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Study On Ship Course Fuzzy Self-learning Control System
Liu Qing (Automation School, WHUT, Wuhan, China)
Wu Xiu-Heng (Institute of Transportation Engineering, WHUT, Wuhan, China)
Zou Zao-Jian (Institute of Transportation Engineering, WHUT, Wuhan, China)
Abstract: Fuzzy control has shown success in some application areas and emerged as an alternative to some conventional control schemes. There are also some drawbacks to this approach, such as it is hard to justify the choice of fuzzy controller parameters and control precision is lower, and so on. Fuzzy control is developing towards self-learning and adaptive. In this article based on the repeat control of the robot the self-learning arithmetic is presented. The arithmetic is realized in fuzzy logic way and is used in cargo ship steering. Our simulation results show that the arithmetic is an effective way to raise steady precise of fuzzy control system and has several potential advantages over conventional fuzzy control.
Key words: fuzzy control; self-learning; ship steering
Introduction
In recent years, to improve fuel efficiency and reduce wear on ship components, autopilot systems have been developed and implemented for controlling the directional heading of ships. Generally, the autopilots utilize simple control schemes such as PID control. Often, however, the capability for manual adjustments of the parameters of the controller is added to compensate for disturbances acting upon the ship such as wind and current. Although conventional fuzzy control has many advantages in some application areas, it is difficult to adjust the fuzzy controller parameters in order to adapt the disturbances variations upon the ship when it is used in the autopilots. While the "fuzzy model reference learning controller" introduced in [1] and [2], "the self-organizing fuzzy controller" introduced in [3] and "the adaptive fuzzy controller" introduced in [4] are the way to improve conventional fuzzy control. But the arithmetic in [3] is difficult and is related to the form of the mathematical model of the cargo ship. The FMRAC system in [1], [2] is more difficult and its stability is not ensure. In this article based on the repeat control of the robot the self-learning arithmetic is presented. The arithmetic is realized in fuzzy logic way and is used in cargo ship steering. It is simpler than [3] and the fuzzy self-learning system is also simpler than [1], [2].
Self-learning Principle
The robot usually finishes a kind of work or a process repeatedly. The control to robot is called repeat control. R.H.Middleton in Austrian Newcastle university presents a kind f repeat control arithmetic of robot. Suppose that H denotes the transfer function of process and HC denotes repeat controller's transfer function. P denotes control period. Control variable U is
if Hc = Krz-p+d (d is pure delay) then
U(z) - z-pU(z) = Krz-p+de(z) (2)
by z inverse transforming, the formula (2) is changed into
U(n) = U(n - P) + Kre(n - P + d) (3)
Because P is a period, n and n-P are the same time corresponding in two periods to formula (3). e(n-P+d) is the error in n+d time. So U(n) is related to U(n-P) and e(n-P+d) from formula (3). For convenience of derivation, formula (3) can be written as
Uj(k) = Uj-1(k) + Krej-1(k+d) (4)
Subscripts of j and j-1 express the times of repeat periods. Subscript of k expresses sampling time. Subscript of d expresses the delay.
If U1(k), U2(k), Λ Um (k) expresses the control variables in 1, 2, ∧ m periods, then
When the subscript of control variable is expressed in j, the normal formula is
By accumulating the errors in the (k+d) time of foregoing periods, the summation is used to modify control variable in the k time in some scale. The formula (6) is a kind of arithmetic of self-learning because it uses experiences obtained in the past to decide present control variable. The arithmetic is realized in fuzzy logic way in the paper.
3. The Design Of Self-learning Fuzzy Controller
3.1 The Universes of Discourse And Membership Functions of Input/Output Linguistic Variables
In ship heading control system, the heading error e and the change of heading error
are input variables, and the angle of rudder δ is output variable. The universes of discourse are defined as follow:
e: [-12 12] (degree);
ε: [-0.6 0.6] (degree/second)
δ: [-12 12] (degree)
the levels of quantization of e, ε, δ and Σe are showed in table 1.
Table 1 The Levels of Quantization Of e, ε, δ and Σe
| e |
ε |
δ |
?e |
The elements of discre universes of discourse |
| -12 |
-0.6 |
-12 |
-18 |
-6 |
| -10 |
-0.5 |
-10 |
-15 |
-5 |
| -8 |
-0.4 |
-8 |
-12 |
-4 |
| -6 |
-0.3 |
-6 |
-9 |
-3 |
| -4 |
-0.2 |
-4 |
-6 |
-2 |
| -2 |
-0.1 |
-2 |
-3 |
-1 |
| 0 |
0 |
0 |
0 |
0 |
| 2 |
0.1 |
2 |
3 |
1 |
| 4 |
0.2 |
4 |
6 |
2 |
| 6 |
0.3 |
6 |
9 |
3 |
| 8 |
0.4 |
8 |
12 |
4 |
| 10 |
0.5 |
10 |
15 |
5 |
| 12 |
0.6 |
12 |
18 |
6 |
|
There are seven values in every Linguistic variable which are positive bigger (PB), positive middling(PM), positive smaller (PS), zero (ZO), negative smaller (NS), negative middling (NM), negative bigger(NB). The membership functions of these values of Linguistic variables are followed in table 2.
Table 2 The Membership Function of Seven Values of Linguistic Variables
| Membership degrees |
The values of linguistic variable |
| PB |
PM |
PS |
ZO |
NS |
NM |
NB |
| The Elements of Discrete
Universes of Discourse |
-6 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
| -5 |
0 |
0 |
0 |
0 |
0 |
0.5 |
0.5 |
| -4 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
| -3 |
0 |
0 |
0 |
0 |
0.5 |
0.5 |
0 |
| -2 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
| -1 |
0 |
0 |
0 |
0.5 |
0.5 |
0 |
0 |
| 0 |
0 |
0 |
0.5 |
0.5 |
0 |
0 |
0 |
| 1 |
0 |
0 |
0.5 |
0.5 |
0 |
0 |
0 |
| 2 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
| 3 |
0 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
| 4 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
| 5 |
0.5 |
0.5 |
0 |
0 |
0 |
0 |
0 |
| 6 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
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