All language subtitles for 03_design-considerations.en

In the previous segment,

we looked at control using
a very simple idealized model.

What's wrong with that idealized model?

The biggest thing that's wrong is that we
assumed that the motors were capable of

producing whatever thrust
the controller required.

So in reality, if you look at this model,
the motor thrusts are limited,

because the motors have
a limited capacity.

So if I write down this equation again,
and look at forces in the vertical

direction, clearly the thrusts have
to compensate for the weight, and

the thrust that exceeds the weight,
will produce a quadratic acceleration.

But the thrust that the motor can
produce is limited by the peak torque.

So let's assume that this peak
torque is known to us, and

that in turn determines the maximum
thrust we can produce, T sub-max.

This in turn determines
the maximum acceleration.

If you look at that model,
u, the control input,

is now determined by the sum of
the motor thrust and the weight.

And of course,
this has to be a vector sum.

You have to remember that the thrust
points in the opposite direction

to the weight.

Assuming you know what Tmax is,
you can calculate umax

by simply taking the maximum thrust and
adding it to the weight.

Again, remember that the thrust is in
the vertical direction pointing up.

The weight is in the vertical
direction pointing down.

And you really need to take
the vector sum to get umax.

So now when we do PD control, u(t)

is determined not just by the proportion
of the derivative control law.

But also the maximum thrust
that can be applied.

So if you take the minimum
of these two functions,

that'll give you the true value of
the controlled input that can be applied.

The same for the PID control.

I'm gonna now show you two videos.

The only thing that's
different in the two videos

is the assumed value of maximum thrust.

On the left side,
the maximum thrust to weight ratio is 2.

And on the right side the maximum
thrust to weight ratio is 1.2.

So these two videos or

simulations illustrate the differences
between using two different motors.

Or you could ask the question,

what happens if you keep the motors
the same, but change the payload?

Again, it's only the thrust
to weight ratio that changes.

And you qualitatively get
different performances,

as you can see in these simulations.

Now, what I want you to do is
to use the same simulator,

using the control law we had before.

And study how changing
the thrust to weight ratio

effects the response of the quadrotor.

Change the mass or the payload of the
robot and see how the response changes.

Using this simulation,

you should also be able to determine the
maximum payload that the robot can carry.

Such that the performance is
within acceptable levels.