If the Quadcopter is a MIMO Nonlinear System, How Can it be Controlled using PID?
Exactly as you mention later:
Does the model need to be linearized so that PID algorithms can be used?
Yes, that's correct.
To be a little more explicit, you need two things:
- linearise the system (usually around a so-called "working point", e.g. cruise conditions)
- de-couple the system (because a linearised MIMO is still a MIMO, you need a set of 4 SISOs)
Achieving the first is fairly simple, as I mentioned, you "only" have to select a working point. The second is instead a little more elaborate, and requires making assumptions on the flight conditions that will be encountered, plus it is not always possible, some vehicles have their dynamics so coupled that de-coupling is not an option (and thus simple PIDs tend to be not a viable option if you have to tune them manually).