|
3.2 Fuzzy Control Rules
According to the ship steering experience of operator, the steering rules is summarized in language and the rules are converted into fuzzy control rules followed in table 3.
Table 3 fuzzy control rules
| δ |
e |
| NL |
NM |
NS |
ZO |
PS |
PM |
PL |
| ε |
NL |
NL |
NL |
NL |
NL |
NM |
NS |
ZO |
| NM |
NL |
NL |
NL |
NM |
NS |
ZO |
PS |
| NS |
NL |
NL |
NM |
NS |
ZO |
PS |
PM |
| ZO |
NL |
NM |
NS |
ZO |
PS |
PM |
PL |
| PS |
NM |
NS |
ZO |
PS |
PM |
PL |
PL |
| PM |
NS |
ZO |
PS |
PM |
PL |
PL |
PL |
| PL |
ZO |
PS |
PM |
PL |
PL |
PL |
PL |
|
And also the self-learning arithmetic is converted into self-learning control rules followed in table 4.
Table 4 Self-learning control rules
| ?e |
PB |
PM |
PS |
ZO |
NS |
NM |
NB |
| Modifying variable V |
PM |
PS |
PS |
ZO |
NS |
NS |
NM |
|
3.3 Fuzzy Self-learning Arithmetic
In fuzzy control system there are two factors, which are δc derived in fuzzy control rules and V derived in self-learning control rules, to affect control variable δ. The relation formula is
in which β is the weight of modifying variable.
4. The Ship Dynamics Model
Generally, ship dynamics are obtained by applying Newton's laws of motion to the ship. For very large ships, the motion in the vertical plane may be neglected since the "bobbing" or "bouncing" effects of the ship are small for large vessels. The motion of the ship is generally described by a coordinate system which is fixed to the ship. A simple model which describes the dynamical behavior of the ship may be expressed by the following differential equation[5]:
Where Ψ is the heading of the ship and δ is the rudder angle. Assuming zero initial condition, (7) can be written
where K, T1,T2 and T3 are parameters which are a function of the ship's constant forward velocity and its inherence parameters. In normal steering motion, the change rate of rudder angle is limited and the ship inertia is bigger. A ship often makes only small deviations from a straight line path. The ship steering motion is low-frequency. So (8) can be approximated by
(9) is called one order equation of steering motion or Nomoto equation. It expresses the essence of ship dynamics. And also it is very simple. Take a kind of cargo as a simulation object in this paper. The cargo's parameters are showed in table 5.
Table 5 the cargo's parameters
| Length |
152(m) |
| Width |
20(m) |
| K |
0.051(1/sec) |
| T |
20(sec) |
| Rudder angle limit |
±35(deg) |
| Change rate Of rudder angle |
≥30(1/sec) |
| Cargo's velocity |
17.2
(km) |
|
|
