# All advanced controller - Are they always used as optimized controllers?

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.

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