FUZZY CONTROL

- an identification module using (fuzzy/ lazy learning/ classical linear) techniques.
- a multiple input, multiple ouput, multiple step ahead, direct self-adaptive fuzzy controller.

GPC controllers have often some difficulties with minimum phase systems. In these kind of systems, we must first increase the error

The red box underneath is a roller cart controlled by a motor that pulls
it to the left or right according to the controller's command. A blue pendulum
is attached on top of the roller cart. The goal of the controller is to use
the motor to keep the pendulum in balance (vertical) and the roller cart at
a precise * x** position. If
the current position is

You can see an example of control of an inverted pendulum in the java applet
above. The blue line is the current * x*
position of the cart. The green line is the control signal

The regulator develloped in IRIDIA is able to simulate the behavior of the
process to control using (fuzzy/ lazy learning/ classical linear) predictors
(or a mix of them, one different predictor for each output of the system to
control). The lazy learning predictor can be trained on-line as illustrated
in the figure below (manifold pressure control in a Gasoline
Direct Injection engine(GDI)). The TAKSUG line stands for *Takagi Sugeno
fuzzy sets* predictor. The LAZY line stands for the *lazy learning*
predictor.

Another example is the control of this simple toy problem: .

The result is the following:

Once again, note the typical pattern present in the non minimum phase systems

"Edy Bertolissi, Antoine Duchâteau, Hugues Bersini, Frank Vanden Berghen. Direct Adaptive Fuzzy Control for MIMO Processes, Accepted to the FUZZ-IEEE 2000 conference, San Antonio, Texas, 7-10 May, 2000" is downloadable here.

A chapter of a book in french on fuzzy control is downloadable here.

An internal IRIDIA report describing in more depth the algorithm is available here (only in French).

A paper describing the identification modules of the NLMIMO toolbox is here.

The latest version of the NLMIMO toolbox (july 2000) is here. You must have matlab 5.0, 5.1 or 5.2 to have all functionalities. In matlab 5.3, the control modules are not functioning. In matlab 6.0, nothing works (there is a conflict between the name of the new function called 'system' in matlab and the name of the 'system' class).

An on-line
book on control theory with many examples in java applets.

A revolutionary methodology for optimal control : the Q-learning.

R. Babuska. Fuzzy
Modeling for Control. Kluwer Academic Publishers, Boston, 1998.

HANUS, Raymond ; BOGAERTS, Philippe, Introduction à l'automatique.
1, systèmes continus

Bruxelles : De Boeck Université 1996, 312 p.ISBN: 2-8041-2108-9 is
an excellent french book. You can order it here.

HANUS, Raymond ; BOGAERTS, Philippe , Introduction à l'automatique.
2, systèmes discrets et échantillonnés

Bruxelles : De Boeck Université 2000, 296 p. ISBN: 2-8041-2368-5 is
an excellent french book. You can order it here.