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So I've been wondering this for a while; is PID just a simple but slightly outdated control method / isn't state-space (SS) a far superior method in pretty much every way?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.

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    $\begingroup$ PID is simple and works adequately for a range of applications. There are masses of classical and modern control algorithms which will be better for any single specific application. $\endgroup$
    – Eric S
    Feb 5, 2021 at 23:48
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    $\begingroup$ PID control (so-called three term controllers, which typically have upwards of 30 parameters in commercially available implementations) may well be overused, but they get the job done for many single loop applications. PID is easy to explain to beginners too, i.e. understand a little calculus but not frequency domain. As you say, state space is for multi dimensional applications, IMO. More difficult SISO situations are solved with more customized forms, pole placement etc // also state space is not necessarily time domain, I wouldn't agree with that // fractional order is a cool technique too $\endgroup$
    – Pete W
    Feb 6, 2021 at 0:34
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    $\begingroup$ A big chemical company I know of has about 100,000 closed-loop controllers in the various systems at their main plant. Imagine designing a sophisticated MPC controller for each of them. In fact, 90 % are PID controllers because it's a) good enough b) very easy to design. Only the top level control is done with sophisticated control algorithms. $\endgroup$
    – OpticalResonator
    Feb 6, 2021 at 11:20

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I do not think so. Instead of looking directly at PID, lets look at Frequency domain loop shaping in general compared to State-space control (eg, Lead-Lag filters, Notch filters and PID). On top of the fact that in the current industry over 90% of all controllers are PID's or controllers I just mentioned isnt just because they are much easier to learn, but also for a few more reasons:

  1. The bodeplot gives an amazing insight in how the controlled system is going to respond. The bandwidth, gain margin and phase margin show instant bounds in robustness and operating range. On top of that, the sensitivity bode-plot gives direct margins on how well the controlled system functions when influenced by noise. While there are some methods to assess controller robustness in State-space, these are incredibly complex to use and to analyze.
  2. Controller elements directly "shape" the bode plot (hence the name loop-shaping). eg: do you want a larger phase-margin? add a lead filter, do you want to reduce or remove the resonance peak? add a notch filter and so on. Tuning these filters use frequency values you can read directly from the current bode plot. In state-space, you have no clue whether your designed LQR-filter did remove the resonance peak other than doing a frequency analysis. If it didnt, you have no clue what to change to ensure it does.
  3. In a practical environment, the model of the system is often obtained using system-identification. Using frequency response identification, you obtain in essence the bode plot of the system, so even without an actual Laplace model of the system, you can already design a controller for it. On top of that, the nyquist plot can be used to assess stability, so really no model is required. State-space domain identification requires first of all the estimation of the number of states. On top of that, the only thing known from the returning model is that the output responds the same to the input as the actual system, what happens to the states on the other hand, is not known.
  4. While I agree that controlling MIMO systems using State Space is indeed much easier, it is in fact possible to create frequency domain controllers of a MIMO system by either decoupling or sequential loop shaping. These methods are however a tad more complex to understand and properly apply.

Of course, there are many application to which a state-space controller would outperform a frequency domain controller, but then again, there are many applications to which implementing a simple frequency domain controller that just does the job is much cheaper and faster.

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