What is a modelling? What is a control?

The history of control engineering may be started from the feedback for tracking problem. Just feedback difference of a current and an ideal point to an actuator. It had been simple on the start. Behind that, there are laplace transform, linear algebra, and many other mathematics. Thinking mathematically, it is possible to change dynamical characteristics of dynamics of a system such as a robot. If it were possible to modify dynamical characteristics of a system by control input, design of a system is not required to be accurate? What is a modelling? What is a control, then?

What is a modelling? Enough structure to express actual thing. If it were article of physics, that is fine. Fitting or correlation between experiment and theory made could be around 70%. 100%? That cannot be.

What is a control? It would be said that that is to make better behaviour of controlled dynamics. Feedback is a better strategy to make better dynamics.

That would be OK for parameter difference. That would be OK for unmodelled dynamics whose effect is not so large. If major dynamical behaviour is not so different.

That would not be OK to cancel out major nonlinear effect since it could be large control input and there may be limitation of control input. That means that is not OK even one can deploy linear control analysis technique for system with cancelling out nonlinear effect. For worst case, a system would be broken because of large control input. The another point is author would suppose that nonlinear nominal system has better robustness and it has very interesting characterics. Thus, it would be said that it is nonsense to cancel out system's nonlinear effect.

It is not possible to make 100% correct model even modelling gets complex. The first one it was seen by author is experimental result of master's student of CFRP group of University of Tsukuba. But that's fine since there is robust control. But better understanding of modelling is required as described above since there is limitation of control input.

If it were linear system, linear algebra or laplace transform is enough to control. If it were nonlinear? Not sure. But cancel effect of nonlinear? No as described above. But it is supposed that it would be better to utilized nonlinear specific characteristics to control with minimum effort. Author suppose that there would be control method which utilize better than linear one in the sense of transient response and energy applied or even robustness of a system gets better if nominal system is nonlinear.

One can imagine that if control effect is dominant to dynamics of an actual system and change the dynamical behaviour as better way. If the objective of control is just tracking, that is fine to do negative feedback. However, if an objective of control is to make better behaviour and that cannot be done by mechanical design of implementation, control would be required. In theory, that is correct. But in practice, it is sometimes incorrect. Since there are control input limitation described as above.

That means that control engineering is interaction between theory, numerical simulation, experiment and application. An idea of feedback control seems simple, but as desicussed as above, phylosophically speaking, it is complex since one should think what is a control even for practical situation.