Isn't it more apropriate to have a multidimentional PID c
ntroller rather
than multipl

1 dimentional PID controllers? Or is that just the same?

I'm not sure what you mean by multidimentional PID controller, but I believe
that that it would be the same as multiple one dimentional PID controllers.

The one described is one dimentional because all variables are scalars. In a multidimentional version the target, input and output would be vectors and gains matrices. With the matrices you should be able to express interaction between the components. e.g. as you said rudder and ailerons have overlapping effects. I'd say with two 1-dimenational controllers you ignore that fact and get imperfect results.

What is the benefit of cascading PID controllers?

Lets look at an autopilot that is supposed to steer the aircraft towards the heading bug. Suppose that the only thing we can man pulate is the aileron. Obviously we need a PID controller with aileron as its output. We choose roll angle as input. Now we can set the reference to say 20 degrees, and a properly tuned PID controller will hold a 20 degree roll angle.

But how do e get it to steer towards the heading but? One solution is for
the pilot to set the reference roll angle apropriately so that the aircraft
steers toward the heading bug. Another is to let another PID controller
set the reference roll angle. The outp
t of this controller is then connected
to the reference of the first controller. This is what we call a cascade
configuration. For this example the benefit is that, well without cascading
we wouldn't be able to do what we wanted (steer towards the h
ading bug).
For situations where cascading is not required, it can still be used and
might give a more robust or smoother control loop.

could you not take the heading as input and aileron controll as output directly, since the effect of the ailerons (roll) is directly connected to change of heading.


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