APPLYING FUZZY LOGIC CONTROL TO PLEASURE CRAFTS STEERING SYSTEMS

Transcription

1 APPLYING FUZZY LOGIC CONTROL TO PLEASURE CRAFTS STEERING SYSTEMS Dong-Taur Su Department of Shipping Technology, National Kaohsiung Marine University, Nanzih, Kaohsiung, Taiwan 81143, R.O.C., H. Joseph Wen Accounting and MIS, Harrison College of Business, Southeast Missouri State University, Cape Girardeau, Missouri 63701, USA, Ching-Hsiewn Ou Environmental Biology & Fisheries Science, National Taiwan Ocean University, Keelung, Taiwan, 20224, R.O.C., Tzeng-Yuan Heh Chung Cheng Institute of Technology, National Defense University, Taoyuan, Taiwan 33509, R.O.C., ABSTRACT Given a large amount of information that a pleasure craft operator must manage in a dynamic environment, craft steering automation can reduce operation stress. This paper seeks to propose a new method for steering of pleasure crafts based on fuzzy logic control. We developed a set of fuzzy logical rules using actual pleasure crafts steering data. A global positioning system (GPS) device and a stopwatch were used to measure the turning circle of pleasure crafts. The number of passengers, rudder angle, engine power (rpm), speed, tactical diameter, and turning time were all recorded. The results of the experiment showed the proposed fuzzy logic controller performed amazingly well in imitating human steering operation. 1. INTRODUCTION Pleasure crafts are lightweight, short and accelerate quickly. They are therefore highly maneuverable and are frequently used for fishing, water skiing, patrolling coastlines, and performing emergency rescue missions. However, the lightness of pleasure crafts causes their maneuverability to be strongly affected by their speed, load, power of the engine, and environmental factors, such as wind, waves and currents. These external and internal effects make the maneuvering of pleasure crafts nonlinear (Bob-Manuel, 2002; Lee, 1995). Therefore, an autopilot has not yet been designed for a pleasure craft. Humans still steer pleasure crafts, based on their experience. A steering system of large ship can be controlled by assuming that the relevant dynamics 30

2 equation is linear, so linear theory can be applied. A successful autopilot system requires that the maneuvering of the ship must be robust and insensitive (Kumar, 2005; Yang and Chen, 2006). Poor controller performance may cause the course to oscillate, increasing the distance and the time of a trip, and therefore, the amount of fuel consumed. Few studies of pleasure crafts have been published. Polkinghorne (1995) has demonstrated the effectiveness of fuzzy logic control in this area. Tzeng (1999) proposed fuzzy method for designing an autopilot, based a combining the control knowledge in expert linguistic rules with numerical data. This study proposes a fuzzy logic controller build on repeatedly obtained discrete experimental data from different pleasure crafts. Unlike the previous studies, this study addresses factors such as the number of people, the rudder angle, the power of the engine, and the speed of the boat. This paper helped in bridging the existing gap of pleasure craft autopilot control systems. 2. FUZZY LOGIC CONTROL There are certain particular characteristics of fuzzy systems that give them better performance for specific applications (Hayashi and Otsubo, 1998; Metcalfe, 2005). In general, fuzzy systems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difficult to derive. For example, the input and parameter values of a system may involve fuzziness, be inaccurate, or incomplete. Similarly, the formulas or inference rules to derive conclusions may be incomplete or inaccurate. Fuzzy logic allows decision making with estimated values under incomplete information (Gavish, Zaslavsky, and Kandel, 2000). Note that the decision may not be correct and can be changed at a later time when additional information is available. Complete lack of information will not support any decision making using any form of logic. For difficult problems, conventional non-fuzzy methods are usually expensive and depend on mathematical approximations (e.g., linearization of nonlinear problems), which may lead to poor performance. Under such circumstances, fuzzy systems often outperform conventional methods. Fuzzy system approaches also allow us to represent descriptive or qualitative expressions such as "slow" or "moderately fast," and these are easily incorporated with symbolic statements. These expressions and representations are more natural than mathematical equations for many human judgmental rules and statements. Fuzzy logic control is based on the fuzzy expert system implying a collection of fuzzy membership functions and rules. Fuzzy logic control proceeds in several steps. These are: (1) Fuzzification - linguistic variables that present inputs and output of the model are defined. Membership functions are applied to their actual values to determine the degree of truth for each rule premise. (2) Inference - setting the "If... and... then" rules. One fuzzy subset is assigned to each output variable for each rule. Usually, it relates to fuzzy logic AND or fuzzy logic OR. (3) 31

3 Rules evaluation - the real input numbers, called readings, are translated to proper terms of the corresponding linguistic variables. (4) Aggregation (conflict resolution) - choosing control action as a result of the application of a control rule. It relates to fuzzy logic MAX or fuzzy logic SUM. (5) Defuzzification - decoding the output. This is the operation that produces a non-fuzzy control action presenting the membership function of an aggregated fuzzy action in the form of a single crisp value. In this study, the ability of fuzzy systems to formulate human knowledge in a systematic manner is the reason why fuzzy logic control is adopted to address the problem of combining status information in pleasure craft steering automation. Fuzzy logic is particularly suited to this problem since both human expert knowledge and system status information can be combined in the controller. The expert knowledge is represented by linguistic rules described in the controller rule base, while status information is obtained through observations of steady state behavior of a human expert. 3. EXPERIMENTAL DATA In order to construct membership functions for each fuzzy variable, some experimental data are required to determine the range of the input variables. Data collection was performed near the pleasure craft dock on the Ji-Long River, near where it meets the Tamsui River in Taiwan. The width of the Ji-Long River is about 200 meters (m), and the river flow is tided because it is near the ocean outlet. It is 5 m deep at low tide, and high tide and low tide differ by 2.5 m. Experiments were performed when the wind speed was under 3 m/s, the flow speed was under 0.1m/s, and the tide speed was within ±0.6m/s, to minimize environmental effects on the experiments. The experiments involved two pleasure crafts, whose specifications are as shown in Table 1. In the experiments, the pleasure crafts were turned under various conditions. The turning circle is defined as the trajectory of the pleasure craft s center of gravity during motion at constant velocity, with the rudder kept at a fixed angle. The experiment is commonly used to measure the turning circle of a vessel. Table 1 Pleasure craft specifications Pleasure craft A Pleasure craft B Material FRP FRP 32

4 Hull weight (Tons) LOA (M) Breadth (M) Draft (M) Freeboard (M) Maximum dead weight (Kg) Gas volume ( l ) Engine power (Hp) 225 (3000~4000rpm) 90 (3000~4000rpm) Five input parameters are measured when a pleasure craft turns. They are as follows Position and Time Measuring the pleasure craft s position is difficult because it moves fairly quickly. Therefore, a Global Positioning System (GPS), model SRVYII-100 produced by GARMIN Company, was installed in the pleasure crafts. As the pleasure craft followed a turning circle, the positions and times of the pleasure crafts were recorded using GPS and a stopwatch. The speed of the pleasure crafts were then calculated according to time and speed data Rudder Angle In each run, the rudder was set to a different angle, presented in Table 2. Table 2 Rudder angle Right full angle Right angle Left full angle Left angle Pleasure craft A Pleasure craft B Number of Passengers Pleasure crafts are light, so load influences stability. Different numbers of passengers were the facts of our evaluation on the pleasure crafts during the turns, as listed in Table 3. Table 3 Number of passengers Passengers 33

5 Pleasure craft A Pleasure craft B Engine Power The engine power (revolutions per minute, rpm) is also importantly affects the turning circle of a pleasure craft. The engine power was set to 1000 rpm or 2000 rpm as given in Table 4. Table 4 Engine power Engine power (rpm) Pleasure craft A Pleasure craft B THE PROPOSED FUZZY LOGIC CONTROLLER When pleasure craft is turning a circle, the proposed fuzzy controller receives four input variables - engine power (rpm), angle of rudder, number of passengers and speed of pleasure craft. The controller then determines the diameter and turning time of the tactical turning circle. Figure 1 shows the structure of the proposed fuzzy logic controller. Fuzzy control Data base & Rule base Fuzzification Defuzzification Fuzzy inference mechanism Experiment numerical data Fig.1. Block diagram of the proposed fuzzy logic controller Using the MATLAB fuzzy toolbox, the proposed controller was built in the following three steps Selecting the membership functions and scale factors 34

6 First, experimental data of pleasure craft steering operation was collected. It was then transferred into a membership function of the Fuzzy Set. In this study, two pleasure crafts separately moved through left and right turning circles. All the membership functions were triangular, and scaling factors were based on try and error. The membership functions were then compared with experimental data. Finally, an if-then rule was generated according to the relationship of each input-output data pair Executing fuzzy control The pleasure craft s motion is quick and complex, so no mathematical representation of the control rules using fuzzy rules exists. Accordingly, experts inputs and rules of thumb from craft steering guides were used in this fuzzy logic analysis. The rules were fine tuned to match the experimental data to ensure a better fuzzy logic control Defuzzification Finally, recommended by the previous studies (Zadeh, 1965), crisp values of fuzzy control system are determined using center of gravity defuzzification. method. Or Y y * y * Y k yb y dy i i 1 k i 1 B y dy y B B y y i i (1) (2) These multiple functions of the controller are used to determine the error between fuzzy controls and the experimental data. 5. DATA ANALYSIS AND RESULTS There are two different membership functions of engine power in which the scaling factor is 10-3, so 1000(rpm) x 10-3 =1, and 2000(rpm) x 10-3 =2. Each set was identified by different linguistic label for Slow Speed as (SS), and Dead Slow Speed as (DSS). There are two other different membership functions of the number of people are Light Load (LL) and Full Load (FL) in which the scaling factor is 1, so 2 (people) x 1=2, and 6 (people) x 1=6. There are four membership functions of angle are right full rudder (RF), right angle (RH), left full rudder (LF) and left angle (LH) in which the scaling factor is 0.2, so 15(LH) x 0.2=3, 26(LF) x 0.2=5.2, 18(RH) x 0.2=3.6, and 30(RF) x 0.2=6. The pleasure craft speed is determined by dividing the diameter of the turn, obtained from the GPS, by the time taken to move through the turning circle. Figures 2 plots the GPS recorded 35

7 Tactical diameter (m) Tactical diameter (m) positions and Tables 5 and 6 presents the different conditions speeds. There are six membership functions as Speed 1 (S1 = 1.58), Speed 2 (S2 = 1.97), Speed 3 (S3 = 2.67), Speed 4 (S4 = 3.14), Speed 5 (S5 = 4.06) and Speed 6 (S6 = 5.6). Human Operator 1150 Longitudinal position (m) 1190 Longitudinal position (m) Pleasure craft A Right full rudder angle Pleasure craft A Left full rudder angle Fuzzy Controller Fig. 2. Comparison the performance of fuzzy controller of the craft A Table 5 The experimental data (right turning circle of pleasure craft A) RPM Rudder People Diameter Time Speed Table 6 The experimental data (left turning circle of pleasure craft A) RPM

8 Rudder People Diameter Time Speed The diameter of the turning circle is calculated from the GPS recorded data, first, the position of the center of the circle is estimated, and then the distance of any point to the center of the circle is evaluated, yielding the diameter of the circle. Table 5 and 6 show the diameters. There are four membership functions are diameter 1 (D1 =1.7), diameter 2 (D2 = 3.1), diameter 3 (D3 = 3.9), and diameter 4 (D4 = 5.0) in which the scaling factor is 0.15, so all the tactical diameters are changed for statistical convenience. A stopwatch was used to measure the time taken to move through the turning circle. Tables 5 and Tables 6 list these times. There are four different membership functions are time1 (T1 = 2.2), time2 (T2 = 2.9), time3 (T3 = 3.7), and time4 (T4 = 5.1) in which the scaling factor is A controller that uses a fuzzy algorithm based on experimental data involves linguistic control rules that can be applied by an experienced skipper who is manually operating the boat. Linguistic control rules are sets of rules such as if the boat at slow speed (rpm=ss), the load is light (number of people=ll), the angle of the rudder is right full (angle=rf), and the speed is S2 (speed=s2), then the diameter is D1 (diameter=d1), and the time is T3 (time=t3). Table 7 expresses all if-then rules, with input items included engine power, rudder angle, number of people and speed of pleasure craft speed, and two output items included tactical diameter and turning circle time. Table 7 The fuzzy rules RPM Number Angle Speed Diameter Time 1 SS LL RF S2 D1 T3 2 SS LL RH S2 D2 T4 3 SS FL RF S1 D1 T3 4 SS FL RH S3 D3 T4 37

9 5 DSS LL RF S3 D1 T1 6 DSS LL RH S6 D4 T2 7 DSS FL RF S3 D1 T1 8 DSS FL RH S5 D4 T3 9 SS LL RF S1 D1 T3 10 SS LL RH S2 D2 T4 11 SS FL RF S1 D1 T3 12 SS FL RH S2 D2 T4 13 LS LL RF S3 D1 T1 14 LS LL RH S5 D4 T3 15 LS FL RF S4 D1 T1 16 LS FL RH S4 D2 T2 Comparing the results of the fuzzy control system with experimental data, it shows that the developed fuzzy logic controller is highly accurate. The results reveal that the average error between the actual and the simulated diameter is 7.7%, and that the average error between the actual and simulated turning circle time is 4.4%. For pleasure craft B, the average error between the actual and simulated diameter is 7.6%, and the average error between the actual and simulated turning circle time is 4.2%. A pleasure craft is a non-linear, time-variant system. Even although extra environmental factors affect the magnitude and direction of any disturbances due to wind, waves and current, the fuzzy controller perform very well. 6. CONCLUSIONS This study increases our understanding of the maneuvering characteristic of a pleasure craft. The dynamic behavior of a pleasure craft during sailing is quite complex, so its equation of motion cannot be easily determined. Hence, a novel means of controlling a nonlinear system using fuzzy control, based on experimental data, is presented. 38

10 When fuzzy systems are applied to appropriate problems, particularly the type of problem described in this study, their typical characteristics are faster and smoother response than with Boolean systems. This translates to efficient and more comfortable operations for such tasks as steering pleasure crafts. In fuzzy systems, describing the control rules is usually simpler and easier, often requiring fewer rules, and thus the systems execute faster than Boolean systems. Fuzzy systems often achieve tractability, robustness, and overall low cost. In turn, all these contribute to better performance. In short, Boolean methods are good for simpler problems, while fuzzy systems are suitable for complex problems or applications that involve human descriptive or intuitive thinking. 7. REFERENCE Bob-Manuel, K.D.H. (2002). Probabilistic prediction of capsize applied to small high-speed craft, Ocean Engineering 29, Gavish, G. Zaslavsky, R. and Kandel, A. (2000). Longitudinal Fuzzy Control of a Submerged Vehicle, Fuzzy Sets and Systems 115, Hayashi K. and Otsubo, A. (1998). Simulator for Studies of Fuzzy Control Methods, Fuzzy Sets and Systems 93, Kumar, S. Ressler, T. and Ahrens, M. (2005). Systems thinking, a consilience of values and logic, Human Systems Management 24(4), Lee, C.W. (1995). Depth control of a midwater trawl gear using fuzzy logic, Fisheries Research 24, Metcalfe, M. (2005). Using reflective argument to design human systems, Human Systems Management 24(2), Polkinghorne, M.N. Roberts, G.N. Burns, R.S. and Winwood, D. (1995). The implementation of fixed rule base fuzzy logic to the control of small surface ships, Control Eng. Practice, 3(3), Tzeng, C.Y. Ho, S.K. and Su, H.P. (1999). Feasibility study of a unified fuzzy ship steering autopilot, Journal Society of Naval Architects and Marine Engineers 18(4), Yang, C. W. and Chen, J. C. (2006). Applying human reliability growth analysis to system performance enhancement, Human Systems Management 25(1), Zadeh, L.A. (1965). Fuzzy sets, Information and Control 8,