JP5571743B2 - Ship automatic steering system - Google Patents

Description

  The present invention relates to a marine vessel automatic steering apparatus, and more particularly to a marine vessel automatic steering apparatus capable of improving performance at the time of changing the course.

  The marine vessel automatic steering device is a device that controls the rudder so that the heading from the gyrocompass follows the set course, and is described in Patent Document 1 by the present applicant as an improvement in performance at the time of turning. Is known. The configuration will be briefly described with reference to FIG. FIG. 1 is an overall block diagram including an automatic marine steering apparatus 12, a steering machine 16, and a hull 18, and the steering machine 16 and the hull 18 serve as a hull plant to be controlled 14.

A set course, that is, a desired course change amount, a set value, and a heading are input as input signals to the marine vessel automatic steering device 12, and a command steering angle is output as an output signal.

  The marine vessel automatic steering apparatus includes a trajectory calculation unit that receives a set course and outputs a reference course, a feedforward controller, a feedback controller, and first and second adders. .

  In Patent Document 1, the transfer function of this feedforward controller is set so as to have an inverse characteristic of the transfer function P (s) of the hull plant to be controlled. Specifically, Nomoto's primary model

を用いて

Using

となるように設定される。ここで、Ｋ_S、Ｔ_Sは船体パラメータで、それぞれ旋回力ゲインと時定数、ｓはラプラス演算子である。

Is set to be Here, K _S and T _S are hull parameters, respectively, a turning force gain and a time constant, and s is a Laplace operator.

The trajectory calculation unit calculates and outputs a reference course using the set course, the set value, and the heading. The set value, there is a maximum value of the angular velocity [delta] _FF 'of veering during turning angular velocity, the maximum value of the feedforward steering angle [delta] _FF and feedforward steering angle. The heading is used to obtain these values when the turning angular velocity and turning angular acceleration are not zero at the start of changing the course, such as when another course is changed during the course.

The reference course is configured to satisfy the following conditions.
(1) It is composed of three modes, an acceleration mode, a constant speed mode, and a deceleration mode, and time management is performed for each mode. The reference course ψ _R (t) is a function having the time t as a variable for each mode.
(2) In the acceleration mode and the deceleration mode, the second order derivative with respect to time t of the reference course ψ _R (t) is a quadratic function.
(3) In the constant velocity mode, the first order derivative with respect to time t of the reference course ψ _R (t) is constant, and the second order derivative is zero.
(4) In the acceleration mode, the reference course ψ _R (t) takes in the values of the turning angular acceleration C _1a and turning angular velocity C _2a of the ship as initial values.

JP-A-8-207894

Although Cited Document 1 has an advantage that it is possible to realize a changing course planning in consideration of the characteristics of the controlled object, there are the following problems.
・ If the turning angular velocity and turning angular acceleration are not zero at the start of turning, such as when a new turning is performed during changing the hull motion, the initial angular acceleration C _1a and initial angular velocity C _2a and the maximum turning When the relationship with the angular velocity r _R is C _2a > r _R , C _1a <0 or C _2a <r _R , C _1a > 0, the reference course cannot be set appropriately.
_-If there is an angular acceleration initial value C _1a and an angular velocity initial value C _2a , if the amount of needle change necessary to attenuate the initial value is greater than the amount of needle change set, there is a risk that the needle changing time will be longer and appropriate. Can not cope with.
・ The angular acceleration initial value C _1a and the angular velocity initial value C _2a are obtained from the signal from the heading, but the signal from the heading is stable because small noise is superimposed even if it passes through the filter. It is difficult to obtain a simple initial value.

  An object of the present invention is to solve the above-described problems and to realize an automatic steering apparatus for a ship that realizes a more optimal course changing course and thus enables stable and efficient ship maneuvering.

In order to achieve this object, the invention according to claim 1 of the present invention includes a trajectory calculation unit that calculates and outputs a reference course for a desired course change amount of a ship, and feedforward steering from the reference course. A feedforward controller that calculates an angle and performs open-loop control, and the trajectory calculation unit outputs the reference course separately in an acceleration mode, a constant speed mode, and a deceleration mode, and starts changing the needle in the acceleration mode. In the marine vessel automatic steering apparatus that takes in the initial value C _1a of the turning angular acceleration at the time and the initial value C _{2a of the} turning angular velocity and calculates the reference course,
The trajectory calculation unit does not exceed the maximum steering speed at which the steering speed of the feedforward steering angle output from the feedforward controller based on the reference course calculated by setting the initial values C _1a and C _2a to zero, respectively. Thus, the angular velocity rR at the end of the acceleration mode and the constant velocity mode when each mode is determined is calculated, and C _1a <0 is satisfied with C _2a > r _R or C _2a <r _{R When 1a} > 0 is satisfied, the turning angular speed r _R is corrected so that the maximum steering speed generation time in the acceleration mode is always the same in each case, and the corrected turning angular speed r _R is satisfied and calculated. Based on the reference course, the reference course of each mode is calculated so that the steering speed of the feedforward steering angle output from the feedforward controller does not exceed the maximum steering speed. The steering speed of the non turning angular velocity r _R satisfied and feedforward steering angle output from the computed is referenced feedforward controller based on the course is to compute a reference course of each mode so as not to exceed the maximum steering speed It is characterized by.

According to a second aspect of the present invention, the calculation of the turning angular velocity r _R of the trajectory calculation unit according to the first aspect is performed with a constant ratio of a constant speed time and a deceleration time that is a time of each of the constant speed mode and the deceleration mode. When the result is equal to or higher than the specified turning angular velocity, the specified turning angular velocity is set, and when the result is equal to or lower than the specified turning angular velocity, the calculation result is set as the angular velocity.

The invention according to claim 3 includes a trajectory calculation unit that calculates and outputs a reference course with respect to a desired amount of course change of a ship, and a feed that performs open loop control by calculating a feed forward steering angle from the reference course. The trajectory calculation unit outputs the reference course separately in an acceleration mode, a constant speed mode, and a deceleration mode, and in the acceleration mode, the initial value C _1a of the turning angular acceleration at the start of the change of needle In an automatic steering device for a ship that takes in an initial value C _2a of a turning angular velocity and calculates a reference course,
The trajectory calculation unit obtains the turning angular velocity r _R at the end of the acceleration mode and the constant velocity mode by setting the initial values C _1a and C _2a to zero, and at this time, the turning angular velocity r _R becomes the designated turning angular velocity r _0. when it is assumed to be equal to, when the feed-forward steering angle output from the feedforward controller based on the reference course which is calculated to satisfy the permissible steering angle following conditions, turn angular velocity r _R specified turning angular velocity r ₀ determined to, when not satisfied the conditions, feed forward when determining the smallest angular velocity deviation between the permissible steering angle feedforward steering angle to the turning angular velocity r _R, it was determined turning angular velocity r _R Find the maximum steering speed of the feed forward steering angle output from the controller,
When C _2a > r _R satisfies C _1a <0, or C _2a <r _R satisfies C _1a > 0, the maximum steering speed generation time in the acceleration mode is always the same in each case. The turning angular speed r _R is corrected to satisfy the corrected turning angular speed r _R , and the steering speed of the feed forward steering angle output from the feed forward controller based on the calculated reference course does not exceed the maximum steering speed. Thus, the reference course of each mode is calculated, and in cases other than the above, the steering angle of the feedforward steering angle that satisfies the turning angular velocity r _R that is not corrected and that is output from the feedforward controller based on the calculated reference course is calculated. The reference course of each mode is calculated so that the speed does not exceed the maximum steering speed.
The invention according to claim 4 includes a trajectory calculation unit that calculates and outputs a reference course with respect to a desired amount of course change of a ship, and a feed that performs open-loop control by calculating a feed forward steering angle from the reference course. The trajectory calculation unit outputs the reference course separately in an acceleration mode, a constant speed mode, and a deceleration mode, and in the acceleration mode, the initial value C _1a of the turning angular acceleration at the start of the change of needle In the marine vessel automatic steering device that calculates the reference course by taking the value when the initial value C _2a of the turning angular velocity is not zero,
The trajectory calculation unit sets the acceleration mode to an attenuation that attenuates the initial value when the azimuth change necessary to attenuate the initial values C _1a and C _2a in the acceleration mode is larger than the desired amount of change of the needle. The reference course of each mode is calculated by dividing the mode into a normal mode for converging to the turning angular velocity r _R in the constant speed mode.

The invention according to claim 5, the initial value C _2a of the initial value C _1a and the turning angular velocity of the slewing angular acceleration according to any one of claims 1 to 4, when that was being veering at veering start It is obtained from the value at the start of the course change of the second-order derivative and the first-order derivative of the reference course calculated by the trajectory computation section with respect to the previous course change.

According to the first and third aspects of the invention, when C _2a > r _R satisfies C _1a <0, or when C _2a <r _R satisfies C _1a > 0, C _2a and r _R In order to avoid such a problem, the time at which the rudder speed is always maximized is generated. By keeping the steering speed constant so that the steering speed at that time does not exceed the maximum steering speed, stable, efficient and safe boat maneuvering can be performed.

  According to the second aspect of the present invention, it is possible to save energy with an appropriate changeover time by making the constant velocity time ratio constant. If the constant speed time ratio is not constant, the changeover time can be shortened with a large turning angular velocity, but this is not preferable from the viewpoint of energy saving. According to the present invention, by making the constant speed time ratio constant, it is possible to save energy compared to the case where there is no constant speed time.

  According to the fourth aspect of the present invention, if the desired amount of change of needle is small, the amount of change in direction necessary to attenuate the initial value may be larger. When calculating the course, there is a possibility that the time for changing the needle will be too long, but there is a risk that the acceleration mode will be divided into the attenuation mode and the normal mode, and appropriate parameters will be set in each mode for proper reference. The course can be calculated.

  According to the fifth aspect of the present invention, if a new needle change is being made, the initial value at the start of the new needle change can be obtained using the reference course calculated for the previous needle change. Therefore, an initial value that is not affected by noise can be obtained.

It is the whole block diagram of the automatic steering device for ships of this invention, and a control object. It is a graph which shows the time change (in the case of a stable ship) of a reference course and feedforward rudder angle. It is a graph which shows the time change of the 2nd-order differentiation of the reference course in each mode, and the 1st-order differentiation. It is a graph showing the relationship between the rudder speed and the amount of needle change. Is a graph representing two Kaibubun characteristic of the reference course of the acceleration mode (when the 0 <C _1a at r _R> C _2a). It is a graph showing the time change of the change course response of the reference course based on Nomoto's primary model and the first-order differential of a reference course. (A) is a block diagram of Nomoto's primary model, and (b) is a block diagram of Nomoto's secondary model. It is a block diagram of the hull model employ | adopted by this invention. It is a flowchart showing the process performed by a track | orbit calculating part. It is a flowchart showing the calculation process of the reference course performed in a track | orbit calculating part. It is a flowchart showing the calculation process of the attenuation | damping mode performed by a track | orbit calculating part. It is the simulation result of this invention, and represents the time of large angle turning of an unstable ship. It is a simulation result of this invention, (A) represents the stable ship, (B) represents the time of small angle change of each of the unstable ship. It is a block diagram of the orbital calculation part by the modification which made variable the equal reduction ratio of this invention. Steering speed δ _R '= dδ / dt for an equal reduction ratio is a graph representing the characteristic of the steering angle [delta] _R and veering time T _t. (A) is a simulation result when the constant reduction ratio of the present invention is fixed, and (B) is a simulation result when the constant reduction ratio of the present invention is variable. It is a schematic diagram showing the relationship between the propeller of a hull and a rudder. It is a graph showing the relationship between the heading and the heading ratio when the propulsive force is changed. It is a graph which shows the relationship between the wake speed when a propulsive force changes, and a ship speed. It is a block diagram of the principal part of the modification which performed the robustness improvement at the time of the acceleration / deceleration of this invention.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is an overall block diagram including a marine vessel automatic steering device 12 according to the present invention and a control object 14 including a steering machine 16 and a hull 18. Similarly to Patent Document 1, the automatic steering device 12 for a ship according to the present invention includes a trajectory calculation unit 12-1, a feedforward controller 12-2, a feedback controller 12-3, and first and second additions. And containers 12-4 and 12-5.

The trajectory calculation unit 12-1 calculates a time function of the reference course satisfying the course changing condition using the desired amount of change Δψ ₀ and the set value, and sequentially outputs the reference course ψ _R with the passage of time. It is.

The feedforward controller 12-2 calculates the feedforward steering angle δ _FF from the reference course. The feedforward controller 12-2 constitutes an open loop system in the automatic steering system, and this open loop system operates so that the heading immediately coincides with the reference course.

The feedback controller 12-3 constitutes a closed loop system in the automatic steering system, and calculates the feedback steering angle δ _FB with respect to the deviation between the heading and the reference course. The course changing system basically makes the heading follow the reference course without delay by the operation of the reference course from the trajectory calculation unit 12-1 and the feedforward control by the feedforward controller 12-2. Sometimes, when a deviation error ERR occurs between the reference course and the heading, the closed loop system operates to reduce the deviation error ERR. However, since this deviation error ERR is slight, in the present invention, this closed loop system has the same configuration as that of Patent Document 1.

Hereinafter, a basic concept of calculating the reference course ψ _R in the trajectory calculation unit 12-1 will be described.

1. Basic Design The reference course ψ _R output from the trajectory calculation unit 12-1 needs to be a time function that satisfies the changing condition. As the change condition,
Course condition: Course condition for desired amount of course change and turning angular speed Restriction condition: Restriction condition for feedforward rudder angle and rudder speed considering characteristics of steering 16 Initial value condition: Caused by hull motion immediately before course change The initial value conditions of the angular acceleration and angular velocity of the azimuth can be mentioned.

  Table 1 shows the relationship between the reference course variable and the setting value of the needle changing condition.

表１において、所望される変針量Δψ₀は、変針直前の針路と設定針路との変化量として与えられるものとする。角速度ｒ_Ｒは、参照針路ψ_Ｒの１階微分値を、舵角δ_FFはフィードフォワード舵角を、舵速度δ'_FFは、舵角δ_FFの１階微分値をそれぞれ示す。ｒ₀は指定旋回角速度、δ₀は許容舵角、δ₀’は許容舵速度である。参照針路ψ_Ｒは、変針量Δψ_ＲがΔψ₀に一致するように、そして、他の変数ｒ_Ｒ、δ_FF、δ'_FFの絶対値の最大値は、各々、指定旋回角速度、許容舵角、許容舵速度以下になるようにする。

In Table 1, the desired course change amount Δψ ₀ is given as a change amount between the course just before the course change and the set course. Angular velocity r _R is a first derivative of the reference course [psi _R, the steering angle [delta] _FF is a feed-forward steering angle, steering speed [delta] _'FF shows first derivative of the steering angle [delta] _FF respectively. r ₀ is a specified turning angular velocity, δ ₀ is an allowable steering angle, and δ ₀ ′ is an allowable steering speed. The reference course ψ _R is such that the amount of change Δψ _R coincides with Δψ ₀ , and the maximum absolute values of the other variables r _R , δ _FF , δ ′ _FF are respectively the designated turning angular velocity and the allowable steering angle. , Make it below the allowable rudder speed.

Figure 2 shows the time variation of the reference course [psi _R feedforward steering angle [delta] _FF (provided that when a stable boat). For the sake of simplification, the start time of the course change is set to zero, and the initial value of the hull movement is set to zero. As in Patent Document 1, the reference course ψ _R is composed of three modes: an acceleration mode, a constant speed mode, and a deceleration mode. t represents time, and T _a , T _v , and T _d represent acceleration time, constant speed time, and deceleration time, respectively. In the following, the subscripts (•) _a , (•) _v , (•) _d mean acceleration, constant speed, and deceleration modes, respectively. In addition to the three modes, the needle changing system can have a static definite mode after the deceleration mode. However, in the static deterministic mode, the amount of needle change is constant, and the description thereof is omitted.

  The reference course has a condition of a time function capable of second order differentiation using Nomoto's primary model. The second-order differential value of the reference course needs to be zero at the end of the mode and the start of the next mode to ensure continuity between modes. Since the function of the minimum dimension that satisfies this requirement is a quadratic function, a quadratic function is used as the reference course for second-order differentiation.

1.2 Reference Course Time Function Hereinafter, the reference course in each mode will be described (FIG. 3).
1.2.1 Acceleration mode The second order derivative of the reference course is a quadratic function, and has initial values of angular acceleration C _1a and angular velocity C _2a . In the acceleration mode, the angular acceleration is made zero at the end of the acceleration mode.

  The second-order differentiation, first-order differentiation, and reference course of the reference course in the acceleration mode are expressed as follows.

Here, ψ _Ra represents the reference course in the acceleration mode, and β _a represents the acceleration constant. The time range is [0 ≦ t ≦ T _a ]. Since the time the angular acceleration T _a is zero, [psi than _"Ra (T _a) = 0

となる。

It becomes.

C _1a and C _2a which are initial values of angular acceleration and angular velocity are values of angular acceleration and angular velocity when t = 0.

1.2.2 Constant velocity mode In the constant velocity mode following the acceleration mode, the angular velocity of the reference course is constant and the angular acceleration is zero. Accordingly, the second-order differentiation, first-order differentiation, and reference course of the reference course in the constant speed mode are expressed as follows.

Here, ψ _Rv represents the reference course in the constant velocity mode, and r _R represents the angular velocity. The time range is [T _a ≦ t ≦ T _a + T _v ]. C _3V is an initial value. From the continuity relationship ψ ′ _Rv (T _a ) = ψ ′ _Ra (T _a ) and ψ _Rv (T _a ) = ψ _Ra (T _a ) between the constant speed mode and the acceleration mode,

を得る。

Get.

1.2.3 Deceleration mode The reference course coincides with the amount of change at the end of the mode (at the end), and its angular velocity and acceleration are attenuated to zero at the end of the mode. Therefore, the second-order differentiation, first-order differentiation, and reference course of the reference course in the deceleration mode are expressed as follows.

Here, ψ _Rd represents the reference course in the deceleration mode, and β _d represents the deceleration constant. The time range is [T _a + T _v ≦ t ≦ T _a + T _v + T _d ]. C _2d and C _3d are initial values. Relationship between continuity between deceleration mode and constant speed mode φ ′ _Rd (T _a + T _v ) = φ ′ _Rv (T _a + T _v ) and φ _Rd (T _a + T _v ) = φ _Rv (T _a + T _v ) From

を得る。さらに、終端時間ｔ＝Ｔ_a＋Ｔ_v＋Ｔ_dで角速度ψ'_Rv（ｔ）をゼロにするために、

Get. Furthermore, in order to make the angular velocity ψ ′ _Rv (t) zero at the end time t = T _a + T _v + T _d ,

を得る。

Get.

1.3 steering angle and the steering speed and the maximum value feedforward controller 12-2 outputs a feedforward steering angle [delta] _FF from the reference course [psi _R. The rudder angle δ _FF is the reciprocal of the hull model P to which the reference course ψ _R is input. Here, assuming that the hull model P uses (Equation 1), the feedforward steering angle δ _FF is obtained from the following.

Here, K _sn and T _sn are the nominal values of the hull model and represent the turning force gain and time constant. K _sn > 0 and T _sn > 0 are defined as stable ships, and K _sn <0 and T _sn <0 are defined as unstable ships. The steering angle δ _FF has an extreme value in the acceleration and deceleration modes since the second derivative of the reference course is a quadratic function. The steering angle δ _FF and the steering speed δ ′ _FF are obtained by substituting (Equation 5) and (Equation 15) of the reference course for each acceleration and deceleration mode into (Equation 19).

になる。ここで、ａ₃、ａ₂、ａ₁、ａ₀はそれぞれ加速モード（添字（・）_a）と減速モード（添字（・）_d）に対して、

become. Here, a ₃ , a ₂ , a ₁ , a ₀ are respectively for the acceleration mode (subscript (•) _a ) and the deceleration mode (subscript (•) _d ).

になる。尚、時間ｔは、加速モードで［０≦ｔ≦Ｔ_a］、減速モードで［０≦ｔ≦Ｔ_d］とする。

become. The time t is [0 ≦ t ≦ T _a ] in the acceleration mode and [0 ≦ t ≦ T _d ] in the deceleration mode.

1.3.1 Maximum rudder angle The maximum or minimum rudder angle is an extreme value that sets the rudder speed to zero.

で与えられる。ここで、分子の±の極性は＋が安定船に、−が不安定船に対応する。舵角の最大値または最小値は時間ｔ_δFFを（２０式）に代入することで求まる。最大舵角δ_R（以降、これを舵角と呼ぶ）は舵角δ_FFの絶対値の最大値

Given in. Here, with respect to the ± polarity of the molecule, + corresponds to a stable ship, and − corresponds to an unstable ship. The maximum value or minimum value of the rudder angle can be obtained by substituting the time _tδFF into (Equation 20). The maximum steering angle δ _R (hereinafter referred to as the steering angle) is the maximum absolute value of the steering angle δ _FF

で定める。

Determined by

1.3.2 Maximum rudder speed The derivative of the rudder speed is a linear function, and as shown in Fig. 2, the maximum or minimum value of the rudder speed is the time at the start or end of each of the acceleration and deceleration modes. It occurs in. The rudder speed is different at the start and end because of the initial value C _{1a in} the acceleration mode, and is the same at the start and end in the deceleration mode. The maximum and minimum values of the rudder speed are from (21 formula) to (23 formula).

になる。最大舵速度（以降これを舵速度と呼ぶ）δ'_Rは舵速度δ'_FFの絶対値の最大値

become. Maximum rudder speed (hereinafter referred to as rudder speed) δ ' _R is the maximum absolute value of rudder speed δ' _FF

で定める。

Determined by

2. Optimal design with an initial value of zero Based on the above relational expression, a reference course that satisfies the changing condition is obtained. For this purpose, first, the angular acceleration C _1a and the angular velocity C _2a, which are the initial values of the hull motion, are set to zero, the design parameters are determined, and the relational expressions of various variables are obtained. For the sake of simplification, the needle change amount Δψ ₀ is positive. As a result, the time T _a = T _d , the constant −β _a = β _d , and the needle change amount Δψ _a = Δψ _d in the acceleration and deceleration modes.

Therefore, the reference course can be obtained by determining the acceleration time T _a , the acceleration constant β _a and the angular velocity r _R (= T _a β _a / 6). As design parameters for obtaining these, a steering speed and a constant reduction ratio that is a ratio of a constant speed time T _v and a deceleration time T _d are used. The constant reduction ratio is set to a fixed value by introducing an evaluation function. Further, the relationship between the maximum rudder speed and the amount of change of needle when the initial value is zero is obtained, and the maximum rudder speed is set as a variable corresponding to the amount of change of needle.

2.1 Relational expression of reference course The ratio between the constant speed time T _v and the deceleration time T _d is _defined as a constant deceleration ratio R _vd . That is,

とする。尚ここで、減速時間Ｔ_dを用いている理由は、減速モードが初期値Ｃ_1a、Ｃ_2aに無関係であるからである。加速時間Ｔaと加速定数βaと、舵速度δ'_Rとの関係は、（２６式）を用いて、

And Here, the reason for using the deceleration time _Td is that the deceleration mode is irrelevant to the initial values C _1a and C _2a . The relationship between the acceleration time Ta, the acceleration constant βa, and the rudder speed δ ′ _R is expressed using (Equation 26):

となる。ここで、Ｃ_R≡δ_R’Ｋ_sn／Ｔ_snを舵定数と呼ぶ。変針量Δψ_Rと変針時間Ｔ_tとは、（５式）、（１１式）等から

It becomes. Here, C _R ≡δ _R 'K _sn / T _sn is called a rudder constant. The change amount Δψ _R and the change time T _t are obtained from (Formula 5), (Formula 11), etc.

になる。

become.

2.2 Steering angle relational expression The steering angle is expressed by (19) and is the sum of the first and second derivative of the reference course, so the extreme value of the steering angle is the first derivative of the second derivative. The position is shifted by the effect of differentiation.

Since the second derivative of the reference course becomes zero at the end time of the acceleration mode or the start time of the deceleration mode, the steering angle component is the first derivative, that is, the angular velocity r _R (from the condition Δψ _R > 0, r _R > 0. )become. In other words,

となり、不安定船では、

And in an unstable ship,

It becomes. The polarity of the rudder angle is positive for stable ships (K _sn > 0) and negative for unstable ships (K _sn <0). Therefore, the maximum absolute value of the rudder angle is generated as the maximum rudder angle in the acceleration mode in which the angular velocity component is added in the stable ship due to the influence of the first-order differential value, and the minimum rudder angle in the deceleration mode in which the angular velocity component is subtracted in the unstable ship. Arises as Hereinafter, the maximum value of the steering angle of each of the stable ship and the unstable ship is obtained.

2.2.1 In the case of a stable ship Obtain the time to take the extreme value from (Equation 24). When T _sn > T _a and up to the second order of the Taylor expansion,

になるから、極値の時間は、

So the extreme time is

になる。上記式の括弧内の第１項は参照針路の２階微分の極値時間に相当し、第２項は参照針路の１階微分の極値時間に相当する。よって、舵角の最大値は（３７式）を（２０式）に代入して、

become. The first term in parentheses in the above equation corresponds to the extreme time of the second derivative of the reference course, and the second term corresponds to the extreme time of the first derivative of the reference course. Therefore, the maximum value of the rudder angle is substituted (Expression 37) into (Expression 20),

になる。ここで、Ｔ_sn＞Ｔ_aの関係により２乗項と４乗項とを省く。こうして、舵角の最大値と加速時間Ｔ_a、加速定数β_aとの関係を（３８式）で示すような簡単な式で表すことができるようになる。

become. Here, the square term and the fourth power term are omitted due to the relationship of T _sn > T _a . In this way, the relationship between the maximum value of the steering angle, the acceleration time T _a , and the acceleration constant β _a can be expressed by a simple expression such as (Expression 38).

2.2.2 In the case of an unstable ship Except for generating a minimum rudder angle in the deceleration mode, the extreme time is the same as in the case of a stable ship.

となる。舵角の最小値は、

It becomes. The minimum rudder angle is

になる。

become.

2.2.3 Summary of maximum rudder angle Summarizing (38 types) and (40 types), the maximum rudder angle is

になる。安定船と不安定船の船体パラメータの絶対値が同じであれば、最大舵角は同じになり、参照針路の１階微分はＴ_a／Ｔ_snまたはＴ_d／Ｔ_snで影響する、という特性が得られる。

become. If the absolute values of the hull parameters of the stable ship and the unstable ship are the same, the maximum rudder angle will be the same, and the first derivative of the reference course will be affected by T _a / T _sn or T _d / T _sn Is obtained.

2.3 Design of constant reduction ratio The constant reduction ratio of design parameters is determined using an evaluation function. First, since obtaining a constant velocity time _{T v = 6Δψ R / (β} a T a) -T a more veering amount [Delta] [phi] _R from (31 type) or the like, veering time T _t is

になる。ここで、Ｔ_d＝Ｔ_a、β_a＝−β_dの条件を用いている。

become. Here, the conditions of T _d = T _a and β _a = −β _d are used.

When the acceleration time T _a that minimizes the needle changing time T _t is obtained,

を得る。このとき、等速時間Ｔ_vは０となる。舵速度が一定の条件下で加速時間が最大になると角速度ｒ_Rが最大になるので、変針時間を短くすれば角速度ｒ_Rを大きくすることになる。変針動作の運動エネルギーは角速度の２乗に比例すると想定すると、単に変針時間を短くすることにのみ着目することは省エネルギーの観点から得策ではない。よって、変針時間を許容範囲内に設定して角速度を低くするために、変針時間と角速度とを用いた評価関数を導入し、それを最小にする等減速比を求めることにする。

Get. At this time, the constant velocity time T _v is zero. When the acceleration time is maximized under a condition where the rudder speed is constant, the angular velocity r _R becomes maximum. Therefore, if the changeover time is shortened, the angular velocity r _R is increased. Assuming that the kinetic energy of the needle changing operation is proportional to the square of the angular velocity, it is not a good idea from the viewpoint of energy saving to pay attention only to shortening the needle changing time. Therefore, in order to set the needle changing time within an allowable range and reduce the angular velocity, an evaluation function using the needle changing time and the angular velocity is introduced, and an equal reduction ratio that minimizes it is determined.

Eliminating β _a from (Equation 31) and (Equation 38) to create a quadratic equation for T _a and finding its solution,

を得る。但し、

Get. However,

を仮定した。

Was assumed.

Similarly, when β _a is obtained and the needle changing time T _t and the angular velocity r _R are obtained,

になる。（４６式）及び（４７式）において等減速比以外の変数は設定値であるから、変針時間Ｔ_tと角速度ｒ_Rは等減速比Ｒ_vdの関数となる。

become. In (Equation 46) and (Equation 47), variables other than the equal speed reduction ratio are set values, so the needle changing time T _t and the angular velocity r _R are functions of the equal speed reduction ratio R _vd .

Furthermore, from (Equation 46) and (Equation 47), the constant velocity time and the angular velocity ratio with respect to the needle changing time with the constant velocity time being zero (R _vd = 0) and the angular velocity are defined as follows: To do. The evaluation amount is a form in which the coefficient is removed from (Equation 46) and (Equation 47).

  If the evaluation function J is the sum of squares of the respective evaluation quantities,

になり、この評価関数Ｊを最小にする等減速比Ｒ_vdの値を求める。ここで、λは正の重みを示す。評価関数ＪをＲ_vdで微分しそれをゼロとおくと、

Thus, the value of the equal reduction ratio R _vd that minimizes the evaluation function J is obtained. Here, λ represents a positive weight. Differentiating the evaluation function J with R _vd and setting it to zero,

になる。

become.

Table 2 shows the characteristics of the equal reduction ratio R _vd (> 0) that satisfies (Equation 51) and the evaluation function J at that time for various weights λ.

重みλが増加すれば評価関数は増加するが、変針時間の増加に対して、運動エネルギーの抑制効果が十分に期待できる範囲としては、２≦λ≦３の範囲、より好ましくは、λ＝２．３６とするとよいことが分かる。即ち、２≦Ｒ_vd≦２．６１、より好ましくは、Ｒ_vd＝２．２３とするとよく、この等減速比Ｒ_vdを基本的に固定に設定する。

As the weight λ increases, the evaluation function increases. However, the range in which the effect of suppressing the kinetic energy can be sufficiently expected with respect to the increase in the needle changing time is in the range of 2 ≦ λ ≦ 3, more preferably, λ = 2. It can be seen that .36 is preferable. That is, 2 ≦ R _vd ≦ 2.61, more preferably R _vd = 2.23, and this equal reduction ratio R _vd is basically set to be fixed.

2.4 Determination of rudder speed Next, the rudder speed is determined. The rudder speed δ ' _R is

となる。（５２式）を（３８式）、（４０式）に代入すると、β_aの２次方程式ができ、この解を求めると、

It becomes. By substituting (Equation 52) into (Equation 38) and (Equation 40), _a quadratic equation of β _a can be obtained.

として求まる。定数β_aが求まると、定数Ｔ_aも（５２式）から求めることができる。

It is obtained as When the constant β _a is obtained, the constant T _a can also be obtained from (Equation 52).

The only difference between the stable ship and the unstable ship is the calculation of β _a and β _d , so the stable ship is assumed below. For an unstable ship, β _a = β _d may be set for convenience. From (30 formula) and (31 formula)

となる。

It becomes.

When β _a , β _d , or T _a in (Formula 53) and (Formula 54) is substituted into (Formula 55) and deleted, the relational expression between the change amount Δψ _R , the steering angle δ _R, and the steering speed δ ′ _R Is obtained. That is,

となる。

It becomes.

The condition of the steering angle δ _R that makes the needle changing time T _{t the} shortest is to use an allowable value that is the upper limit from (Equation 46).

Since the range of Δψ _R can be set in the variable range of the rudder speed δ ′ _R , the range of δ ′ _{R is} , for example,

と定める。舵速度δ'_Rと変針量Δψ_Rとの関係を図４に示す。

It is determined. The relationship between the veering amount [Delta] [phi] _R and steering velocity [delta] _'R shown in FIG. 4.

The needle change amount Δψ _RL is a value using the upper limit value δ ′ _RH of δ ′ _R , and the needle change amount Δψ _RH is a value using the lower limit value δ ′ _RL of δ ′ _R. The change amount | Δψ _R | is divided into three change regions Small, Middle, and Large by Δψ _RL and Δψ _RH . Middle is an area where the rudder speed changes, and Small and Large are areas where the rudder speed is constant at the upper limit value δ ′ _RH and the lower limit value δ ′ _RL , respectively.

The amount of change Δψ _RL , Δψ _RH is obtained by using (Equation 56) and the like as Δψ _RL when δ ′ _R = δ ′ _RH and Δψ when Δδ _R = δ ′ _RL as Δψ _RH. Can do. That is,

になる。

become.

The middle rudder speed can be calculated by substituting (53) or (54) into (56) and solving the quadratic equation of δ ′ _R ^1/3 .

を得る。ここで−が安定船の場合に＋が不安定船に対応し、

Get. Here, when-is a stable ship, + corresponds to an unstable ship,

であり、変針量Δψ_Rから対応する舵速度δ'_Rを求めることができる。

Therefore, the corresponding steering speed δ ′ _R can be obtained from the amount of change Δψ _R.

As a result, the course change area corresponding to the course change amount is determined, and the maximum steering speed δ ′ _R to be used is determined from the area.

2.5 Specified turning angular velocity The angular velocity r _R is calculated by eliminating T _a and β _a from (Equation 11) or (Equation 31).

で求まる。

It is obtained by

Using the obtained angular velocity r _R , the maximum steering angle δ _R is obtained using the equation (41), the maximum steering angle δ _R is compared with the allowable steering angle δ ₀ (see Table 1), and the maximum steering angle When δ _R is larger than the allowable steering angle δ ₀ , r _R that satisfies the allowable steering angle δ _R = δ ₀ is determined, and the calculated r _R and the specified turning angular velocity r ₀ (see Table 1) Investigate the size relationship. When the obtained angular velocity r _R is equal to or higher than the specified turning angular velocity r ₀ , r _R = sign (ψ _R ) r _{0 is set} as a reference angular velocity. If the angular velocity is less than or equal to r _0, r _R is used as the reference angular velocity as it is. In the former case, since the angular velocity changes, the condition of the equal reduction ratio R _vd = 2.23 is not satisfied. Therefore, the changing condition is satisfied by adjusting the constant speed time. The change amount Δψ _Rv and constant speed time T _v in constant speed mode are

になる。

become.

3. Design Considering Initial Values Next, a case where initial values C _1a and C _2a of ship motion are considered will be described. The initial value is incorporated only in the acceleration mode. At the end of one acceleration mode, the initial angular acceleration value C _1a becomes zero, but the initial angular velocity value C _2a may not converge to the reference angular velocity r _R of the reference course. This is because the magnitude of the initial value C _{2a that} can be handled in one acceleration mode is limited by the steering angle limitation. Therefore, the influence of the magnitude of the initial value is eliminated by combining the acceleration modes a plurality of times.

Using the reference angular velocity r _R obtained by setting the initial value to zero, the rudder speed δ determined from the amount of change of the needle so that the angular velocity becomes r _R at the end of the acceleration mode and the rudder speed is C _1a and C _2a is zero. 'Set the acceleration time T _a and the acceleration constant β _a so as not to exceed _R. However, depending on the combination of the magnitude relationship between the initial values C _2a and r _R and the positive / negative relationship between the initial values C _1a , it may be inappropriate to use the reference angular velocity r _R. In this case, the reference angular velocity r _R is corrected.

3.1 Incorporation of initial values First, ignoring the rudder angle limitation, the acceleration mode constants including the initial values are determined. The rudder speed varies depending on the initial value C _{1a at the} start or end. Set the larger the absolute value of both the steering speed [delta] _'R.

When the acceleration time T _a and the acceleration constant β _a are related using the rudder speeds of (Equation 26) and (Equation 30),

を得る。ここで、Ｃ_Raは加速モードの舵定数を、flg_aは極性定数をそれぞれ示し、ｔ＝０、ｔ＝Ｔ_aは最大舵速度の発生時刻でそれぞれ開始と終端とを示す。

Get. Here, C _Ra indicates a steering constant in the acceleration mode, flg _a indicates a polarity constant, and t = 0 and t = T _a indicate the start and end, respectively, at the generation time of the maximum steering speed.

Relationship of acceleration mode including the initial value is obtained if you put the left side of the reference angular velocity determined by the initial value to zero angular velocity r _R (11 type). Substituting β _a in (Equation 64) into (Equation 11), _a quadratic equation relating to T _a

を得る。Ｃ_Ra≠０から加速時間は、

Get. From C _Ra ≠ 0, the acceleration time is

になり、β_aは（６４式）から求まる。

And β _a is obtained from (Equation 64).

3.1.1 once the time of occurrence of the maximum steering speed corresponding to the determined initial value of the time of occurrence of the maximum steering velocity, T _a from (66 type), beta _a is obtained from (64 type). The generation time of the maximum steering speed is obtained separately for the case of C _2a = r _{R and} the case of C _2a ≠ r _R.

In the case of C _2a = r _R , β _a <0 if C _1a > 0, the angular acceleration ψ ″ _Ra of the reference course is convex downward, and if C _1a <0, β _a > 0. The angular acceleration ψ " _Ra of the reference course is convex upward. For this reason, the maximum rudder speed occurs at the start.

In the case of C _2a ≠ r _R , it is further divided into a case where the difference in magnitude relationship between the two is large and a case where it is small. In this case, when the difference is large in (Equation 66), the (C _2a −r _R ) component is dominant, and when the difference is small, the C _1a component is dominant.

First, consider the case where the difference is large. If C _2a >> r _R, then β _a <0 and the reference course angular acceleration ψ " _Ra is convex downward, and the maximum steering speed occurs at the start if C _1a ≧ 0, and at the end if C _1a <0. . Similarly, if C _2a «r _R, angular acceleration [psi _"Ra reference course become beta _a> 0 becomes upwardly convex, the maximum steering speed is at C _1a> 0 if termination, if C _1a ≦ 0 Occurs at the start. Table 3 summarizes.

ところが、Ｃ_2aとｒ_Rの差が小さい場合、特に、Ｃ_2a＞ｒ_RでＣ_1a＜０及びＣ_2a＜ｒ_RでＣ_1a＞０の場合は、上記表３とは異なり、以下で説明するように、最大舵速度の発生時刻が終端時ではなく開始時に起こり、最大舵速度の発生時刻が異なり、Ｃ_2aとｒ_Rの大小関係で発生時刻を一義的に決定することができなくなる。そのため、それらの場合には角速度ｒ_Rに修正量を加えて差が大きい場合に変更することで、その条件から回避する必要がある。

However, when the difference between C _2a and r _R is small, in particular, when C _2a > r _R and C _1a <0 and C _2a <r _R and C _1a > 0, unlike Table 3, the following description will be given. As described above, the generation time of the maximum rudder speed occurs not at the end but at the start, the generation time of the maximum rudder speed is different, and the generation time cannot be uniquely determined by the magnitude relationship between C _2a and r _R. Therefore, in those cases, it is necessary to avoid the condition by adding a correction amount to the angular velocity r _R and changing when the difference is large.

3.1.2 Angular velocity correction amount For C _2a > r _R and C _1a <0, and C _2a <r _R and C _1a > 0, the termination time t = _Ta is examined. | C _2a -r _R | when> 0 the difference between the two is small, the t = T _a (66 type),

となり、加速時間Ｔ_aは差に比例して微小になる。ここで、Δｒ＝−６（Ｃ_2a−ｒ_R）とおく。但し、Ｃ_1a＜０のときに√の係数を−にしている。このとき、（６４式）のβ_aはＴ_a成分よりもＣ_1a成分が支配的になる。即ち、

Next, acceleration time T _a becomes small in proportion to the difference. Here, it is assumed that Δr = −6 (C _2a −r _R ). However, the coefficient of √ is − when C _1a <0. In this case, beta _a is C _1a component is dominant than T _a component (64 type). That is,

になる。ここで、ε＝Ｃ_RaＴ_aとしている。上式を（３式）に代入し、（６式）を用いる
と、

become. Here, it is a ε = C _Ra T _a. Substituting the above equation into (Equation 3) and using (Equation 6),

になり、（６９式）を微分すると

And differentiating (Equation 69)

になる。

become.

  Rudder speed from (19 formula)

で与えられる。開始及び終端時刻でのψ"_Ra、ψ"' _Ra、は、

Given in. Ψ " _Ra and ψ"' _Ra at the start and end times are

になるから、舵速度の大小関係は絶対値をとって開始及び終端時刻とで比較をすると（｜ａ＋ｂ｜≦｜ａ｜＋｜ｂ｜）、

Therefore, when the magnitude relation of the rudder speed is an absolute value and compared with the start and end times (| a + b | ≦ | a | + | b |),

になる。但し、ここで、Ｔ_a／Ｔ_sn＜２とする。よって、Ｃ_2a−ｒ_Rの差が小さいときには、最大舵速度はｔ＝Ｔ_aではなく、ｔ＝０で生じて、表３と矛盾が生じることが分かる。

become. However, here, and T _a / T _sn <2. Therefore, when the difference between the C _2a -r _R is small, the maximum steering speed rather than t = T _a, occurs at t = 0, it is understood that consistent with Table 3 is generated.

Therefore, finding a condition for the rudder velocity at t = 0 the same as t = T _a. In that case, ψ ″ ′ _Ra (t) is the same at time t = 0 and T _a . The coefficient α _a of ψ ″ _Ra (t) when the difference is small is α _a = C _1a −ε, The coefficient α _a of ψ ” _Ra (t) when the difference is large is α _a = −C _Ra T _a + C _1a and the polarity is reversed. That is, α _a becomes zero depending on the magnitude of the difference. When α _a is zero, that is, when β _a = −C _1a , ψ ″ ′ _Ra is independent of time, so the contribution to the rudder speed is constant. That is,

となり、舵速度に比例するψ"'_Ra＋（１／Ｔ_sn）ψ" _Raは、

Ψ "' _Ra + (1 / T _sn ) ψ" _Ra proportional to the rudder speed is

となる。β_aによるψ"_Raの様子を図５に示す（但し、Ｃ_2a＜ｒ_RでＣ_1a＞０の場合）。

It becomes. FIG. 5 shows the state of ψ ″ _Ra due to β _a (provided that C _2a <r _R and C _1a > 0).

When the magnitude relation of the rudder speed when β _a = −C _1a is examined,

になり、（７３式）に比べ差の大きさは小さくなる。しかし、最大舵速度の時刻はＴ_sn項の影響を受けるため、安定船の場合、ｔ＝Ｔ_aで最大となり、Ｃ_2a＞ｒ_RでＣ_1a＜０、及びＣ_2a＜ｒ_RでＣ_1a＞０の場合の条件を満足するが、不安定船の場合には、ｔ＝０で最大となり、条件を満足できない。以下各々の場合を説明する。

Therefore, the magnitude of the difference is smaller than that of (Expression 73). However, since the time of the maximum steering rate affected the T _sn terms, in the case of stable vessels, t = maximum at T _a, C _2a> r _R in C _1a <0, and C _2a <r _R in C _1a The condition for> 0 is satisfied, but in the case of an unstable ship, the maximum is reached at t = 0, and the condition cannot be satisfied. Each case will be described below.

For cases stable ship 3.1.2.1 stable vessels, the maximum steering speed is t = T _a by T _sn terms in (76 type).
(i) When C _2a > r _R and C _1a <0, β _a ≦ −C _1a may be set. Therefore, when this inequality is transformed using (Equation 64),
_{β a = C Ra T a -2C} 1a ≦ -C 1a
C _Ra T _a ≦ C _1a
It becomes.

Since C _2a > r _R and C _1a <0 and C _Ra <0,
T _a ≧ C _1a / C _Ra , from (Equation 66)

となる。２乗して極性に注意して整理すると、

It becomes. If you square it up and keep your polarity in mind,

となる。

It becomes.

(ii) When C _2a <r _R and C _1a > 0, it may be set such that β _a ≧ −C _1a . Similarly, if this inequality is transformed,
_{β a = C Ra T a -2C} 1a ≧ -C 1a
C _Ra T _a ≧ C _1a
And
Since C _2a <r _R and C _1a > 0 and C _Ra > 0,
T _a ≧ C _1a / C _Ra

となる。２乗して極性に注意して整理すると、

It becomes. If you square it up and keep your polarity in mind,

となる。

It becomes.

3.1.2.2 For unstable ship when unstable ship, since they produce a maximum value of the steering rate than T _sn <0 at t = 0 not t = T _a in (76 expression), t = 0 the steering speed may be set below the steering speed at t = T _a at.
(i) When C _2a > r _R and C _1a <0 (Equation 26), (Equation 64)

が得られる。さらに、

Is obtained. further,

を得る。これを、（６４式）のｔ＝Ｔ_aのβ_aに代入すると、

Get. Substituting this into β _a of t = T _a in (Equation 64),

になる。ここで、

become. here,

である。（８３式）及び（８４式）からＴ_aを取り出して、それを（６６式）に代入すると、

It is. (83 type) and taken out T _a from (84 type), substituting it into (66 type),

となる。さらにこれを極性に注意して整理すると、

It becomes. Furthermore, if you organize this with attention to polarity,

として求まる。

It is obtained as

(ii) When C _2a <r _R and C _1a > 0
From (26) and (64) as in (i)

が得られる。そして、同様の計算を行なうと、

Is obtained. And when doing the same calculation,

を得る。

Get.

3.1.2.3 Summary of angular velocity correction amount In formulas (78), (80), (86), and (89), r _C represents the angular velocity correction amount and is opposite to the polarity of C _Ra . As a result, when these equations are satisfied, the maximum rudder speed is generated at the end time, and becomes the set value. When not satisfied, the angular speed r _R is determined using the correction amount r _C and the initial value C _2a.

に置き換えることによって、安定船不安定船の双方で時刻ｔ＝０とｔ＝Ｔaの舵速度の大きさは等しく、その最大舵速度とすることができる。

By replacing with, the magnitudes of the rudder speeds at the times t = 0 and t = Ta are equal in both the stable ship and the unstable ship, and the maximum rudder speed can be obtained.

  The following table summarizes the above relationships.

3.2 Derivation of rudder angle including initial values
The maximum rudder angle may be increased by the initial value and exceed its allowable value. Therefore, the rudder angle formula including the initial value is obtained. Substituting (Expression 64) into (Expression 35) and (Expression 36) and approximating up to the first order term of the initial value C _1a ,

になる。（９２式）は安定船不安定船の双方に対応する。舵角の極値である最大舵角はβ_aに依存するため、最大舵速度の発生時間毎に求める。

become. (Formula 92) corresponds to both stable ships and unstable ships. Since the maximum steering angle is the extreme values of the steering angle is dependent on the beta _a, determined for each time of occurrence of the maximum steering speed.

3.2.1 If the maximum steering speed occurs at the starting time relationship between the acceleration time steering angle is an expression of beta _a and the steering angle of the t = 0 in the extreme time t _p (64 type) ( Substituting into equation (20) and approximating up to the first order term of C _1a ,

As obtained. (40 type) at is used a quadratic equation of T _a, is used here to cubic equation. This is because the third order coefficients T _a of C _1a can not be omitted not sufficiently small compared with the second-order coefficient. From (Expression 93), the steering angle can be calculated using the acceleration time _Ta and the initial values _C1a and _C2a . When the calculated absolute value of the rudder angle exceeds the allowable rudder angle that is the set value, the absolute value of the rudder angle is made to coincide with the allowable rudder angle by changing the acceleration time. That is, by replacing the permissible steering angle [delta] ₀ is a setting value steering angle [delta] _R in (93 type), cubic equation of T _a is

になり、Ｔ_aは求まる。Ｔ_aよりβ_aが求まり、角速度ｒ_Rは（１１式）より求まる。

And T _a is obtained. Β _a is obtained from T _a , and angular velocity r _R is obtained from (Equation 11).

3.2.2 relational expression between when the steering angle maximum steering speed occurs at the end time acceleration time is substituted into an expression of beta _a and the steering angle of the extreme time t _p t = T _a (64 type) And approximating up to the first order term of C _1a

As obtained. Similarly, when the absolute value of the calculated steering angle exceeds the allowable steering angle, the absolute value of the steering angle is matched with the allowable steering angle by changing the acceleration time. That is, when replacing the steering angle [delta] _R in the allowable steering angle [delta] ₀ (95 type), cubic equation of T _a is

になり、Ｔ_aは求まり、また、Ｔ_aよりβ_aが求まり、角速度ｒ_Rは（１１式）より求まる。

T _a is obtained, β _a is obtained from T _a , and angular velocity r _R is obtained from (Equation 11).

4). Corresponding to small angle When C _1a ≠ 0 and C _2a ≠ 0, where the initial value of the hull motion is not zero, the reference course is configured to attenuate the initial value and match the amount of change. At this time, if the amount of change in needle is small, the turning angular velocity is set small. However, when the amount of azimuth change necessary for attenuating the initial value is larger than the amount of change of the needle, there is a problem that it takes time for changing the needle because of turning at a small turning angular velocity. This state is called a small angle.

  As a response to this, if it is determined that the amount of azimuth change is greater than the amount of change of needle, the acceleration mode is divided into the attenuation mode and the normal mode as a small angle correspondence, and after the initial value is attenuated in the attenuation mode, The reference course in the acceleration mode is obtained by replacing the sum of the azimuth change and the change amount with the change amount again.

The specific calculation for determining whether or not to generate the attenuation mode is performed by first _obtaining the azimuth change amount ψ _ini resulting from the initial value. The azimuth change amount ψ _ini resulting from the initial value can be obtained from (Expression 5) and (Expression 6) by _obtaining the acceleration time T _a and the acceleration constant β _a.

で得られる。次いで、この方位変化量ψ_iniと変針量とを比較して、小角度対応するかどうかを決定する。

It is obtained by. Next, the azimuth change amount ψ _ini and the amount of change of needle are compared to determine whether or not to correspond to a small angle.

5. Modification of Hull Model In the above description, it is assumed that the transfer function of the feedforward controller 12-2 has an inverse characteristic of the transfer function P (s) of the hull plant. Analysis is performed using the same (Equation 1) as shown.

  However, in the marine automatic steering apparatus using the primary model of Nomoto of (Formula 1) in Patent Document 1, an overshoot may occur in the actual ship after the course is changed. The cause of the overshoot is considered to be that the difference between the actual hull characteristics and the hull model of the control system cannot be ignored. Therefore, it is necessary to specify an appropriate hull model.

FIG. 6 shows the change over time of the reference course and the first-order differential change response of the reference course. The deviation error of the heading direction ψ with respect to the reference course ψ _R is so small that it can be ignored in the course change state, and the start of the static state is started. At times, the deviation error is almost zero, then overshoot occurs and converges to zero again. The deviation error of the turning angular velocity dψ / dt with respect to the reference angular velocity dψ _R / dt coincides in the acceleration mode at the end of the needle changing state, causes an error in the constant velocity mode, has an error not returning to zero in the deceleration mode, and has an error. In the state, the starting error (initial value) converges to zero. Therefore, it is considered that the occurrence of the overshoot in the azimuth direction in the static state is caused by the initial value of the angular velocity.

First, consider Nomoto's primary model and secondary model as models.
Nomoto's secondary model is

Represented as: Here, δ _c indicates the command rudder angle, K _s , T _s1 , T _s2 , and T _s3 indicate hull parameters and turning force gain, and three time constants. The polarities of the hull parameters are T _s2 > 0, T _s3 > 0, K _s > 0, T _s1 > 0 for stable ships, and K _s <0, T _s1 <0 for instability. The magnitude relationship of the time constants is | T _s1 |> T _s3 > T _s2 . Block diagrams of Nomoto's primary model and secondary model are shown in FIGS. 7 (a) and 7 (b), respectively. In the figure, ψ (0), ψ ′ (0), ψ ′ ₁ (0), and ψ ′ ₂ (0) indicate initial values and r = dψ / dt.

  The static state becomes a closed loop response by the feedback controller 12-3.

Here, K _P and K _D are feedback gains, which respectively indicate a proportional gain and a differential gain. The initial condition of the static state is

と定める。ここで、ψ_R0は参照針路の変針量を示す。

It is determined. Here, ψ _R0 indicates the amount of change in the reference course.

  Substituting (99) into (98),

になる。但し、ψ'₁₀＝ψ'₁（０）、ψ'₂₀＝ψ'₂（０）としている。上式に静定状態の初期条件を当てはめると、

become. However, ψ ′ ₁₀ = ψ ′ ₁ (0), ψ ′ ₂₀ = ψ ′ ₂ (0). When the initial condition of the static state is applied to the above equation,

となる。ここで、特性多項式を実数ａ、減衰係数ζ及び固有周波数ω_nで因数分解することができると仮定している。

It becomes. Here, it is assumed that the characteristic polynomial can be factored with the real number a, the attenuation coefficient ζ, and the natural frequency ω _n .

The response in the static state is that the first term is a constant value from the above equation, and the second term is the initial value response of ψ ′ ₁₀ and ψ ′ ₂₀ by the first-order lag elements of the time constants T _s1 and T _s2 , respectively. Become. The difference between the two initial value responses is determined by the numerator coefficient and the magnitude of the initial value since the characteristic polynomial of the denominator is common. To examine the difference,

を定める。ここで、Ｔ_cは時定数、Ｇはゲインを示す。上記の時間解は０＜ζ＜１とおく
と、

Determine. Here, T _c is a time constant, and G is a gain. If the above time solution is 0 <ζ <1,

になる。ここで、

become. here,

を示す。（１０４式）より、応答の振幅およびピーク値はＧの大きさに比例し、ピーク時間はsin項のみの場合に比べcos項の係数Ａに比例して早まる。（１０１式）の特性方程式

Indicates. From (Equation 104), the amplitude and peak value of the response are proportional to the magnitude of G, and the peak time is earlier in proportion to the coefficient A of the cos term than in the case of only the sin term. Characteristic equation of (101)

から、実数ａの近似解は時定数の大小関係｜Ｔ_s1｜＞Ｔ_s3＞Ｔ_s2より｜Ｔ_s1｜≫Ｔ_s2を用いると、

From approximate solution time constant magnitude of the real _{a | T s1 |> T s3} > T s2 than | T _s1 | With »T _s2,

になる。また、Ａ，Ｂの分母は、ａ²−２ζω_nａ＋ω_n ²＝（ａ−ζω_n）²＋ω_n ²（１−ζ²）＞０となる。ψ'₁₀、ψ'₂₀との初期値応答は、（１０４式）の特性により次のようになる。

become. The denominators of A and B are a ² −2ζω _n a + ω _n ² = (a−ζω _n ) ² + ω _n ² (1−ζ ² )> 0. The initial value responses of ψ ′ ₁₀ and ψ ′ ₂₀ are as follows according to the characteristics of (Equation 104).

In the case of the initial value ψ ′ ₁₀ , T _c = T _s2 and G = ψ ′ ₁₀ can be approximated to A≈0 and B≈1. In (Equation 104), the response is almost the same as in the case of the primary model, with the sine term dominant. As a result, ψ ′ ₁₀ ≈ψ ′ ₀ .
In the case of the initial value ψ ′ ₂₀ , A> 0 and B <1 from T _c = T _s3 and G = ψ ′ ₂₀ T _s3 / T _s1 . Assuming that the peak value is ψ ′ ₂₀ ≒ ψ ′ ₁₀ compared to the case of the initial value ψ ′ ₁₀ ,

になるため減少し、ピーク時間が早まる。

The peak time is shortened.

Thereby, the initial value response in the static state is dominant due to the time constant T _s1 than from the time constant T _s2 . Therefore, the 1 · BR> 汳 X deviation element of the time constant T _s2 corresponding to the initial value ψ ′ ₂₀ can be omitted from the denominator of the secondary model. On the other hand, the time constant T _s3 of the second-order model molecule needs to be present to suppress the occurrence of overshoot.

  Therefore, in the present invention, as shown in FIG.

を採用し、フィードフォワード制御器１２−２の伝達関数は、その逆数の特性となるように、

So that the transfer function of the feedforward controller 12-2 has a reciprocal characteristic.

と設定し、時定数Ｔ_s3を更なる船体パラメータとする。

And set the time constant T _s3 as a further hull parameter.

However, the configuration of the trajectory calculation unit 12-1 is not changed, and the calculation is performed using the primary model as described in the previous items 1 to 4. This is because the set maximum rudder angle and maximum rudder speed are suppressed by the low-pass filter effect due to the presence of the time constant T _s3 , so that the demand on the steering machine is reduced. This is because there is no change to the initial value of movement.

6). Process of Trajectory Calculation Unit The process performed by the trajectory calculation unit 12-1 will be described with reference to the flowcharts of FIGS.

Step S10: First, a needle changing condition is input. The course changing conditions are a desired course changing amount Δψ ₀ , a specified turning angular velocity r ₀ , initial values C _1a and C _{2a of} the hull motion, nominal values T _sn and K _{sn of} the hull parameters, an allowable steering angle δ ₀ and an upper limit of the steering speed. There is a value δ ′ _RH , a lower limit value δ ′ _RL, and the like.

The initial values C _1a and C _2a of the hull movement are the start of the course change between the second and first order differentials of the reference course that was calculated by the trajectory calculation unit for the previous course when the course was being changed at the start of the course change. It is determined from the time value. That is, when the next course change is set at time t ′ at the previous course change, the initial value is the second-order derivative ψ ″ _R (t ′) = C _1a of the reference course at the previous course change and the first floor. Differentiating ψ ′ _R (t ′) = C _2a , whereby an initial value that is not affected by noise can be obtained.

Step S12: Next, variables are set. 4 is set for the steering speed limit values δ ′ _RH and δ ′ _RL . At this time, Δψ _RL and Δψ _RH can be obtained from (Expression 56) and (Expression 58).

Step S14: Next, it is determined whether or not the initial value of the hull motion is attenuated, that is, the small angle correspondence is performed. Specifically, the azimuth change amount ψ _ini and the needle change amount Δψ ₀ are compared. The azimuth change amount is obtained from (Equation 97). The acceleration time T _a and the acceleration constant β _a in (Equation 97) were obtained from (Equation 66) and (Equation 64) as r _R = 0 and δ ′ _{R as} a limit value (upper limit value or lower limit value). Use things.

  Step S20: When only the normal mode is performed without executing the attenuation mode, the reference course described below is calculated.

  Step S40: When executing the attenuation mode, the attenuation of the initial value and the amount of change of the needle described below are calculated. After step S40, the reference course in step S20 is calculated.

  Next, the calculation of the reference course in the normal mode of the acceleration mode is performed based on the flowchart shown in FIG. 10, and the reference course is obtained from the desired amount of change of needle, the set angular velocity, and the initial value.

Step S22: The change amount Δψ ₀ , the angular velocity r ₀ and the initial values C _1a and C _2a of the hull motion are input. Therefore, an initial value that is not affected by noise can be obtained.

Step S24: the initial value C _1a, without using a C _2a, obtains the steering speed [delta] _'R and the angular velocity r _R for veering amount [Delta] [phi] _R.

That is, it is determined which one of the shift regions in FIG. 4 set in step S12 with respect to the given change amount Δψ _R and the corresponding steering speed δ ′ _R is obtained. Further, the turning angular velocity is obtained using (Equation 61). When the turning angular velocity exceeds the specified turning angular velocity r ₀ , the angular velocity r _R = sign (ψ _R ) r ₀ is set.

Step S26: Calculate acceleration, constant speed, and deceleration modes. Find the constant for each mode. For acceleration mode attenuates the initial value under the condition that the maximum steering angle equal to or less than the allowable steering angle, and sets the turning angular velocity during termination to match the reference velocity r _R. However, for the reference angular velocity r _R , the conditions shown in Table 4 are determined. When C _2a > r _R and C _1a <0, and when C _2a <r _R and C _1a > 0, ).

The acceleration time T _a and the acceleration constant β _a are obtained from (Expression 66) and (Expression 64), and the rudder angle δ _R determined by (Expression 93) or (Expression 95) is the set value. When the allowable steering angle is exceeded, T _a is obtained from (Equation 94) or (Equation 96), the acceleration constant β _a is obtained from (Equation 64), and the angular velocity r _R is obtained from (Equation 11).

The error between the amount of needle change Δψ _R and the sum of the amount of needle change in each mode is canceled by correcting the constant velocity time. That is, the constant speed time is

become. Here, Δψ ₀ , Δψ _Ra , Δψ _Rv , Δψ _Rd are the amount of change of the needle, the set value, acceleration, constant speed, and deceleration of the mode, respectively, (•) ^* is the correction value, and T _v is the constant speed. Time, r _R represents angular velocity.

  Step S28: It is determined whether the constant velocity time is not negative and the angular velocity has become the reference angular velocity (angular velocity obtained in step S24). The determination proceeds to the next step when the constant velocity time is zero or more and the error of the absolute value between the angular velocity and the reference angular velocity is equal to or smaller than the convergence value ε, and returns to the loop repeatedly when not.

  Step S30: If the determination is no in step S28, the cumulative amount of needle change and the initial value are updated. An azimuth change in acceleration mode is added to the amount of change of needle, and the angular velocity at the end of acceleration mode is replaced with the initial value of angular velocity. That is,

になる。ここで、Δψ^* ₀は修正変針量を、ΣΔψ_Raは加速モードの累積値をそれぞれ示す。

become. Here, Δψ ^* ₀ indicates the corrected amount of change in needle, and ΣΔψ _Ra indicates the cumulative value in the acceleration mode.

  Next, the damping mode is performed based on the flowchart shown in FIG. 11, and the absolute value of the initial value is made asymptotic to zero with the steering speed as a limit value without considering the amount of change of the needle, and the azimuth change generated in the process is accumulated.

Step S42: The initial value of the hull motion is input and the reference angular velocity is set to zero.
Step S44: The acceleration mode angular velocity end value and the needle change amount (Equation 97) are calculated.
Step S46: It is determined whether or not the angular velocity end value is zero. The determination proceeds to the next step when the absolute value of the terminal value is equal to or smaller than the convergence value ε, and returns to the loop repeatedly when not.
Step S48: The same processing as step 30 is performed.

The reference course calculated as described above is sequentially output to the feedforward controller 12-2, where the feedforward steering angle δ _FF is calculated, and the feedback steering angle from the feedback controller 12-3 is calculated. δ _FB is added by the adder 12-5 and then output to the steering device 16. The reference course is calculated based on K _sn and T _sn , but since the ship model includes T _s3n (Equation 109), the calculation in the feedforward controller 12-2 is expressed as (Equation 110). Thus, the reference course is a time function solution that has passed through a first-order lag system of T _s3n . As a result, overshoot at the time of changing the needle is prevented.

12 and 13 show simulation results under various conditions. FIG. 12 shows a large angle change of an unstable ship. One acceleration mode is performed under the conditions of Δψ ₀ = −15 deg, C _1a = 0.01 deg / s ² , and C _2a = 0.3 deg / s. In this example, two acceleration modes are combined because they cannot converge to the reference turning angular velocity. FIG. 13 (A) shows a small angle change of the stable ship, and it is initial in two decay modes under the conditions of Δψ ₀ = 0 deg, C _1a = 0 deg / s ² , C _2a = 0.9 deg / s In this example, the value is attenuated and converged to the reference angular velocity in one normal mode. FIG. 13B shows a small angle change of an unstable ship. Seven attenuation modes are performed under the conditions of Δψ ₀ = 0 deg, C _1a = 0 deg / s ² , and C _2a = −0.8 deg / s. This is an example in which the initial value is attenuated in step 1 and then converged to the reference angular velocity in one normal mode.

7). In the above description, the constant reduction ratio is designed with a fixed value as described in the previous section 2.3, and this places importance on the balance between acceleration, constant speed, and deceleration. However, in this design, if not a major veering, it is impossible to match the angular speed r _R in the specified turning angular velocity r _0.

FIG. 14 shows a trajectory calculation unit 12-1 based on a modification in which the constant reduction ratio is changed from fixed to variable. The trajectory calculation unit 12-1 includes an equal reduction ratio calculation unit 12-1-1 and a reference course calculation unit 12-1-2, and the reference course calculation unit 12-1-2 includes the trajectory calculation of FIG. It shall perform the same action as the part 12-1. In equal speed reduction ratio calculating unit 12-1-1 obtains a turning angular velocity r _R the initial value C _2a of the turning angular velocity as the initial value C _1a of the slewing angular acceleration of veering beginning zero, at that time, the turning angular velocity r _R Is assumed to be equal to the specified turning angular velocity r ₀ , the turning angular velocity r _R is determined as the specified turning angular velocity r ₀ when the steering angle δ _R satisfies the condition of the allowable steering angle δ ₀ or less. When not satisfied, the angular velocity that minimizes the deviation between the steering angle δ _R and the allowable steering angle δ ₀ is determined as the turning angular velocity r _R , and is set as a new designated turning angular velocity. Then, the maximum steering speed δ _R ′ at the determined designated turning angular speed is set as the steering speed upper limit value.

Then, when determining whether or not the steering angle δ _R satisfies the condition of the allowable steering angle δ ₀ or less, it is determined whether or not the condition is satisfied while changing the equal reduction ratio R _vd . If the steering angle condition is not satisfied even if the equal reduction ratio R _vd is changed, the angular velocity r _R is changed to find the angular velocity r _R that satisfies the steering angle condition. Specific processing performed by the equal reduction ratio calculation unit 12-1-1 will be described below.

7.1 Preparation Here, the relational expressions that have appeared in the above explanation and are used in the following explanation are arranged. In this equal reduction ratio calculation unit 12-1-1, a relational expression that does not consider the initial values C _1a and C _2a is used.

であり、Ｃψ、Ｃ_Rは、（３０式）、（６０式）から

And a, Cψ, C _R is (30 type), from (60 type)

である。

It is.

7.2 Angular speed at which the constant reduction ratio R _vd ≧ 0 can be realized at the maximum steering angle _{Assuming that the} steering speed is not limited, an allowable steering angle δ ₀ and a specified turning angular speed r ₀ that can be realized at the constant reduction ratio R _vd ≧ 0 are obtained. When r _R in (Equation 119) is replaced with r ₀ and δ _R in (Equation 120) is replaced with δ ₀ , respectively, a quadratic equation of R _vd is obtained.

を得る。ここで、各係数は、以下の通りである。

Get. Here, each coefficient is as follows.

When the discriminant D = b ² -4ac ≧ 0, r ₀ is realized, and when D <0, r ₀ is not realized. When D <0, r ₀ that satisfies D = c ₁ ² −1 / 4 = 0 is an angular velocity that can be realized. In summary, the angular velocity that can be achieved under the allowable steering angle is

により決まる。

It depends on.

7.3 Angular speed at which the constant reduction ratio R _vd ≧ 0 can be realized with the allowable steering speed Further, the allowable steering speed δ ₀ ′, the maximum steering angle is not limited, and the angular speed r _R that can be realized with the constant reduction ratio R _vd ≧ 0 is obtained. If C _R corresponding to δ ₀ is C _R0 ,

になる。等減速比Ｒ_{vd max}がεより小さいときには、ｒ_Ｒは実現できないので、その場合には、角速度ｒ_Ｒを

become. When the constant reduction ratio R _{vd max} is smaller than ε, r _R cannot be realized. In this case, the angular velocity r _{R is set} to

のように下げる。ここで、εは１０⁻³程度の設定値とする。まとめると、

Lower like. Here, ε is set to about 10 ⁻³ . Summary,

となる。

It becomes.

7.4 Comparison with the maximum rudder angle Check whether the maximum rudder angle value does not exceed the allowable rudder angle δ ₀ when R _vd and r _R determined in (Expression 130) and (Expression 131) above. To do. Specifically, the rudder speed δ _R ′ is obtained from the equations (116), (117), and (119) using R _vd and r _R determined in (130) and (131). Using the obtained steering speed δ _R ′, the steering angle δ _R is obtained from (Equation 120), the obtained steering angle δ _R is compared with the allowable steering angle δ _0, and if δ _R ≦ δ ₀ , 7 is obtained. Proceed to step 7. If δ _R > δ ₀ , first, R _vd > 0 having the lowest priority is adjusted to meet the changing condition, and then r _R having the second lowest priority after R _vd is adjusted to satisfy the changing condition. Adapt. As preparation for that, first, the characteristic regarding the equal reduction ratio R _vd of the steering angle δ _{R and} the characteristic regarding the angular velocity r _R are examined.

7.4.1 Characteristic relating to equal reduction ratio R _vd of steering angle δ _R (Equation 119) is substituted into (Equation 120) to obtain the first and second derivatives of R _vd of δ _R. Then

となり、これにより、δ_RはＲ_vdに関して下に凸関数で、極小値は、

Thus, δ _R is a downward convex function with respect to R _vd , and the local minimum is

のとき生じることが分かる。変針条件によってＲ_vdmin＜０になる場合が生じるが、その場合は条件Ｒ_vd＞εから単調増加の関数として扱う。

It can be seen that In some cases, R _vdmin <0 occurs depending on the needle changing condition. In this case, the condition R _vd > ε is treated as a monotonically increasing function.

7.4.2 Characteristics related to angular velocity r _R of steering angle δ _R Similarly, (119) is substituted into (120), and the first and second derivatives of δ _R with respect to r _R are obtained. Then

になる。これにより、δ_Rはｒ_Rに関して単調増加の関数であることが分かる。

become. This shows that δ _R is a monotonically increasing function with respect to r _R.

As adjust the aforementioned 7.5 mag reduction ratio R _vd, etc reduction ratio R _vd becomes minimum [delta] _R when R _Vdmin, also, maximum [delta] _R when R _Vdmax when becomes [delta] ₀ ' Value. In FIG. 15, the horizontal axis represents the equal reduction ratio R _vd , and the vertical axis represents the steering speed δ _R ′, the steering angle δ _R, and the needle changing time T _t . Steering angle [delta] _R becomes minimum at R _Vdmin, a [delta] ₀ in R _Vdmax. Therefore, in order to shorten the needle change time T _t and make one solution, the search range of R _vd is [R _vdmin , R _vdmax ], and the error between δ _R and δ ₀ is minimized within this range. R _vd is obtained by an arbitrary method such as golden section.

7.6 Adjustment of Angular Speed r _R Using R _vd obtained in 7.5, the steering angle δ _R is obtained using the procedure of 7.4, and the steering angle δ _R is compared with the allowable steering angle δ _0. If δ _R ≦ δ ₀ , proceed to step 7.7. If δ _R > δ ₀ , the angular velocity r _R that minimizes the error between δ _R and δ _{0 in} the range [0, r _R ] is obtained by an arbitrary method such as golden section.

7.7
Using the equal reduction ratio R _vd , angular velocity r _R , and rudder speed δ _R ′ determined by the above procedure, the angular speed r _R and the rudder speed δ _R ′ are respectively set to the specified turning angular velocity r ₀ and the upper limit value δ of the rudder speed in the changing condition. _{As RH} ′, the lower limit value δ _RL ′ = δ _RH ′ × 0.5 is input to the reference course calculation unit 12-1-2. The reference course calculation unit 12-1-2 is the same as the above-described 6. The process of the trajectory calculation unit is executed. The upper limit value δ _RH ′ of the steering speed is equal to or less than the allowable steering speed δ ₀ ′.
At step S24 in the "6 process trajectory calculation unit", this veering area Small, since the steering speed becomes [delta] _RH ', the angular velocity r _R will be possible to realize a specified turning angular velocity r _0.
FIG. 16 shows the simulation results. FIG. 16A shows the case where the constant reduction ratio R _vd is constant at 2.23, and FIG. 16B shows the case where the constant reduction ratio R _vd is variable. By making the constant reduction ratio R _vd variable, the angular velocity r _R can be matched with the designated turning angular velocity r ₀ .

8). Robustness improvement at the time of acceleration / deceleration The positional relationship between the propeller and the rudder is lined up and down as shown in FIG. 17, and the wake by the propeller follows the rudder. Since the turning force gain K _s of the maneuverability index is proportional to the flow speed around the rudder, the turning force gain changes in the same manner when the rotation speed or pitch angle of the propeller changes. On the other hand, the speed of the hull changes slowly due to the first-order lag system with a large time constant. For this reason, a response difference between the wake speed and the ship speed occurs, and even if the turning force gain is corrected by the ship speed, the effect cannot be expected, and the amount of change of needle and the angular speed are as shown in FIG. This causes a problem that the set value cannot be retained. The time constant of the maneuverability index tends to be governed by the relationship between the hull and the ship speed rather than the influence of the wake. Therefore, from the start of acceleration / deceleration until the steady ship speed is reached, the time constant of the maneuverability index changes slowly with a first-order delay, and the turning force gain changes more quickly than that. Therefore, the improvement of the robustness of the needle changing control system with respect to the parameter uncertainty of the turning force gain becomes an issue.

8.1 Solution The ship speed can be obtained from the speedometer attached to the hull from Fig. 17, but the wake speed cannot be obtained directly. As shown in FIG. 19, the time response of both is expected to be faster at the wake speed than at the ship speed. The steady value of the wake speed is higher than that of the ship speed from the pressure difference. Therefore, since the turning force gain at the time of ship speed change is implemented in the state where the wake speed is already close to the steady value, it is difficult to correct the turning force gain due to the change in the wake speed.

  Therefore, the azimuth error or angular velocity error associated with the change in the turning force gain is reduced by utilizing a phenomenon in which the thrust change during acceleration / deceleration appears as an azimuth deviation. Since the change-over response is not based on feedback but based on feedforward, countermeasures are taken against feedforward.

The azimuth ratio ψ / ψ _R of the response from the reference course ψ _R to the bow azimuth ψ is as shown in FIG. 18B when referring to FIG. The azimuth ratio is 1 or more during acceleration and 1 or less during deceleration.
Azimuth ratio, or transfer function, is ignored because the closed-loop response to propulsion changes is slow,

の様に旋回力ゲイン比と等価になる。ここで、添字（）_aは実際値、（）_nはノミナル値を表しており、また、推進力変化は、プロペラ回転数に相当し、プロペラの下流部にある舵に作用するので、操縦性指数のうち、時定数Ｔ_sa、Ｔ_s3aへの影響を無視し、旋回力ゲインＫ_saに影響すると定め、Ｔ_sn＝Ｔ_sa、Ｔ_s3n＝Ｔ_s3aとする。これよりψ＝ψ_Rとするために、方位比

This is equivalent to the turning force gain ratio. Here, the subscript () _a represents the actual value, and () _n represents the nominal value, and the propulsive force change corresponds to the propeller rotation speed and acts on the rudder downstream of the propeller. Of the exponents, the influence on the time constants T _sa and T _s3a is ignored and it is determined that the turning force gain K _sa is affected, and T _sn = T _sa and T _s3n = T _s3a . From this, in order to set ψ = ψ _R , the orientation ratio

をフィードフォワード舵角δ_FFに掛けることによって、推進力変化を起因とする方位誤差を低減する。

Is multiplied by the feedforward steering angle δ _FF to reduce the azimuth error caused by the change in propulsive force.

8.2 Configuration FIG. 20 is a block diagram illustrating a configuration of a modified example in which robustness is improved during acceleration / deceleration. As shown in the figure, an azimuth ratio multiplier 12-6 is provided downstream of the feedforward controller 12-2, and an azimuth ratio calculation unit 12-7 and an azimuth ratio restriction unit 12-8 are further provided.
Orientation ratio multiplier 12-6 is for multiplying the orientation ratio R _K feedforward steering angle [delta] _FF output from the feedforward controller 12-2.

Orientation ratio calculation unit 12-7 is for calculating the orientation ratio R _K used in the orientation ratio multiplier 12-6. If (Expression 138) is used directly, the azimuth is 360 degrees and it is difficult to handle, so the azimuth deviation ψ _e = ψ _R −ψ is used (the reference course ψ _R is the amount of change from zero).

の関係を使用してＲ_Kを求める。ここでＲ_Kの初期値は１である。

Seek R _K by using the relationship. Here, the initial value of R _K is 1.

Furthermore, Patameta uncertainty applies a limit to the change of the orientation ratio R _K orientation ratio multiplier 12-6 orientation ratio limit unit 12-8 in order to reduce such by the influence the noise component. Limiting is performed by providing a dead zone to change the R _K. The dead zone may be 10% to 30% due to parameter uncertainty. For example, when the dead zone is 10%, the threshold value Slash Hold Value SHV = 0.1 when the initial value R _K = 1, and the azimuth ratio R _K obtained by the azimuth ratio calculation unit 12-7 is 0.9. less, or when it exceeds than 1.1, rewrites the orientation ratio R _K orientation ratio multiplier 12-6.
When the boat speed also changes with the change in propulsive force, the boat speed is corrected. That is,

であり、Ｖ、Ｖ₀は船速で現在値と直前値を表す。なお船速修正はノミナル値や制御ゲインを更新するもので、参照方位やフィードフォワード舵角には反映されない。変針命令時に更新されたパラメータを用いて軌道計画が構成される。つまり船速修正の効果は変針命令がないと発揮されない。

V and V ₀ are the ship speed and represent the current value and the previous value. The ship speed correction is to update the nominal value and control gain, and is not reflected in the reference direction and feedforward rudder angle. The trajectory plan is configured using the parameters updated at the time of changing the needle command. In other words, the effect of the ship speed correction cannot be demonstrated without a change instruction.

Since the wake speed around the rudder has already reached a steady value, when the ship speed is corrected, K _sn = K _sa and the turning force ratio becomes 1, and as a result, the azimuth ratio gradually approaches 1. Since the azimuth ratio cannot be asymptotic to 1 if the restriction of the azimuth ratio restriction unit 12-8 is maintained, the operation of the azimuth ratio restriction unit 12-8 is limited to once for each change of needle.

Further, in the azimuth ratio limiting unit 12-8, it is possible to add another limitation in addition to SHV. When the amount of needle change is less than a small set value, it is also possible to restrict by taking the AND of SHV and logical product.
It is possible to use an angular velocity ratio with good responsiveness instead of the azimuth ratio, but it is desirable to correct the azimuth ratio because of the large error due to noise components. In addition, an upper limit value can be set as a threshold value as a countermeasure against runaway.

  The marine vessel automatic steering apparatus that controls the heading to follow the set course described above can also be used as part of a route control system that follows the hull position on the planned route.

12 Marine Steering Device 12-1 Trajectory Calculation Unit 12-2 Feedforward Controller 12-3 Feedback Controller r _R Turning Angular Speed C _1a Turning Angular Acceleration Initial Value C _2a Turning Angular Speed Initial Value

Claims (5)

A trajectory calculation unit that calculates and outputs a reference course for a desired course change amount of a ship, and a feedforward controller that calculates a feedforward steering angle from the reference course and performs open loop control, the orbital computing section, the acceleration mode the reference heading, and outputs the divided constant speed mode and the deceleration mode, in the acceleration mode, the initial value C _1a of the slewing angular acceleration of veering the beginning and the initial value C _2a of the turning angular velocity In the ship automatic steering device that takes in and calculates the reference course,
The trajectory calculation unit does not exceed the maximum steering speed at which the steering speed of the feedforward steering angle output from the feedforward controller based on the reference course calculated by setting the initial values C _1a and C _2a to zero, respectively. Thus, the turning angular velocity r _R at the end of the acceleration mode and the constant velocity mode when each mode is determined is calculated, and C _1a <0 is satisfied with C _2a > r _R or C _2a <r _R When C _1a > 0 is satisfied, the turning angular speed r _R is corrected so that the maximum steering speed generation time in the acceleration mode is always the same in each case, and the corrected turning angular speed r _R is satisfied and calculated. The reference course of each mode is calculated so that the steering speed of the feedforward steering angle output from the feedforward controller does not exceed the maximum steering speed based on the reference course to be adjusted. The steering speed of the non turning angular velocity r _R satisfied and feedforward steering angle output from the computed is referenced feedforward controller based on the course is to compute a reference course of each mode so as not to exceed the maximum steering speed A marine vessel automatic steering device characterized by the above. The calculation of the turning angular velocity r _R of the trajectory calculation unit is performed under the condition that the ratio of the constant speed time and the deceleration time, which is the time of the constant speed mode and the deceleration mode, is constant, and the result is equal to or greater than the specified turning angular velocity. The automatic steering device for a marine vessel according to claim 1, wherein the specified turning angular velocity is set to an angular velocity obtained as a result of calculation when the specified turning angular velocity is equal to or less than the specified turning angular velocity. A trajectory calculation unit that calculates and outputs a reference course for a desired course change amount of a ship, and a feedforward controller that calculates a feedforward steering angle from the reference course and performs open loop control, the orbital computing section, the acceleration mode the reference heading, and outputs the divided constant speed mode and the deceleration mode, in the acceleration mode, the initial value C _1a of the slewing angular acceleration of veering the beginning and the initial value C _2a of the turning angular velocity In the ship automatic steering device that takes in and calculates the reference course,
The trajectory calculation unit obtains the turning angular velocity r _R at the end of the acceleration mode and the constant velocity mode by setting the initial values C _1a and C _2a to zero, and at this time, the turning angular velocity r _R becomes the designated turning angular velocity r _0. when it is assumed to be equal to, when the feed-forward steering angle output from the feedforward controller based on the reference course which is calculated to satisfy the permissible steering angle following conditions, turn angular velocity r _R specified turning angular velocity r ₀ determined to, when not satisfied the conditions, feed forward when determining the smallest angular velocity deviation between the permissible steering angle feedforward steering angle to the turning angular velocity r _R, it was determined turning angular velocity r _R Find the maximum steering speed of the feed forward steering angle output from the controller,
When C _2a > r _R satisfies C _1a <0, or C _2a <r _R satisfies C _1a > 0, the maximum steering speed generation time in the acceleration mode is always the same in each case. The turning angular speed r _R is corrected to satisfy the corrected turning angular speed r _R , and the steering speed of the feed forward steering angle output from the feed forward controller based on the calculated reference course does not exceed the maximum steering speed. Thus, the reference course of each mode is calculated, and in cases other than the above, the steering angle of the feedforward steering angle that satisfies the turning angular velocity r _R that is not corrected and that is output from the feedforward controller based on the calculated reference course is calculated. A marine vessel automatic steering apparatus, wherein a reference course for each mode is calculated so that a speed does not exceed the maximum rudder speed. A trajectory calculation unit that calculates and outputs a reference course for a desired course change amount of a ship, and a feedforward controller that calculates a feedforward steering angle from the reference course and performs open loop control, the orbital computing section, a reference course acceleration mode, and the output is divided into constant speed mode and the deceleration mode, in the acceleration mode, the initial value C _2a is an initial value of zero C _1a and the turning angular velocity of the slewing angular acceleration of veering beginning In the case of an automatic steering device for a ship that takes the value and calculates the reference course when it is not,
The trajectory calculation unit sets the acceleration mode to an attenuation that attenuates the initial value when the azimuth change necessary to attenuate the initial values C _1a and C _2a in the acceleration mode is larger than the desired amount of change of the needle. An automatic steering apparatus for a ship, which is divided into a mode and a normal mode for converging to the turning angular velocity r _R in the constant speed mode, and calculates a reference course for each mode. The initial value C _2a of the initial value C _1a and the turning angular velocity of the slewing angular acceleration is second-order derivative of the reference course that was calculated by the trajectory calculating section with respect to the previous veering when that was being veering at veering start The marine vessel automatic steering device according to any one of claims 1 to 4, wherein the marine vessel automatic steering device is obtained from a value at the start of changing the needle and the first-order differential.

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