So I've been wondering this for a while; is PID just a simple but slightly outdated control method / isn't state-space (SS) a far superior method in pretty much every way?
SS allows for MIMO, PID just SISO. SS allows for non-linear models, PID does not do non-linear models. SS allows you to see and control the states of your system, this is kind of lost in the laplace transform of PID... So given this; why do I encounter PID everywhere? Is it simpler and cheaper and good enough if it works?
I've asked this question to my mechatronic systems design professor, but I did not really find his answer all that satisfying: "State space is not going to do magic if loopshaping way of designing PID reaches its edge. State-space is time domain to design linear control while loopshaping is frequency domain. With both you can design PID."
His research group is focused on the high-tech side of things, and has made a 'fractional order' PID controller toolbox (FLOreS - Fractional order loop shaping MATLAB toolbox, essentially you place a bunch of zeros and poles close to each other to mimic something which is between e.g. s^1 and s^2). In any event, I think he might be biased so I wish to get some perspective.