CN112256026A - Ship course model predictive control algorithm design method under multi-constraint condition - Google Patents

Ship course model predictive control algorithm design method under multi-constraint condition Download PDF

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CN112256026A
CN112256026A CN202011098643.6A CN202011098643A CN112256026A CN 112256026 A CN112256026 A CN 112256026A CN 202011098643 A CN202011098643 A CN 202011098643A CN 112256026 A CN112256026 A CN 112256026A
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CN112256026B (en
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张子昌
赵光
郭亦平
***
谌兴良
刘浩
徐雪峰
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707th Research Institute of CSIC Jiujiang Branch
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Abstract

The invention discloses a design method of a ship course model predictive control algorithm under a multi-constraint condition, which comprises the following steps: establishing a ship low-noise motion control simulation model; designing a course model prediction controller of the ship according to the ship motion control simulation model and establishing a control objective function for the model prediction controller; determining hard constraint conditions such as rudder angle and rudder speed of a rudder according to a control objective function and actual operation requirements of a ship, and processing the hard constraint conditions; properly relaxing the course deviation aiming at the control objective function to form a soft constraint condition, and processing the soft constraint condition; and according to the control objective function, the hard constraint condition and the soft constraint condition, performing online optimization to obtain the optimal controller output. The invention effectively solves the problem of noise of the steering device caused by frequent steering of the ship in the maneuvering process, and ensures stable and low-noise navigation of the ship.

Description

Ship course model predictive control algorithm design method under multi-constraint condition
Technical Field
The invention relates to the technical field of ship motion control, in particular to a ship course model predictive control algorithm design method under a multi-constraint condition.
Background
For a ship control system, a rudder angle and a rudder speed are important parameters for representing the operation state of a steering engine, and the maneuvering capacity, stability and control quality of a ship are restrained by the maximum rudder angle and the maximum rudder speed; in order to meet the ship steering requirement, the steering angle and the steering speed are determined by the heading speed and the like in the maneuvering process and are directly related to hydrodynamic noise. Under the working condition of low noise, low-frequency manual steering is usually adopted, namely, the steering is carried out at the lowest possible frequency by widening the course during navigation and adopting a smaller steering angle; however, under the low-noise working condition, due to the low navigational speed and poor rudder effect of the ship, the change of the motion state of the ship is difficult to predict effectively for a long time when a crew operates the ship in a follow-up manner.
Therefore, how to realize real-time control of the maneuvering process of the ship under the low-noise sailing condition is a problem to be solved urgently by the technical personnel in the field.
Disclosure of Invention
In view of the above, the invention provides a design method of a ship course model predictive control algorithm under multiple constraint conditions, which can effectively predict the ship motion state change, output control and realize real-time control of the maneuvering process of a ship under a low-noise sailing condition.
In order to achieve the purpose, the invention adopts the following technical scheme:
a ship course model predictive control algorithm design method under multiple constraint conditions comprises the following steps:
step 1: establishing a ship low-noise motion control simulation model;
step 2: establishing a control objective function for the course model prediction controller according to the motion control simulation model;
and step 3: determining a hard constraint condition according to the control objective function and the actual operation requirement of the ship;
and 4, step 4: forming a soft constraint condition according to the control objective function and the allowable course deviation condition; the allowable course deviation condition is that the allowable course control command has a deviation of +/-2 degrees in the target course direction;
and 5: and according to the control objective function, the hard constraint condition and the soft constraint condition, performing online optimization to obtain the output of the optimal course model prediction controller.
Preferably, the motion control simulation model in the step 1 comprises a ship nonlinear motion model and a steering engine model;
the establishment process of the ship nonlinear motion model is as follows:
the ship nonlinear motion model is mainly a ship nonlinear equation, wherein the ship underwater state motion equation comprises an axial force equation, a lateral force equation, a rolling moment equation, a yawing moment equation and an auxiliary equation, which are respectively expressed as follows:
axial force equation:
Figure BDA0002724588310000021
lateral force equation:
Figure BDA0002724588310000022
roll moment equation:
Figure BDA0002724588310000023
yaw moment equation:
Figure BDA0002724588310000024
auxiliary equation:
Figure BDA0002724588310000031
wherein m is the ship mass; i isx、IzThe rotational inertia of the ship rotating around the x axis and the z axis respectively; u, v, p and r are respectively the longitudinal speed, the transverse inclination speed and the yaw speed under a ship body coordinate system; phi, phi,
Figure BDA0002724588310000037
Xi and eta are respectively transverse inclination, heading, longitudinal displacement and transverse displacement under a fixed coordinate system; deltarIs the rudder angle of the rudder; the other parameters are standard hydrodynamic derivatives of the international pool conference;
the steering engine model is established as follows:
the ship steering engine servo system has the nonlinear characteristics of dead zones, saturation and the like, and the functional relation between the input and the output of the steering engine is expressed as follows:
Figure BDA0002724588310000032
wherein deltadThe command input angle of the steering engine is, delta is the actual output angle of the steering engine, and sigma is deltad-δ；
Figure BDA0002724588310000033
σ1、σ2The maximum steering engine speed, the upper limit of the response dead zone and the lower limit of the saturation zone are respectively.
Preferably, the control objective function of the heading model predictive controller of the ship is established as follows:
step 21: linearizing the motion process of the ship to obtain a motion state space model as follows:
Figure BDA0002724588310000034
Figure BDA0002724588310000035
step 22: expressing the motion state space model of the ship as follows:
Figure BDA0002724588310000036
y＝Cx；
wherein A matrix is
Figure BDA0002724588310000041
B matrix is
Figure BDA0002724588310000042
C matrix is [ 001 ]]；
Step 23: discretizing the motion state space model of the continuous time domain and introducing an increment control form of input quantity to obtain:
Figure BDA0002724588310000043
and simplifying the above formula to obtain a discrete simplified state space model:
Figure BDA0002724588310000044
wherein z (k) ═ x (k), u (k-1)]T，
Figure BDA0002724588310000045
Figure BDA0002724588310000046
Co＝[C 0]；
Step 24: predicting the prediction step length of the discrete simplified state space model obtained after the dispersion and simplification, wherein the prediction step length is nyThe control step is set to nuWherein n isu<nyAnd at a time sampling step k>nuAnd meanwhile, considering that the increment of the control input quantity is 0, keeping the input quantity unchanged, and obtaining a state quantity prediction equation:
Figure BDA0002724588310000047
the output quantity prediction equation is as follows:
Figure BDA0002724588310000051
and summarizing the state quantity prediction equation and the output quantity prediction equation to obtain:
Figure BDA0002724588310000052
Figure BDA0002724588310000053
step 25: introducing an error d (k) between the single-step predicted output quantity and the actual output measured value at the current moment, and obtaining a state quantity prediction equation and an output quantity prediction equation which are respectively as follows:
Figure BDA0002724588310000054
Figure BDA0002724588310000055
the simplified form is:
Figure BDA0002724588310000056
Figure BDA0002724588310000057
step 26: obtaining an objective function according to the state quantity prediction equation and the output quantity prediction equation in the step 25 as follows:
Figure BDA0002724588310000061
wherein
Figure BDA0002724588310000062
For a preset reference track, Q is a weight matrix of an output error, R is a weight matrix of an input quantity, and the specific forms are respectively as follows:
Figure BDA0002724588310000063
Q＝diag(q1,…qny)
R＝diag(r1,…rnc)；
step 27: substituting the output quantity prediction equation into the objective function to obtain the control objective function:
Figure BDA0002724588310000064
preferably, the hard constraints include rudder angle, rudder speed, and the like, and the hard constraints are established and processed as follows:
step 31: the hard constraints, which are mainly the rudder speed Δ u and rudder angle u of the steering engine, can be mathematically expressed as:
umin＜u＜umax
Δumin＜Δu＜Δumaxwherein u ismin,umaxRespectively representing the minimum value and the maximum value of the rudder angle u; Δ umin,ΔumaxRespectively represent the minimum value and the maximum value of the rudder speed Deltau;
step 32: because the input quantity of the rudder angle is in the whole control step lengthAre limited by the magnitude of the rudder speed, the upper and lower bounds defining the rudder speed being denoted by Δ, respectivelyuAnd
Figure BDA0002724588310000065
the constraint relation of rudder speed amplitude limiting in the prediction process is as follows:
Figure BDA0002724588310000066
the conversion into a matrix is in the form:
Figure BDA0002724588310000067
wherein the I matrix has dimension NcThe unit matrix of (a) is,
Figure BDA0002724588310000071
Figure BDA0002724588310000072
step 33: because the rudder angle input quantity is limited by the rudder angle amplitude in the whole control step length, the upper limit and the lower limit for defining the rudder angle are respectively expressed asuAnd
Figure BDA0002724588310000073
the constraint relation of rudder angle amplitude limiting in the prediction process is as follows:
Figure BDA0002724588310000074
the above equation is expressed in the form of the constraint of rudder speed, and the result is:
Figure BDA0002724588310000075
wherein
Figure BDA0002724588310000076
Further conversion into matrix form:
Figure BDA0002724588310000077
preferably, the soft constraint condition includes an output variable constraint, an intermediate state variable constraint, and the like, and the soft constraint condition is established and processed as follows:
introducing a reference track constraint method to make the reference track
Figure BDA0002724588310000078
Is rewritten into
Figure BDA0002724588310000079
The matrix M is used for changing a reference track into a vector which is the same as the prediction step length, alpha is the reference track to be solved, and the matrix M meets the following soft constraint processing conditions:
Figure BDA00027245883100000710
Figure BDA00027245883100000711
kxis the lower limit of the state variable constraint interval,
Figure BDA00027245883100000712
is the upper limit of the state variable constraint interval;
kyis the lower limit of the output variable constraint interval,
Figure BDA00027245883100000713
the upper limit of the interval is constrained for the output variables.
Preferably, the specific steps of obtaining the output of the controller are as follows:
step 51: processing the reference track in the soft constraint processing condition
Figure BDA00027245883100000714
Substituting into the objective function to obtain:
Figure BDA0002724588310000081
wherein Q is the weight matrix of the output error, and k is a time sampling step length; ignoring constant terms in the control objective function, and sorting to obtain a final objective function form as follows:
J＝cTSc+2fTc
wherein:
Figure BDA0002724588310000082
step 52: combining the hard constraint condition and the soft constraint condition, combining a matrix expression form of the rudder angle constraint condition, a matrix expression form of the rudder speed constraint condition and a constraint expression form of the soft constraint condition into a matrix to obtain expression forms of all the constraint conditions:
Figure BDA0002724588310000083
wherein:
Io＝[I(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
Mo＝[0(m×ny)×(n×nu) I(m×ny)×(m×ny) 0(m×ny)×(m×ny)](m×ny)×(n×nu+m×ny+m×ny)
Co＝[CI/Δ(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
Figure BDA0002724588310000091
Aeq＝[I(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
n is the dimension of the output variable, m is the dimension of the input variable;
step 53: generalizing said final objective function form and said all constraint forms:
minJ＝cTSc+2fTc
s.t.CCx≤dmax
wherein S is a symmetric positive definite matrix, c is an optimization variable, the objective function optimization problem forms a standard quadratic programming problem, the final objective function is optimized and solved by applying a quadprog quadratic programming solving function to obtain the optimal control input sequence at the current moment,
step 54: and (4) performing predictive control output on the rolling optimization ship course model, only taking the first row of the optimal control input sequence at the current moment as the output value of the controller at the current moment, returning to the step 53 at the next moment, and repeating optimization.
Compared with the prior art, the invention discloses a ship course model predictive control algorithm design method under the multi-constraint condition, which comprises the following steps: establishing a ship low-noise motion control simulation model; designing a course model prediction controller of the ship according to the ship motion control simulation model and establishing a control objective function for the model prediction controller; determining hard constraint conditions such as rudder angle and rudder speed of a rudder according to a control objective function and actual operation requirements of a ship, and processing the hard constraint conditions; properly relaxing the course deviation aiming at the control objective function to form a soft constraint condition, and processing the soft constraint condition; and according to the control objective function, the hard constraint condition and the soft constraint condition, performing online optimization to obtain the optimal controller output. The invention effectively solves the problem of noise of the steering device caused by frequent steering of the ship in the maneuvering process, and ensures stable and low-noise navigation of the ship.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of a design of a ship course model predictive control algorithm provided by the invention;
FIG. 2 is a block diagram of a steering engine model according to the present invention;
FIG. 3 is a graph of course curves under the action of a course model predictive controller under an automatic direction change condition according to the present invention;
FIG. 4 is a plot of rudder angle of a rudder under the action of a heading model predictive controller under an automatic turning condition, provided by the invention;
FIG. 5 is a graph showing a course curve under the action of a PID controller under an automatic turning condition according to the invention;
FIG. 6 is a rudder angle curve diagram of a rudder under the action of a PID controller under the automatic turning condition provided by the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a design method of a ship course model predictive control algorithm under a multi-constraint condition, which comprises the following steps:
s1: establishing a ship low-noise motion control simulation model; the motion control simulation model comprises a ship nonlinear motion model and a steering engine model;
s11: the establishment process of the ship nonlinear motion model is as follows:
the ship nonlinear motion model is mainly a ship nonlinear equation, wherein the ship underwater state motion equation comprises an axial force equation, a lateral force equation, a rolling moment equation, a yawing moment equation and an auxiliary equation, which are respectively expressed as follows:
axial force equation:
Figure BDA0002724588310000111
lateral force equation:
Figure BDA0002724588310000112
roll moment equation:
Figure BDA0002724588310000113
yaw moment equation:
Figure BDA0002724588310000114
auxiliary equation:
Figure BDA0002724588310000115
wherein m is the ship mass; i isx、IzThe rotational inertia of the ship rotating around the x axis and the z axis respectively; u, v, p and r are respectively the longitudinal speed, the transverse inclination speed and the yaw speed under a ship body coordinate system; phi, phi,
Figure BDA0002724588310000116
Xi and eta are respectively transverse inclination, heading and longitudinal displacement under a fixed coordinate systemAnd transversely displacing; deltarIs the rudder angle of the rudder; the other parameters are standard hydrodynamic derivatives of the international pool conference;
s12: the steering engine model is established as follows:
the ship steering engine servo system has the nonlinear characteristics of dead zones, saturation and the like, and a structural block diagram for establishing a steering engine model is shown in FIG. 2:
the functional relationship between the steering engine input and output is expressed as follows:
Figure BDA0002724588310000121
wherein deltadThe command input angle of the steering engine is, delta is the actual output angle of the steering engine, and sigma is deltad-δ；
Figure BDA0002724588310000122
σ1、σ2The maximum steering engine speed, the upper limit of the response dead zone and the lower limit of the saturation zone are respectively;
s2: constructing a course model prediction controller of the ship according to the motion control simulation model, and establishing a control objective function for the course model prediction controller; the control objective function establishment process is as follows:
s21: linearizing the motion process of the ship to obtain a motion state space model as follows:
Figure BDA0002724588310000123
Figure BDA0002724588310000124
s22: the motion state space model of the ship is expressed as follows:
Figure BDA0002724588310000125
y＝Cx；
wherein A matrix is
Figure BDA0002724588310000126
B matrix is
Figure BDA0002724588310000127
C matrix is [ 001 ]]；
S23: discretizing the motion state space model of the continuous time domain and introducing an increment control form of input quantity to obtain:
Figure BDA0002724588310000128
and simplifying the above formula to obtain a discrete simplified state space model:
Figure BDA0002724588310000131
wherein z (k) ═ x (k), u (k-1)]T，
Figure BDA0002724588310000132
Figure BDA0002724588310000133
Co＝[C0]；
S24: predicting the prediction step length of the discrete simplified state space model obtained after the dispersion and simplification, wherein the prediction step length is nyThe control step is set to nuWherein n isu<nyAnd at a time sampling step k>nuAnd meanwhile, considering that the increment of the control input quantity is 0, keeping the input quantity unchanged, and obtaining a state quantity prediction equation:
Figure BDA0002724588310000134
the output quantity prediction equation is as follows:
Figure BDA0002724588310000135
and (3) summarizing the state quantity prediction equation and the output quantity prediction equation to obtain:
Figure BDA0002724588310000136
Figure BDA0002724588310000137
s25: introducing an error d (k) between the single-step predicted output quantity and the actual output measured value at the current moment to obtain a state quantity prediction equation and an output quantity prediction equation which are respectively as follows:
Figure BDA0002724588310000141
Figure BDA0002724588310000142
the simplified form is:
Figure BDA0002724588310000143
Figure BDA0002724588310000144
s26: the objective function is obtained from the state quantity prediction equation and the output quantity prediction equation in S25 as follows:
Figure BDA0002724588310000145
wherein
Figure BDA0002724588310000146
For a preset reference track, Q is a weight matrix of an output error, R is a weight matrix of an input quantity, and the specific forms are respectively as follows:
Figure BDA0002724588310000147
Q＝diag(q1,…qny)
R＝diag(r1,…rnc)；
s27: substituting the output quantity prediction equation into the objective function to obtain a control objective function:
Figure BDA0002724588310000148
s3: determining a hard constraint condition according to the control objective function and the actual operation requirement of the ship, and processing the hard constraint condition; the hard constraint conditions comprise a rudder angle, a rudder speed and the like of a rudder, and the hard constraint conditions are established and processed as follows:
s31: the rudder speed Δ u and rudder angle u of the steering engine as main hard constraints can be mathematically expressed as:
umin＜u＜umax
Δumin＜Δu＜Δumaxwherein u ismin,umaxRespectively representing the minimum value and the maximum value of the rudder angle u; Δ umin,ΔumaxRespectively represent the minimum value and the maximum value of the rudder speed Deltau;
s32: because the rudder angle input quantity is limited by the rudder speed amplitude in the whole control step length, the upper bound and the lower bound of the rudder speed are defined and respectively expressed as deltauAnd
Figure BDA0002724588310000151
the constraint relation of rudder speed amplitude limiting in the prediction process is as follows:
Figure BDA0002724588310000152
the conversion into a matrix is in the form:
Figure BDA0002724588310000153
wherein the I matrix has dimension NcThe unit matrix of (a) is,
Figure BDA0002724588310000154
s33: because the rudder angle input quantity is limited by the rudder angle amplitude in the whole control step length, the upper limit and the lower limit for defining the rudder angle are respectively expressed asuAnd
Figure BDA0002724588310000155
the constraint relation of rudder angle amplitude limiting in the prediction process is as follows:
Figure BDA0002724588310000156
the above equation is expressed in the form of the constraint of rudder speed, and the result is:
Figure BDA0002724588310000157
wherein
Figure BDA0002724588310000158
Further conversion into matrix form:
Figure BDA0002724588310000159
s4: forming a soft constraint condition according to the control objective function and the allowable course deviation condition, and processing the soft constraint condition; the allowable course deviation condition is that the allowable course control command has a deviation of +/-2 degrees in the target course direction; the soft constraint conditions comprise output variable constraints, intermediate state variable constraints and the like, and the establishment and processing processes of the soft constraint conditions are as follows:
introducing a reference track constraint method to make the reference track
Figure BDA0002724588310000161
Is rewritten into
Figure BDA0002724588310000162
The matrix M is used for changing the reference track into a vector which is the same as the prediction step length, alpha is the reference track to be solved, and the matrix M meets the following soft constraint processing conditions:
Figure BDA0002724588310000163
Figure BDA0002724588310000164
kxis the lower limit of the state variable constraint interval,
Figure BDA0002724588310000165
is the upper limit of the state variable constraint interval;
kyis the lower limit of the output variable constraint interval,
Figure BDA0002724588310000166
an upper limit of the output variable constraint interval;
s5: according to the target function, the hard constraint condition and the soft constraint condition, performing online optimization to obtain the output of an optimal course model prediction controller;
s51: processing reference track in soft constraint condition
Figure BDA0002724588310000167
Substituting into the objective function yields:
Figure BDA0002724588310000168
wherein Q is a weight matrix of the output error, and k is a time sampling step length; neglecting constant terms in the control objective function, and obtaining a final objective function form by sorting:
J＝cTSc+2fTc
wherein:
Figure BDA0002724588310000169
s52: combining the hard constraint condition and the soft constraint condition, combining the matrix expression form of the rudder angle constraint condition, the matrix expression form of the rudder speed constraint condition and the constraint expression form of the soft constraint condition into a matrix to obtain the expression forms of all the constraint conditions:
Figure BDA0002724588310000171
wherein:
Io＝[I(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
Mo＝[0(m×ny)×(n×nu) I(m×ny)×(m×ny) 0(m×ny)×(m×ny)](m×ny)×(n×nu+m×ny+m×ny)
Co＝[CI/Δ(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
Figure BDA0002724588310000172
Aeq＝[I(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
n is the dimension of the output variable, m is the dimension of the input variable;
s53: generalizing the final objective function form and all constraint forms:
minJ＝cTSc+2fTc
s.t.CCx≤dmax
the optimization method comprises the following steps that S is a symmetric positive definite matrix, c is an optimization variable, an objective function optimization problem forms a standard quadratic programming problem, and optimization solving can be carried out by applying a quadprog quadratic programming solving function to obtain an optimal control input sequence at the current moment;
s54: according to the idea of a rolling optimization ship course model predictive control algorithm, only the first row of an optimal control input sequence is used as the output value of a controller at the current time, and the process is repeated at the next time.
Examples
Taking a certain ship motion control system as an example, the heading model prediction controller parameter values are as follows: n isy＝35，nu＝15，Q＝0.2Iny×ny，R＝20Inu×nuThe amplitude of the rudder angle of the rudder is set to 10 degrees, the amplitude of the rudder speed is limited to 1.5 degrees/s under the condition of adding state quantity constraint, the initial course is 30 degrees, the target course is 60 degrees, the initial speed is set to 8kn, the simulation sampling time is set to 0.1s, the course deviation is widened by 2 degrees, the simulation result is shown in figures 3 and 4, the control effect under the PID control algorithm under the same simulation condition is shown in figures 5 and 6, the horizontal coordinate represents time, and the vertical coordinate represents the change angle.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. A ship course model predictive control algorithm design method under multiple constraint conditions is characterized by comprising the following steps:
step 1: establishing a ship low-noise motion control simulation model;
step 2: establishing a control objective function for the course model prediction controller according to the motion control simulation model;
and step 3: determining a hard constraint condition according to the control objective function and the actual operation requirement of the ship;
and 4, step 4: forming a soft constraint condition according to the control objective function and the allowable course deviation condition;
and 5: and according to the control objective function, the hard constraint condition and the soft constraint condition, performing online optimization to obtain the output of the optimal course model prediction controller.
2. The design method of the ship heading model predictive control algorithm under the multi-constraint condition as claimed in claim 1, wherein the motion control simulation model in the step 1 comprises a ship nonlinear motion model and a steering engine model;
step 11: the establishment process of the ship nonlinear motion model is as follows:
the ship nonlinear motion model is a ship nonlinear equation, wherein the ship underwater state motion equation comprises an axial force equation, a lateral force equation, a rolling moment equation, a yawing moment equation and an auxiliary equation, which are respectively expressed as follows:
axial force equation:
Figure FDA0002724588300000011
lateral force equation:
Figure FDA0002724588300000012
roll moment equation:
Figure FDA0002724588300000013
yaw moment equation:
Figure FDA0002724588300000021
auxiliary equation:
Figure FDA0002724588300000022
wherein m is the ship mass; i isx、IzThe rotational inertia of the ship rotating around the x axis and the z axis respectively; u, v, p and r are respectively the longitudinal speed, the transverse inclination speed and the yaw speed under a ship body coordinate system; phi, phi,
Figure FDA0002724588300000023
Xi and eta are respectively transverse inclination, heading, longitudinal displacement and transverse displacement under a fixed coordinate system; deltarIs the rudder angle of the rudder; the other parameter is the standard hydrodynamic derivative of the international pool conference.
Step 12: the steering engine model is established as follows:
the ship steering engine servo system has dead zone and saturated nonlinear characteristics, and the functional relation between the input and the output of the steering engine is expressed as follows:
Figure FDA0002724588300000024
wherein deltadThe command input angle of the steering engine is, delta is the actual output angle of the steering engine, and sigma is deltad-δ；
Figure FDA0002724588300000025
σ1、σ2The maximum steering engine speed, the upper limit of the response dead zone and the lower limit of the saturation zone are respectively.
3. The method for designing the ship heading model predictive control algorithm under the multi-constraint condition as recited in claim 2, wherein the control objective function establishing process of the heading model predictive controller of the ship in the step 2 is as follows:
step 21: linearizing the motion process of the ship to obtain a motion state space model as follows:
Figure FDA0002724588300000031
step 22: expressing the motion state space model of the ship as follows:
Figure FDA0002724588300000032
y＝Cx；
wherein A matrix is
Figure FDA0002724588300000033
B matrix is
Figure FDA0002724588300000034
C matrix is [ 001 ]]；
Step 23: discretizing the motion state space model of the continuous time domain and introducing an increment control form of input quantity to obtain:
Figure FDA0002724588300000035
and simplifying to obtain a discrete simplified state space model:
Figure FDA0002724588300000036
wherein z (k) ═ x (k), u (k-1)]T，
Figure FDA0002724588300000037
Co＝[C 0]；
Step 24: predicting the prediction step length of the discrete simplified state space model obtained after the dispersion and simplification, wherein the prediction step length is nyThe control step is set to nuWherein n isu<nyAnd at a time sampling step k>nuAnd meanwhile, considering that the increment of the control input quantity is 0, keeping the input quantity unchanged, and obtaining a state quantity prediction equation:
Figure FDA0002724588300000041
the output quantity prediction equation is as follows:
Figure FDA0002724588300000042
and summarizing the state quantity prediction equation and the output quantity prediction equation to obtain:
Figure FDA0002724588300000043
Figure FDA0002724588300000044
step 25: introducing an error d (k) between the single-step predicted output quantity and the actual output measured value at the current moment, and obtaining a state quantity prediction equation and an output quantity prediction equation which are respectively as follows:
Figure FDA0002724588300000045
Figure FDA0002724588300000051
the method is simplified as follows:
Figure FDA0002724588300000052
Figure FDA0002724588300000053
step 26: obtaining an objective function according to the state quantity prediction equation and the output quantity prediction equation in the step 25 as follows:
Figure FDA0002724588300000054
wherein
Figure FDA0002724588300000055
For a preset reference track, Q is a weight matrix of an output error, R is a weight matrix of an input quantity, and the specific forms are respectively as follows:
Figure FDA0002724588300000056
Figure FDA0002724588300000057
Figure FDA0002724588300000058
step 27: substituting the output quantity prediction equation into the objective function to obtain the control objective function:
Figure FDA0002724588300000059
4. the design method of the ship heading model predictive control algorithm under the multi-constraint condition as claimed in claim 3, wherein the hard constraint condition comprises a rudder angle and a rudder speed, and the hard constraint condition is established and processed as follows:
step 31: taking the rudder speed delta u and the rudder angle u of the steering engine as the hard constraint conditions, the rudder speed delta u and the rudder angle u are expressed as follows:
umin＜u＜umax
Δumin＜Δu＜Δumaxwherein u ismin,umaxRespectively representing the minimum value and the maximum value of the rudder angle u; Δ umin,ΔumaxRespectively represent the minimum value and the maximum value of the rudder speed Deltau;
step 32: the upper and lower bounds for the set rudder speed are denoted by Δ, respectivelyuAnd
Figure FDA0002724588300000069
the constraint relation of rudder speed amplitude limiting in the prediction process is as follows:
Figure FDA0002724588300000061
the conversion into a matrix is in the form:
Figure FDA0002724588300000062
wherein the I matrix has dimension NcThe unit matrix of (a) is,
Figure FDA0002724588300000063
step 33: the upper and lower limits of the rudder angle are respectively indicated asuAnd
Figure FDA0002724588300000064
the constraint relation of rudder angle amplitude limiting in the prediction process is as follows:
Figure FDA0002724588300000065
the above equation is expressed in the form of the constraint of rudder speed, and the result is:
Figure FDA0002724588300000066
wherein
Figure FDA0002724588300000067
The conversion into a matrix is in the form:
Figure FDA0002724588300000068
5. the method for designing the ship heading model predictive control algorithm under the multi-constraint condition as claimed in claim 4, wherein the allowable heading deviation condition is a deviation of the allowable heading control command in a target heading direction by ± 2 °, the soft constraint condition comprises an output variable constraint and an intermediate state variable constraint, and the soft constraint condition is established and processed as follows:
introducing a reference track constraint method to make the reference track
Figure FDA0002724588300000071
Is rewritten into
Figure FDA0002724588300000072
The matrix M is used for changing a reference track into a vector which is the same as the prediction step length, alpha is the reference track to be solved, and the matrix M meets the following soft constraint processing conditions:
Figure FDA0002724588300000073
Figure FDA0002724588300000074
kxis the lower limit of the state variable constraint interval,
Figure FDA0002724588300000075
is the upper limit of the state variable constraint interval;
kyis the lower limit of the output variable constraint interval,
Figure FDA0002724588300000076
the upper limit of the interval is constrained for the output variables.
6. The design method of the ship heading model predictive control algorithm under the multi-constraint condition as claimed in claim 5, wherein the concrete steps of obtaining the controller output are as follows:
step 51: processing the reference track in the soft constraint processing condition
Figure FDA0002724588300000077
Substituting into the objective function to obtain:
Figure FDA0002724588300000078
wherein Q is the weight matrix of the output error, and k is a time sampling step length; ignoring constant terms in the control objective function, and sorting to obtain a final objective function form as follows:
J＝cTSc+2fTc
wherein:
Figure FDA0002724588300000079
step 52: combining the hard constraint conditions and the soft constraint conditions to obtain expression forms of all constraint conditions:
Figure FDA0002724588300000081
wherein:
Io＝[I(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
Mo＝[0(m×ny)×(n×nu) I(m×ny)×(m×ny) 0(m×ny)×(m×ny)](m×ny)×(n×nu+m×ny+m×ny)
Co＝[CI/Δ(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
Figure FDA0002724588300000082
Aeq＝[I(n×nu)×(n×nu) 0(n×nu)×(m×ny+m×ny)](n×nu)×(n×nu+m×ny+m×ny)
n is the dimension of the output variable, m is the dimension of the input variable;
step 53: generalizing said final objective function form and said all constraint forms:
min J＝cTSc+2fTc
s.t.CCx≤dmax
wherein S is a symmetric positive definite matrix, c is an optimization variable, the final objective function is optimized by applying a quadprog quadratic programming solving function, the optimal control input sequence at the current moment is obtained by solving,
step 54: and (4) performing predictive control output on the rolling optimization ship course model, only taking the first row of the optimal control input sequence at the current moment as the output value of the controller at the current moment, returning to the step 53 at the next moment, and repeating optimization.
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