4.1 Calculation condition

　

 Table 1 depicts the principal dimension of FPSO used in numerical simulation. Calculation condition is that a FPSO is turned toward the incident angle of external disturbances in order to minimize the influence of external forces as shown in Fig. 6.

　

 We assumed that a FPSO is in a water of 500m depth as operation condition. Control objective is that the horizontal displacement of FPSO is within 25m, which is 5% of water depth. For the condition of external disturbances, the current velocity is Vc = 1.0(m/s) and the wind velocity is VW = 1O(m/s). The incident angle of current, wind and wave are taken 45°. In the measurement error, it is thought that an error of horizontal displacement is the most influential on the position keeping performance of the FPSO. Therefore, in this research, the measurement error of horizontal displacement with random distribution is considered as shown in Fig.7.

　

　

　

　

4.2 Calculation results for changing the magnitude of measurement error

　

 In this section, the influence of the magnitude of measurement error (εx,εy) on the position keeping performance of the FPSO is investigated. As for the design parameters of calculation conditions, the rate of the thruster power change per second δTh is taken as 5% of the maximum thruster power and the control starting time Tr is taken as 10(s). In regard to control parameters, the basic value of gain adjust parameter σB is taken as σB = σ + 0.01. The gain adjust parameter σ is taken as σ = σB x σtimes.

　

 Numerical calculations were then made for σtimes = 1.5 and time constant Ti = 200(s). Also the standard deviation SD of measurement error (εx,εy) is given as 0.0 〜 2.2. This standard deviation is a measure of how widely values are dispersed from the mean value in a set of data. The calculation results are shown in Fig.8 〜 Fig.12. Fig.8〜Fig.12 show the time histories of the velocity (u,v), the position of center of gravity (x0,y0) , the angular velocity r , the heading angle ψ, the thruster power τ , measurement error (εx,εy) , and the trajectory of the FPSO.

　

 Fig.8 shows the calculation result in the case of being without measurement error. When the measurement error is zero, since a thruster power is smoothly changed even if horizontal displacement occurs by external disturbances, the FPSO can return rapidly to the starting point, which is a target point. In this figure, the circle shows the allowable deviation.

　

 In the case of standard deviation SD = 0.2, from the time histories in the left part of Fig.9, which is a result of not applying Kalman filter, it turns out that the thruster power τ and the position of the center of gravity (x0,y0) are fluctuated by the influence of a measurement error contained in a measurement value of the horizontal displacement of the FPSO. On the other hand, when using the Kalman filter as shown in right part of Fig.9 on the control system, although horizontal displacement of the FPSO increases a little compared with that with no measurement error, there is almost no change of other time histories. When the measurement error is small, since the Kalman filter can minimize the influence of the measurement error, it is possible to perform position keeping control of the FPSO based on the estimated value with high accuracy acquired from the Kalman filter.

　

 When standard deviation is 0.7, the maximum measurement error amounts to 2.0(m). As shown in Fig. 10, if the error is contained in a measurement value, it becomes impossible to control the FPSO by the control system without the Kalman filter. However, from the trajectory of the FPSO, it is known that the control objective can be achieved by using the Kalman filter. In the calculation results, to be noted are the time history of the thruster power (τB,τS) and the angular velocity r. As a cause of the fluctuations, it is thought that the estimation accuracy is aggravated by the increase of a measurement error. In the event of τB and τS since the FPSO tends to move from the original trajectory by command of the control system, which has a low-accuracy estimation value, the thruster power is fluctuated in order to prevent such a phenomenon. Also, by the fluctuation of the bow and stern thruster, the value of the angular velocity r is changed greatly.

　

 In the instance of standard deviation SD = 1.2, it turns out that as the measurement error increases, the horizontal displacement of the FPSO increases accordingly. Furthermore, the time history of the thruster power (τB,τS) and the angular velocity r show the same tendency. In this calculation result, it is necessary to remark on the time history of the heading angle. Comparing Fig.11 with Fig.1O, it is known that the FPSO as shown in Fig. 11 has a large overshoot angle. Due to the large overshot angle, achievement of the control objective becomes slow.

　

 Fig.12 shows that when the standard deviation is 2.2, it is impossible to achieve the control objective. In this case, since the estimated value by the Kalman filter has insufficient accuracy, the FPSO, which exceeded the target angle, continues rotation. In addition, for a standard deviation bigger than 2.2, it is impossible to achieve the control objective.