This session, we will discuss about the mathematical modeling of Wacol vehicle is nothing but the math
having its weight.
If we understand the physics, when we applied the force to this vehicle, because we call it the.
Device, which will result in linear motion if we apply the force
perpendicular to the vehicle, it will result in particular velocity.
It will get you some speed and it will travel some distance at the interval of some time.
So mathematical modelling is to represent the vehicle in the form of a mathematical equation so that
we can get the.
Relation between the input and output, their input data applied for this position, it tangentially
to the will through the electric motor and output is speed, velocity and displacement.
So if we.
Represent this system as a bloc in the block diagram form, we can see the vehicle is can be represented
as a mathematical equation such that input into force and resultant output will be speed, velocity
and the distance Clarin.
We consider this terrorist threat equation, that means one will look forward, will you, the one we
your speed, velocity and distance if force is the constant, if we apply the continuous and constant
force, it will result in final, steady state speed.
That means after a certain time, not instantaneously, speed can rise up to final value.
So if we are interested in one, will your speed when we have a velocity or the distance for the airplane
for support, say, for example, speed?
So if we are having the same mathematical equation, so if we applied the force of 10 Newton Meter,
then we will be how we will to answer that for this much amount of force.
The speed will be accordingly from the calculator, from the mathematical equation.
It's called the steady state equation, but we want the dynamic modeling of the vehicle and your time
is important.
So whenever the time is in what it's called the dynamic modeling, because now what we want when we
apply the force after applying the force of a certain amount of time, what will be the speed?
This answer we want so it can be accomplished with the help of dynamic modeling after any vehicle.
So we are interested in dynamic modeling where time is involved.
So we will require the differential equation.
So that we will have the clear eyed understanding of what will be the speed at a certain time and what
the speed response, so we can also find that solution and the response time in terms of settling time
and peak our shoot, that's all requiring controller design.
So we will have the mathematical blup in this situation will represent the Wacol in the mathematical
form when applied force will result in speed and will also have time in our equation.
So we are going to design dynamic modeling of the vehicle.
The vehicle, the force is applied tangential to the wheel in this direction, so if the force is applied
in one direction, then what are the opposing force?
F is equal to M in to the first opposing force will depend upon its mass and acceleration.
If we consider V as a velocity, an acceleration will be DV by the rate of change of relativity.
So if we apply the if force is produced with the help of electric motor, this is tangential force.
The will and the opposing force is the M AI.
So we can write simple mathematical equation.
F is equal to M A is the rate of change of velocity DB with respect.
So there is time in our equation, velocity in our equation.
That means speed and forces.
There is no equation.
So this is the simplest way to represent the vehicle in the dynamic equation.
What other kinds of force that will opposed the applied force?
So depending upon the velocity, the aerodynamic drag force will oppose the vehicle depending upon the
shape of the vehicle and the environment condition that miss.
And density and all, so F.P. is also opposing force, it's called their aerodynamic drag force, which
produces the braking effect.
As with the higher speed, the opposing force will be higher.
So we can take pressure, Applied Force F is equal to M plus F, B, if we can is excerpting Inclan,
then they additional force component of gravitational force will also be opposed to applied force.
So let us understand.
The mathematical equation.
Considering the two will have the vehicle, front wheel and real will, so it will remain same for the
two wheeler as well as four wheeler.
Ideally, we can consider either forces applied to one wheel or we can cut the total supply to combiner.
What will front, as well as if the four wheel drive are considering the case of electric back to will
drive, then run or produce a tranquil platform for produce it would need to consider.
Yet for the simplicity we consider only rear wheel drive and consider this force f x at is produced.
The electric motor, and this is it will drive the vehicle, the incline angle with the horizontal surfaces,
the with yet Yaris, the city of we.
So if we can see if this is perpendicular line to the incline angle and vehicle is moving along with
this that along with this angle.
So this is 90 degrees.
And if we do the 90 degree to the horizontal surface, then this angle will also become a bit that this
is 90 degrees with this and this is 90 degrees.
This angle will become better.
So if we consider.
This component, because we are applying force in this direction, so vehicle will move in this direction
and we lost direction of velocity will be this direction.
So this component will be.
M.G. Sine Theta and this component from this photo.
This is M.G. Course Beta, so M.G. signed beta and energy costs beta.
So this opposing force to their platforms will be M.G. Costs Vita.
Represent the drag force opposing the applying platform.
It opens their platforms.
And this is the third component is also the directional Wakka.
This forces em into a debate.
Did we exist?
The relativity?
They feel that they question the total force f x if both the force mudhole, having the electric motor
then is equal to effects and plus F plus, we consider that the Yarraville that they add is equal to
M, maybe less F less M.G. sine with this all three component of the Applied Force or for their love
and the V.
Now, F.P. is the aerodynamic force, and it is equal to proportional to the square of the velocity,
so as well as it is high, the opposing force will be more the equation that from which f the amount
of meat can be calculated.
One silly is the constant InterOil.
The constant is the constant in Tahrir Square in the sign of V X.
Now you need to understand this.
In many books the FDA is given X minus one by two.
It is the regulation into rule that add density into.
The frontal area of the vehicle and velocity square.
Because.
If you consider this false.
To represent that it is negative force, which, compared to velocity and with the direction of velocity,
is for this negative.
Then also you need to change the SIGNIOR and you need to write the minus Everleigh.
But it will create the confusion in understanding this equation to simplify this.
It is better to write your Safdie the same design with plus because all three are opposing force.
So we need to consider the velocity because velocity and the force can have the difference.
And this velocity we consider is the positive and this sine will reflect it.
Yes.
Why we required this sign of the velocity because the FDA direction of body will depend upon the direction
of velocity, velocity, change.
If vehicle is moving in the right direction, then this force will be changed that direction.
So this will be always, always opposing to the direction of well, of the vehicle so that if we use
only square, then the sine will never come here.
And it always remains the positive.
Right.
So we require the sign-off velocity also so we can have the same function.
It will give only the sign that it's either minus one or plus one, depending upon the sign of the velocity.
It can be accomplished by the different simulation tool also.
But this is only the sign of velocity.
If it is positive, it will be plus one.
That means multiplying by one and if it is in the other direction, then it will be multiplied minus
one so that we will have the sign of that.
They depend upon the relative else because of Square, it will always remain.
So this is why we are having the same function.
Same velocity is used in the equation.
Now to build the simulation.
We can simplify this equation in this form and we today we may need the equal to F into F add that is
force produce and the Yarraville to the motor minus F minus the same B.
So we will also discuss about the Matlab simulation.
With the help of Matlab simulation.
We will build this model when we can discuss Imada.
During that simulation, we will discuss about the different values and components of the rule and but
let's observe the parameters.
And Mr Marcinkiewicz is the horizontal distance of the stage from front axis in meter.
That means from the center of the country to the C.G., this is the center.
The the the area will be currently in our equation.
This parameters are not required at the height of CGA from the ground, but it is required in designing
and analysis.
Analyze the performance of the vehicle.
We will see that later.
A different area in Meter Square.
So we will discuss this, a city and role in the simulation.
When we do the simulation and we see the typical value of a role for the different case.
Frontalot in meters.
Kwanten is the decoction.
We access the longitudinal relativity of a vehicle in Metropol.
Second row is the mass density ahead in Kaiji parameter to FDA.
As we discussed the aerodynamic drag force and this is the Farishta Applied Force and the Rundquist
and therefore is the applied force at the table.
And Adeste, that Eleazar will say if we want to transport the thought and calculate it into force multiplier
by various.
So ultimately this simple mathematical equation F is equal to maybe by DETI plus F.T. Plus M designed
to represent the vehicle in the dynamic.
So the dynamic equation Boutet presenta any vehicle.
This force can be generated by changing our motor or by any way.
But the mathematical equation, dynamic equation of a vehicle will remain c.