in m/sec

The area of the opening can be calculated using the dimensions of the dam gate and the lift of the gate.

Figure(1.1) shows the side view of the entire system. The 3-D view of the dam gate with it’s dimensions

is shown in the figure where,

lm = Length of the gate in metres

hm = Width of the gate in metres

wm = Height of the gate in metres

Figure 3.1: Dimensions of the gate

Similarly, the area of the reservoir can be calculated using the dimensions of the reservoir, the 3-D view

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of the reservoir is shown in figure.

Figure 3.2: Dimensions of the reservoir

where,

lr = Length of the reservoir in metres

hr = Width of the reservoir in metres

wr = Height of the reservoir in metres

4 Model Verification

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:

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 gate(mass) 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 input(400 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 figure(s) displaying the voltage as input, mass lift and the water level as outputs.

- a figure displaying the torque vs current of the motor.

5 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 parameters(i.e sensitivity analysis) can be used to validate our model. Use the following approaches

? 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 deviations(which 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 parameters(one parameter at a

time) ‘m’, ‘Ar

’and ‘Kt

’ on the outputs of the system. Choose your outputs wisely and comment on

why you chose the outputs.

6 State space

Create the state space for the system(Hint: It would be wise to create a state-space for each subsystem

separately). Find the A, B,C and D matrix for this system and model it in simulink to match the results

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with the differential equation model. What do you observe?

Note: You might encounter some problems in the state space of the gate(mass). 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 function(or

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 system’s engineer, you have been asked by your company to downsize your motor(i.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 m-file containing all your pre-processing commands, your simulation commands and your

post-processing commands with proper comments and structure.

? All the files required to run your model.

? A PDF-file 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 m-file for model verification

– The state space obtained the results

– The transfer function for the system and the results

– Analysis on the bonus part(if 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 soft-copy before or on the day of the deadline (October 28,

2019) with the responsible lecturer to their email IDs.

? 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 student’s Simulink model, Matlab-code, 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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