Where the above statement is true for 2D systems, based on my limited
experience on 4D systems, I would like to point out that even near
the set point, a FLC could outperform a P(I)D controller for 4D systems.
The reason is below:
We know for 4D system, a system trajectory oscillates a lot with a P(I)D
controller, and a trajectory goes to the set point after several
oscillations. This kind of trajectory is energy-comsuming, time-consuming.
There are possibilities that a better trajectory exist within the
objective's ability, and all the control commands along this better
trajectory is a nonlinear function of system states. A FLC can approximate
this nonlinear function fairly well whereas a P(I)D could never do.
So even when system is near the set point, a P(I)D controller still
cause lots of oscillation, by contrast, a FLC can directly drive the
objective to the set point without much oscillation.
I have designed a LQR and a TS type FLC for a 4D inverted pendulum, lots
of trajecotries tell me that the FLC drive the pole and cart directly to
the set point, whereas the LQR always drive the pole and cart in an
oscillating way, which costs lots of time and energy.
Since I am sitll quite a naive in this field, I may have wrong
understanding and please excuse me if did make the mistake.
I would thank you very much if you could point out any mistakes. Your time
on this will be highly appreciated.
Feijun Song
Ph.D candidate
Ocean Engineering Dept.
Florida Atlantic Univ..
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