MatLAB Answers

A rain drop of mass 3gm starts to fall from rest under the effect of gravity from a height of

100m. There is an air drag acting on the rain drop, the drag force is given by the equation,

Fd = bv.

Here, b = a × 10^-3kgs^-1s

a = 2

(a) Determine the governing differential of the system.

(b) Build a SIMULINK model of the system using transfer functions.

(c) Show velocity vs time graph with and without the effect of air drag on the same

plot.

(d) Show height vs time graph with and without the effect of air drag on the same

plot.

(e) From your graphs, determine the approximate time required for the rain drop to

reach the ground.

Plot on the same figure the calculated acceleration and the classification variable ds mapping against time. Use left side y-axis and a line style to plot the acceleration. Use right side y-axis to illustrate the driving style classification. Hint: You may use plotyy to complete this task. Add labels to all axes. Add legend to the figure.

Table 1 below : Example of classification

acceleration value

-1.2 1

1.23 1

3.2 2

-4.3 3

9.5 0

ds mapping values

1

1

2

3

On the same figure plot all four obtained powers in kW against time. Use different line styles for each power, e.g. solid line, dashed line, dotted line or dash-dot line. Add labels to all axes. Add title, legend and grid to the figure.

t = 0:1:100;    %Time Step

Load = 10;  % Ohms

P=[ ];       %power

Vel = [ ];   %Speed

Gear= [ ];   %Gear

SOC = [ ];   %Soc

V = [ ];     %Voltage

A = [ ];     %Current

for r=1:length(t)

    V(r)=100*rand;

    A(r) = V(r)/Load;

    P(r) = V(r) * A(r);

    Vel(r) = V(r)*rand();

    SOC(r) = Vel(r)*rand;

    Gear(r) = SOC(r)*rand();

end

scrsz = get(0,'ScreenSize');

Dim=0;

figure('Position',[scrsz(1)+Dim, scrsz(2)+Dim,scrsz(3)-20,scrsz(4)-100]);

    Use the battery voltage and current data imported to calculate the battery power P as follows 

    P = UI where P is the battery power [W], U is the battery voltage [V] and I is the battery current 

    [A] battery voltage in V [Pack Volts]

    battery current in A [Pack Amps]  

 2. Plot each variable listed below against time in a form of subplot. 

    There should be 6 subplots in a single figure aligned in 2 columns and 3 rows. 

    Use different line colour for each data. Add labels to all axes.

    • time in seconds [Time]

    • speed in km/h [Speed]

    • gear [Gear]

    • elevation in meters [Elv]

    • SOC (state-of-charge) in % [SOC]

    • battery voltage in V [Pack Volts]

    • battery current in A [Pack Amps]

%}

On the same figure plot all four obtained powers in kW against time. Use different line styles for each power, e.g. solid line, dashed line, dotted line or dash-dot line. Add labels to all axes. Add title, legend and grid to the figure.

Knowing that average acceleration in a time interval ∆t = ti+1 − ti can be expressed as 𝑎𝑖 = 𝑣𝑖+1 − 𝑣𝑖 / ∆𝑡

where vi+1 − vi is the change in velocity between successive measurements,

write a code to:

Calculate acceleration in m/s2 using speed and time data extracted from the dataset. Hint: You may use for ... end loop to complete this task.

Data extracted:

time in seconds [Time]

• speed in km/h [Speed] 

Plot on the same figure the calculated acceleration and the classification variable ds mapping

against time. Use left side y-axis and a line style to plot the acceleration. Use right side

y-axis to illustrate the driving style classification. Hint: You may use plotyy to complete this

task. Add labels to all axes. Add legend to the figure.

Driving Style: Normal, Acceleration = 0.70 m/s2

Driving Style: Economic, Acceleration = -2.30 m/s2

Driving Style: Economic, Acceleration = 2.31 m/s2

Driving Style: Economic, Acceleration = -3.30 m/s2

Driving Style: Economic, Acceleration = 3.31 m/s2

Driving Style: Agressive, Acceleration = -8.50 m/s2

Ds mapping

NORMAL = 2;

ECONOMIC = 5;

AGGRESSIVE=8;

Create variable ds mapping to store corresponding classification values of 1,2 or 3, which represent different driving style as shown in Table 1. You need to evaluate only the magnitude the of the acceleration/deceleration. If the acceleration value is outside the defined ranges assign 0 as its classification.

Table 1 (4 by 2)

Driving style Economic (1) Normal (2) Aggressive (3)

Acceleration magnitude [m/s2 ] 0.7-2.3 2.31-3.30 3.31-8.5 

Economic (1)

0.7-2.3

Normal (2)

2.31-3.30

Aggressive (3)

3.31-8.5 

Use the battery voltage and current data imported to calculate the battery power P as follows P = UI where P is the battery power [W], U is the battery voltage [V] and I is the battery current [A]

battery voltage in V [Pack Volts]

battery current in A [Pack Amps]

2. Plot each variable listed below against time in a form of subplot. There should be 6 subplots in a single figure aligned in 2 columns and 3 rows. Use different line colour for each data. Add labels to all axes.

• time in seconds [Time]

• speed in km/h [Speed]

• gear [Gear]

• elevation in meters [Elv]

• SOC (state-of-charge) in % [SOC]

• battery voltage in V [Pack Volts]

• battery current in A [Pack Amps]

Knowing that average acceleration in a time interval ∆t = ti+1 − ti can be expressed as 𝑎𝑖 = 𝑣𝑖+1 − 𝑣𝑖 / ∆𝑡

where vi+1 − vi is the change in velocity between successive measurements,

write a code to: 

3) Calculate acceleration in m/s2 using speed and time data extracted from the dataset. Hint: You may use for ... end loop to complete this task.

Driving style Economic (1) Normal (2) Aggressive (3)

Acceleration magnitude [m/s2] 0.7-2.3 2.31-3.30 3.31-8.5

Table format: as seen above

Economic (1)

0.7-2.3

Normal (2)

2.31-3.30

Aggressive (3)

3.31-8.5