CN113296517A - Ship course dynamic surface sliding mode control method based on drift angle compensation - Google Patents

Ship course dynamic surface sliding mode control method based on drift angle compensation Download PDF

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CN113296517A
CN113296517A CN202110570900.XA CN202110570900A CN113296517A CN 113296517 A CN113296517 A CN 113296517A CN 202110570900 A CN202110570900 A CN 202110570900A CN 113296517 A CN113296517 A CN 113296517A
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course
error
ship
drift angle
heading
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CN113296517B (en
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储瑞婷
刘志全
秦毅峰
朱云浩
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Shanghai Maritime University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a ship course dynamic surface sliding mode control method based on drift angle compensation, which is characterized by comprising the following steps of: the obtained expected course psi of the shiprPre-filtering to obtain a filtered reference course psidAnd rate of change of course
Figure DDA0003082637230000011
A smooth transition of (2); according to the estimated drift angle value, the initial heading error e is psih‑ψdCorrecting based on drift angle compensation, wherein the corrected course error is eaWherein ψhThe actual course is taken; designing virtual controls
Figure DDA0003082637230000012
And instruction filtering to prevent the problem of "computing explosion" from occurring; defining a dynamic error e according to the corrected course error and the filtered reference course1、e2(ii) a Calculating the compensation for the instruction filtering of step S3Tracking error v1、υ2And the compensation tracking signal is defined according to the dynamic error of the system to eliminate the influence of the instruction filtering error; calculating a ship yawing control moment command signal tau according to a sliding mode control rule based on an approach lawrThe real-time heading information is updated to step S2.

Description

Ship course dynamic surface sliding mode control method based on drift angle compensation
Technical Field
The invention relates to the technical field of ship course control, in particular to a ship course dynamic surface sliding mode control method based on drift angle compensation.
Background
Heading control is taken as the most basic content of ship motion control in order to ensure the safety and economy of ships sailing on the sea, and is an important research subject in the field of ship control up to now. At present, most ship motion control neglects drift angle influence existing in navigation, and the drift angle causes certain deviation to an expected course. The most direct method to compensate for drift angle is to use GPS, accelerometers and other sensors to make measurements, however, the noise and high cost of the sensors make this method impractical. In addition, the actuator has a saturation constraint problem due to mechanical characteristics, and the rudder saturation problem not only causes actuator abrasion to the ship itself, but also reduces course tracking performance. The ship control belongs to the typical under-actuated system control, and besides the influence of sea surface environment disturbance, the complexity and uncertainty of a ship control model bring huge challenges to ship heading control.
Disclosure of Invention
The invention aims to improve the course tracking performance of an under-actuated ship on the water surface and reduce course errors, and researches ship course dynamic surface sliding mode control based on drift angle compensation. Firstly, a pre-filter is adopted to reduce the influence of a large course change rate when a ship turns, an extended state observer is used for estimating a time-varying drift angle, and course errors are corrected in time through the estimated drift angle. The resulting control effect has good course tracking even in the presence of input saturation.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a ship course dynamic surface sliding mode control method based on drift angle compensation comprises the following steps:
s1, obtaining the expected heading psi of the shiprPre-filtering to obtain a filtered reference course psidAnd rate of change of course
Figure BDA0003082637210000011
A smooth transition of (2);
s2, according to the estimated drift angle value, the initial heading error e is psih-ψdCorrecting based on drift angle compensation, wherein the corrected course error is eaWherein ψhThe actual course is taken;
s3 design virtual control
Figure BDA0003082637210000021
And instruction filtering to prevent the problem of "computing explosion" from occurring;
s4, defining a dynamic error e according to the corrected course error and the filtered reference course1、e2；
S5, calculating a compensated tracking error upsilon for the command filtering of the step S31、υ2And the compensation tracking signal is defined according to the dynamic error of the system to eliminate the influence of the instruction filtering error;
s6, calculating a ship yawing control moment command signal tau according to a sliding mode control rule based on an approach lawrThe real-time heading information is updated to step S2.
Optionally, the second-order pre-filter adopted in step S1 is in the form of:
Figure BDA0003082637210000022
wherein λ isi(i ═ 1,2,3) are prefilter parameters;
the drift angle estimation formula is as follows:
Figure BDA0003082637210000023
wherein the content of the first and second substances,
Figure BDA0003082637210000024
the surging speed and the swaying speed estimated value of the ship are obtained.
Optionally, the expression of the sliding mode in step S6 is:
Figure BDA0003082637210000025
wherein the content of the first and second substances,
Figure BDA0003082637210000026
Figure BDA0003082637210000027
r1k and theta are normal numbers, k is more than 0, and r is more than 01＜1。
Optionally, the command signal τ of yaw control moment in step S6rThe calculation formula of (a) is specifically expressed as:
Figure BDA0003082637210000028
wherein the content of the first and second substances,
Figure BDA0003082637210000029
for the overall estimation of uncertainty terms and external disturbances in the under-actuated vessel model,
Figure BDA00030826372100000210
non-linear term estimates are composed for the yaw rate in the model,
Figure BDA0003082637210000031
k1、k2to design the constants.
Compared with the prior art, the invention has the following advantages:
the under-actuated ship course tracking control method designed by the invention considers drift angle influence and effectively reduces course errors at turning positions; the buffeting is effectively weakened through the sliding mode control based on the exponential approaching law; uncertainty items and external disturbance in the model are estimated and compensated through an observer at the same time, and robustness of course tracking control under severe sea condition navigation conditions is improved.
When the reference course is changed, the drift angle is compensated in the course tracking, so that the time required by the ship to reach the reference course is shortened to a half of the original time; compared with the traditional linear extended state observer, the finite time extended state observer has better estimation performance, and the researched control method enables the surface ship to reduce the course error to be converged to zero in a short time.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention patent, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of a desired heading after drift angle compensation in an embodiment of the invention;
FIG. 2 is a block diagram of a ship heading control that takes into account drift correction in an embodiment of the invention;
FIG. 3 is a schematic diagram illustrating a ship course tracking control result according to an embodiment of the present invention;
FIG. 4 is a schematic view of a ship course tracking error in an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating estimation of the ship surging speed according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating estimation of the swaying speed of the ship according to an embodiment of the present invention;
fig. 7 is a schematic view of the ship yaw control moment designed and calculated in an embodiment of the present 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. It is to be noted that the drawings are in a very simplified form and are all used in a non-precise scale for the purpose of facilitating and distinctly aiding in the description of the embodiments of the present invention. To make the objects, features and advantages of the present invention comprehensible, reference is made to the accompanying drawings. It should be understood that the structures, ratios, sizes, and the like shown in the drawings and described in the specification are only used for matching with the disclosure of the specification, so as to be understood and read by those skilled in the art, and are not used to limit the implementation conditions of the present invention, so that the present invention has no technical significance, and any structural modification, ratio relationship change or size adjustment should still fall within the scope of the present invention without affecting the efficacy and the achievable purpose of the present invention.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
Referring to fig. 2, the embodiment provides a dynamic surface sliding mode control method based on drift angle compensation, which is implemented as follows:
step 1: the obtained expected course psi of the shiprPre-filtering is performed. The main function of the pre-filter is to measure the original reference heading psirFiltering to realize the reference course psi after filteringdAnd rate of change of course
Figure BDA0003082637210000041
Thereby avoiding higher control gain requirements and improving the performance of the controller. The pre-filtering formula is represented by formula (1). Wherein the parameters can be adjusted according to specific objects.
Figure BDA0003082637210000042
Wherein λi(i ═ 1,2,3) are prefilter parameters.
Step 2: and correcting the course error based on the drift angle. Corrected desired heading ψdaError e from courseaRespectively as follows:
Figure BDA0003082637210000043
ea＝ψh-ψda (3)
the drift angle calculation formula is as follows:
Figure BDA0003082637210000044
the drift angle and total disturbance are estimated by the following finite time extended state observer:
Figure BDA0003082637210000051
wherein eta is [ u, v, r ═ r]T，
Figure BDA0003082637210000052
A state vector expanded for the system, which contains unknown external interference and internal unmodeled dynamic terms; observer estimation error is
Figure BDA0003082637210000053
Wherein the content of the first and second substances,
Figure BDA0003082637210000054
Figure BDA0003082637210000055
sigα(z1)＝|z1|αsgn(z1)，
Figure BDA0003082637210000056
and is
Figure BDA0003082637210000057
α2＝2α1-1；mi＞0,niAnd > 0(i ═ 1,2) is a normal number.
And step 3: design of virtual control law
Figure BDA0003082637210000058
To eliminate the effect of 'computing explosion', command filtering is designed
Figure BDA0003082637210000059
Where α is the filtered virtual control law, kα、τ1Is a constant to be designed.
And 4, step 4: defining a dynamic error based on the corrected course error and the filtered reference course
e1＝ea＝ψh-ψda (6)
Figure BDA00030826372100000510
And 5: in order to eliminate the error influence generated by the virtual instruction filtering in the step 3, a compensation tracking signal system is designed according to the dynamic error of the system, and the specific expression of the error compensation signal is as follows:
Figure BDA00030826372100000511
calculating a compensated tracking error v1＝e1-ξ1,υ2＝e2-ξ2。
Step 6: the surface of the sliding form is selected as
Figure BDA00030826372100000512
Wherein the content of the first and second substances,
Figure BDA0003082637210000061
Figure BDA0003082637210000062
r1k and theta are normal numbers, k is more than 0, and r is more than 01＜1。
In order to weaken buffeting, sliding mode control based on an exponential approach law is used, and a moving point is guaranteed to reach a sliding mode within a limited time. In the invention, the initial speed of the surging direction is designed to be 6m/s, and the ship keeps sailing at the speed of 7m/s after acceleration; since the oscillating motion pose v is assumed to be passively bounded, the design of the control law does not need to take this into account. Command signal tau for controlling moment of bowrThe calculation formula of (a) is specifically expressed as:
Figure BDA0003082637210000063
the three-degree-of-freedom water surface under-actuated nonlinear ship motion model based on the invention is as follows:
Figure BDA0003082637210000064
where ψ is the actual heading defined in a fixed coordinate system in degrees; the surging and swaying speeds of the ship are u and v respectively, and the unit is m/s; r is the yaw rate in rad/s. Positive constant mjjJ is more than or equal to 1 and less than or equal to 3, which represents the inertia coefficient of the ship including the additional mass; du、dv、dr、dui、dvi、driRepresenting hydrodynamic damping coefficients in the surge, sway and yaw directions; unknown time-varying term tauwu(t)、τwv(t)、τwr(t) represents the environmental disturbance caused by wind, waves, flow, assuming that the external disturbance is bounded. Propelling force tau of ship on wateru(N) provided by propellers or water jets, yaw moment τr(Nm) results from varying the speed of each propeller or sprinkler. Order to
Figure BDA0003082637210000065
For uncertainty terms and total disturbances in the heading direction,
Figure BDA0003082637210000066
example (b): a monohull ship with the length of 38 meters is taken as a controlled object, and computer numerical simulation is carried out by using MATLAB. The nonlinear ship motion model is adopted as shown in the formula (11), and specific parameters in the model are as follows.
m11＝120×103 m22＝177.9×103 m33＝636×105
du＝215×102 dv＝147×103 dr＝802×104
du2＝0.2du dv2＝0.2dv dr2＝0.2dr
du3＝0.1du dv3＝0.1dv dr3＝0.1dr
In the embodiment, the surging speed is controlled by an independent control system, the initial navigational speed is designed and set to be 6m/s, and the surging speed of 7m/s is maintained after acceleration. The desired heading angles are 0 °, 20 °, 40 °, respectively, and the simulation time is 300 s. The ocean environment disturbance adopts a disturbance model to simulate in consideration of the complex interference factors of the wind wave flow.
Fig. 3-7 show some simulation results based on this invention. FIG. 3 is a real ship navigation course tracking curve, which shows that the course is effectively tracked and controlled, and the heading can be converged to the expected course within 4s of the change of the heading, thereby greatly shortening the time required by ship steering. Fig. 4 is a time variation curve of the course tracking error, and it can be seen that the course deviation can be converged in a smaller neighborhood range. Fig. 5 and 6 show the surging and swaying speeds estimated by the observer, respectively. Fig. 7 shows a time variation curve of the ship heading propulsion control force obtained by calculating the control law of the formula (10).
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (4)

1. A ship course dynamic surface sliding mode control method based on drift angle compensation is characterized by comprising the following steps:
s1, obtaining the expected heading psi of the shiprPre-filtering to obtain a filtered reference course psidAnd rate of change of course
Figure FDA0003082637200000011
A smooth transition of (2);
s2, according to the estimated drift angle value, the initial heading error e is psih-ψdCorrecting based on drift angle compensation, wherein the corrected course error is eaWherein ψhThe actual course is taken;
s3 design virtual control
Figure FDA0003082637200000012
And instruction filtering to prevent the problem of "computing explosion" from occurring;
s4, defining a dynamic error e according to the corrected course error and the filtered reference course1、e2；
S5, calculating a compensated tracking error upsilon for the command filtering of the step S31、υ2And the compensation tracking signal is defined according to the dynamic error of the system to eliminate the influence of the instruction filtering error;
s6, calculating a ship yawing control moment command signal tau according to a sliding mode control rule based on an approach lawrThe real-time heading information is updated to step S2.
2. The ship heading dynamic surface sliding-mode control method based on drift angle compensation as claimed in claim 1, wherein the second-order pre-filter adopted in the step S1 is in the form as follows:
Figure FDA0003082637200000013
wherein λ isi(i ═ 1,2,3) are prefilter parameters;
the drift angle estimation formula is as follows:
Figure FDA0003082637200000014
wherein the content of the first and second substances,
Figure FDA0003082637200000015
the surging speed and the swaying speed estimated value of the ship are obtained.
3. The ship heading dynamic surface sliding-mode control method based on drift angle compensation as claimed in claim 1, wherein the expression of the sliding mode in the step S6 is as follows:
Figure FDA0003082637200000016
wherein the content of the first and second substances,
Figure FDA0003082637200000021
Figure FDA0003082637200000022
Figure FDA0003082637200000023
r1k and theta are normal numbers, k is more than 0, and r is more than 01＜1。
4. The ship heading dynamic surface sliding-mode control method based on drift angle compensation as claimed in claim 1, wherein the heading control moment command signal τ in the step S6rThe calculation formula of (a) is specifically expressed as:
Figure FDA0003082637200000024
wherein the content of the first and second substances,
Figure FDA0003082637200000025
for the overall estimation of uncertainty terms and external disturbances in the under-actuated vessel model,
Figure FDA0003082637200000026
non-linear term estimates are composed for the yaw rate in the model,
Figure FDA0003082637200000027
k1、k2to design the constants.
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