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In real world, PID is dominating because PID is a very good controller and it's very easy to tune in.

But there are also LQR(Linear Quadratic Regulator), LQG(Linear Quadratic Gaussian Regulator), MRAC(Model Reference Adaptive Controller), ILC(Iterative Learning Control), MPC(Model Predictive Control) available etc.

Those controllers are assumed to be very advanced, but I don't agree with that. For example: Do do a MRAC(SISO) controller, just follow these steps:

  1. Choose model complexity $n$ and find $A^o$ and $A^m$.
  2. Estimate ARX model parameters by RLS (Recursive Least Square)
  3. Solve Diophantine Equation
  4. Calculate polynomials $R$ and $S$
  5. Compute polynomial $T = A^oB^m$
  6. Compute control law signal from $u = -\frac{S}{R}y+\frac{T}{S}r$
  7. Go to step 2

So all you need to do is to choose the MODEL STRUCTURE, for example zeros and poles for ARX model. Then you estimate the ARX model by using simple least square.

The Diophantine Equation is only a difference equation. Now, compute the new control law. The end! Those steps can be found in Karl-Johan Åström's famous Book "Adaptive Control".

Question: So why are books so advanced when it comes to control engineering, but the controllers are very simple? Are books assuming that I should use the best optimized LQG controller? When I asking control theorist about LQG, they answer me with that LQG are most of times always tuned in manually because it's to hard to find a linear model who is like a mirror of the real process.

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  • $\begingroup$ It is very difficult to.make sense of what you wrote. $\endgroup$ – Mariano Suárez-Álvarez Jan 8 '18 at 20:35
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    $\begingroup$ So I assume PID does not stand for principle ideal domain? $\endgroup$ – Hagen von Eitzen Jan 8 '18 at 20:57
  • $\begingroup$ My question is simple: Why are control engineering books so advanced, when the controllers are so simple? $\endgroup$ – Daniel Mårtensson Jan 8 '18 at 20:57
  • $\begingroup$ @HagenvonEitzen No. PID stands for Propotional Integrator Derivative. $\endgroup$ – Daniel Mårtensson Jan 8 '18 at 20:58
  • $\begingroup$ @HagenvonEitzen it is a Proportional Integrating Differentiating circuit. Lap transform $a+bs+cs^{-1}$ $\endgroup$ – mathreadler Jan 8 '18 at 22:03
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You already asked a very similar question here: Transfer function technique VS State space technique

The "advanced" techniques simply do not give such a big of performance improvement w.r.t. the simple techniques. In 99% of the systems the small performance which is to be gained by the advanced techniques is neglect-able. Furthermore all the control engineering books you refer to are university grading books.

Again I tell you, take a look at feedforward control. In my work we are dealing with accelerations of 50 m/s^2 but need to obtain nanometer precision of a platform weighing more then 25 kg. We achieve this simply by a simple PID feedback controller with some notches and a very very accurate feedforward controller. About 95% of the energie of the control output is from the FF controller and 5% of the FB controller. Another reason we do this is because the controller needs to be debugged. Again the answer which I provided in the topic I refer to still holds.

Remember: Everything Should Be Made as Simple as Possible, But Not Simpler

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