“We can only use PID control if the system model $\dot{x} = f(x, u)$
is known. Otherwise, we do not know how the states will change over
time, can therefore cannot solve for the gains $K_p$, $K_i$, and
$K_d$.”
Is Ben's claim correct? Circle one.
YES NO
Ben's claim is NOT CORRECT. The gains in PID controller are generally
tuned experimentally, and the system model is not required.
The idea of solving the system model equation for $K_p$, $K_i$, and
$K_d$ does not make much sense, since those gains do not appear in a
typical system model equation.
Note that the system model can make predictions about how the
state will change in the future, which is a different question from
whether the robot can observe the states as they occur. The
latter is what we need to use PID control.
Finally, recall that the whole point of feedback control is that we may
not have an accurate description of how the states will change in
response to actions.