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 Trust's have to compensate
for the weight and the thrust that
exceeds the weight will produce the
required acceleration but the trust 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 you 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 T Max's you can
calculate u max 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 u max so now
when we do PD control U of T is
determined not just by the proportion
plus derivative control law but also the
maximum trust that can be applied so if
you take the minimum of these two
functions that'll give you the true
value of the control input that can be
applied
the same for the PID control I'm going
to 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 two and on the right
side the maximum thrust to weight ratio
is one point two so these two videos or
simulations illustrate the differences
between using two different motors or
you can 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 affects the response of
the quadrotor change the mass or the
payload of the robot and see how the
response changes using the simulation
you should also be able to determine the
maximum payload that the robot can carry
such that the performance is within
acceptable levels