Neuro-Fuzzy Modeling and Fuzzy Control of a Fast Ferry - Fuzzy Modeling and Control: Theory and Applications - page 188

Fig. 10.5 Actuators operating at the encounter frequency, regular waves

10.3.2 Fuzzy-PID Sugeno Type Control

A Sugeno-type controller has also been considered. In this case the inputs are the
error, change in error, and integral of error (PID-like). The error is defined as the
Worst Vertical Acceleration (WVA), that is, the vertical acceleration at theworst place
of the craft (40m to the c.o.g. of the ship). Although it is not physically possible to
completely eliminate the vertical oscillations, the results were better when the system
was forced to minimize the acceleration to the greatest extent possible.
The outputs are the working angles of the actuators. In fact, two different con-
trollers have been implemented, one for the flap and another for the T-foil, with
different output range. The motion of the flap is limited upward (0 ◦ -15 ◦ ) and the
wings of the T-foil can freely move upward and downward (

15 ◦ to 15 ◦ ).
The initial controller is a Mamdani fuzzy PD with a crisp integral action (chosen
to avoid steady state error), that is, a Fuzzy PD

−

I. The seven membership functions
of the input and output variables are triangular, and evenly distributed. The maximum
and the product are used for applying fuzzy inference, and the defuzzyficationmethod
is the center of gravity. The scaling factors of the variables are the gains of the three
inputs and the output of the flap and of the T-foil. These 8 tuning parameters have
been commissioned by applying genetic algorithms. The optimization parameters
used are the following:

+

• 300 generations of 300 individuals each (MPP machine SGI origin 2000).

• 180,000 simulations in 21 different processors, parallelization techniques

• Each chromosome has 16 genes

• Cross-over probability, Pc = 0.8; Mutation probability, Pm = 0.008.

Subtractive clustering is applied to the data provided by the simulation of each
of these controllers, in order to obtain two new FIS, one for the flap and another for
the T-foil. The Sugeno-fuzzy system is now a PID-like controller. It has been proved
that it is equivalent to the previous fuzzy PD I with the tuned gains.

Simulation tests have been carried out with the new fuzzy-PID algorithm. The
gains of this new scheme have been tuned by genetic algorithms until no further
improvement was obtained, following the same procedure. For each epoch, the accel-
eration is checked to assure that its value is smaller than the previous one, and so the

+