CN111498037A - High-speed catamaran longitudinal stabilization method based on variable structure active disturbance rejection control - Google Patents

High-speed catamaran longitudinal stabilization method based on variable structure active disturbance rejection control Download PDF

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CN111498037A
CN111498037A CN202010261955.8A CN202010261955A CN111498037A CN 111498037 A CN111498037 A CN 111498037A CN 202010261955 A CN202010261955 A CN 202010261955A CN 111498037 A CN111498037 A CN 111498037A
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原新
于婧睿
刘志林
杨俊凯
王小虎
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Harbin Engineering University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract

The invention provides a high-speed catamaran longitudinal stabilization method based on variable structure active disturbance rejection control, which comprises the steps of firstly, determining a coordinate system and establishing a simulated sea wave model; establishing a high-speed catamaran model based on the anti-rolling attachment; the heave and pitch of the high-speed catamaran are fed back to the controller, and the attack angle of the anti-rolling attachment is changed through the controller, so that the anti-rolling attachment generates corresponding force and moment to inhibit or counteract disturbance force and moment generated by sea waves; designing a self-disturbance rejection controller which comprises an extended state observer and a nonlinear feedback control law; then designing and selecting a nonsingular terminal sliding mode control law; and finally, improving the observer and control law of active disturbance rejection control according to the selected sliding mode control law to obtain the composite controller of the high-speed catamaran longitudinal anti-rolling control system. The method can be applied to the stability control aspect of military and civil high-speed multi-hull ships, can effectively weaken the influence of sea waves on the longitudinal motion stability of the ships, and improves the comfort level of passengers.

Description

High-speed catamaran longitudinal stabilization method based on variable structure active disturbance rejection control
Technical Field
The invention relates to a high-speed catamaran longitudinal stabilization method based on variable structure active disturbance rejection control, and belongs to the field of high-speed catamaran longitudinal motion stabilization control.
Background
With the wider and wider application of high-performance ships in various fields, people have higher and higher requirements on stability, comfort and safety of ships sailing in the ocean. Compared with the conventional monohull ship, the catamaran has obvious advantages and smaller wave-making resistance, so that the catamaran increasingly becomes an important research object of high-performance ships at home and abroad. However, the strength of the longitudinal movement of the hull also gradually increases during the high-speed navigation, which has a high possibility of causing negative effects on crew passengers and precision equipment on the ship, and at the same time, limits the development of the hull. Therefore, the research on the longitudinal rolling reduction of the high-speed catamaran is significant. It is therefore necessary to find suitable anti-roll appendages to control the longitudinal motion of the vessel and, in addition, finding an excellent control method and a more sophisticated model of the vessel is also the key to the study of longitudinal anti-roll.
The application of the traditional active disturbance rejection control in the multivariable coupling system of the high-speed catamaran has the performance superior to that of other control methods, has great advantages compared with the traditional PID control, and simultaneously makes up the defects of the PID. However, the auto-disturbance rejection control has insufficient capability of estimating disturbance in a more strict high-precision system, and there is still room for enhancement in system stability and fast responsiveness.
The sliding mode control is represented by discontinuity of control, and is a special nonlinear form of control. The structure of the sliding mode control can change along with the current state of the system, and the control quantity is continuously switched to force the state to continuously slide. Therefore, the response characteristic of the sliding mode variable structure control system is more prominent and is easy to realize, and the negative influence caused by parameter variation and interference is not large. The sliding mode control is introduced into the design of the active-disturbance-rejection controller, so that the characteristics of the original active-disturbance-rejection controller are maintained, the adjustable parameters are stably transited in the switching process, the system error is reduced, the control performance is improved, the robustness and the anti-interference capability of the system are improved, and the burden of parameter adjustment is reduced.
Disclosure of Invention
The invention aims to provide a high-speed catamaran longitudinal rolling reduction method based on variable-structure active disturbance rejection control, which aims to better improve the stability of the longitudinal motion of a high-speed catamaran.
The purpose of the invention is realized as follows: the method comprises the following steps:
the method comprises the following steps: establishing a coordinate system and a random sea wave model;
step two: establishing a longitudinal motion model of the high-speed catamaran with the anti-rolling attachment and carrying out linearization processing on the longitudinal motion model to obtain a state space equation for designing a controller;
step three: aiming at the high-speed catamaran longitudinal motion model established in the step two, designing an active disturbance rejection controller for controlling the longitudinal motion of the catamaran, wherein the active disturbance rejection controller comprises an extended state observer and a nonlinear error feedback control law, and designing a static decoupling matrix aiming at the longitudinal motion with a coupling relation of heave and pitch;
step four: and (4) combining a sliding mode variable structure control law, and improving the extended state observer and the nonlinear error feedback control law of the active disturbance rejection controller designed in the third step to obtain the variable structure active disturbance rejection controller of the high-speed catamaran longitudinal stabilization control system.
The invention also includes such structural features:
1. the first step specifically comprises the following steps: the establishment of the coordinate system and the random sea wave model comprises the following steps:
(1) selecting a coordinate system, namely selecting a fixed coordinate system and a moving coordinate system;
(2) and a random sea wave model is established to simulate a sea wave environment, so that a foundation is provided for a simulation experiment.
2. The establishment of the high-speed catamaran longitudinal motion model with the anti-rolling attachment in the second step is specifically as follows:
(1) separating a heave motion equation set and a pitch motion equation set related to the six-degree-of-freedom coupling of the catamaran with the anti-rolling attachment from the motion equation set:
Figure BDA0002439706310000021
Figure BDA0002439706310000022
in the formula: m is the mass of the catamaran; i isyIs the moment of inertia of the vessel relative to the y-axis; x is the number of3、
Figure BDA0002439706310000023
Heave displacement, heave velocity and heave acceleration respectively; x is the number of5、
Figure BDA0002439706310000024
The pitch angle, the pitch angular velocity and the pitch angular acceleration; a isijAn additional mass coefficient of representation; bijRepresents a damping coefficient; c. CijThe score represents the coefficient of restitution; fwaveAnd MwaveRespectively the acting force and moment of the sea wave, FAnti-rolling accessory bodyAnd MAnti-rolling accessory bodyRespectively representing the lifting force and the moment provided by the anti-rolling attachment;
(2) obtaining a linear state space equation:
Figure BDA0002439706310000025
in the formula: a ═ T-1A1，B＝T-1B1，u＝[FM]T，
Figure BDA0002439706310000026
3. The design of the traditional active disturbance rejection controller aiming at the longitudinal motion model of the catamaran specifically comprises the following steps:
(1) omitting a differential tracking link of an active disturbance rejection controller for longitudinal stabilization, and designing an extended state observer and a nonlinear error feedback control law;
(2) the ship longitudinal motion, namely the heave and pitch, has a coupling relation, two active disturbance rejection controllers are designed, a static decoupling matrix is designed, and decoupling control on the heave and pitch motion is realized.
4. The fourth step of combining the sliding mode variable structure control law specifically comprises the following steps:
(1) selecting a nonsingular terminal sliding mode control law to perform variable structure operation on a traditional active disturbance rejection controller, respectively introducing the sliding mode control law into an expansion state observer and a nonlinear error feedback control law, and enabling a system error to approach the system origin along a sliding mode surface to obtain a composite controller for longitudinal stabilization of the double-hull ship;
(2) the control effect of the composite controller is adjusted by adjusting the parameters, so that the effect of longitudinal stabilization is achieved.
Compared with the prior art, the invention has the beneficial effects that: the extended state observer is improved through a variable structure principle, so that the disturbance estimation capability is improved; and non-singular terminal sliding mode control is introduced to replace nonlinear error feedback control quantity, so that the anti-interference capability of the system is improved. Simulation results show that the sliding mode self-disturbance composite control scheme has better control performance, and the performance of the improved composite controller is obviously improved compared with that of the traditional self-disturbance-rejection controller.
Drawings
FIG. 1 is a flow chart of a control method of the present invention;
FIG. 2 is a block diagram of a hull longitudinal motion model of the present invention;
FIG. 3 is an active disturbance rejection control decoupling design of the present invention;
fig. 4 is a block diagram of a composite control method implemented by the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention discloses a high-speed catamaran longitudinal stabilization method based on variable structure active disturbance rejection control, which comprises the following steps:
the method comprises the following steps: establishing a coordinate system and a random sea wave model;
step two: establishing a longitudinal motion model of the high-speed catamaran with the anti-rolling attachment and carrying out linearization processing on the longitudinal motion model to obtain a state space equation which can be used for designing a controller;
step three: aiming at the catamaran longitudinal motion model established in the step one, designing an active disturbance rejection controller for controlling the longitudinal motion of the catamaran, wherein the active disturbance rejection controller comprises an extended state observer and a nonlinear error feedback control law, and designing a static decoupling matrix aiming at the heave and pitch longitudinal motions with a coupling relation;
step four: and (4) combining a sliding mode variable structure control law, and improving the extended state observer and the nonlinear error feedback control law of the active disturbance rejection controller designed in the step two to obtain the variable structure active disturbance rejection controller of the high-speed catamaran longitudinal stabilization control system.
In some embodiments, the coordinate system and the random wave model are specifically established as follows:
(1) selecting a fixed coordinate system and a moving coordinate system to facilitate the study of longitudinal movement;
(2) and the establishment of a random sea wave model simulates a sea wave environment and provides a foundation for simulation.
In some embodiments, the establishing of the high-speed catamaran longitudinal motion model with the anti-rolling appendage is specifically as follows:
(1) separating a heave motion equation set and a pitch motion equation set related to the six-degree-of-freedom coupling of the catamaran with the anti-rolling attachment from the motion equation set:
Figure BDA0002439706310000031
Figure BDA0002439706310000032
the meaning of each symbol in the formula is: m is the mass of the catamaran; i isyIs the moment of inertia of the vessel relative to the y-axis; x is the number of3、
Figure BDA0002439706310000033
Figure BDA0002439706310000034
Heave displacement, heave velocity and heave acceleration, respectively；x5、
Figure BDA0002439706310000035
The pitch angle, the pitch angular velocity and the pitch angular acceleration; a isijAn additional mass coefficient of representation; bijRepresents a damping coefficient; c. CijThe score represents the coefficient of restitution; fwaveAnd MwaveRespectively the force and moment of the sea wave, FAnti-rolling accessory bodyAnd MAnti-rolling accessory bodyRespectively representing the lifting force and the moment provided by the anti-rolling attachment;
(2) the system of equations is simplified to a linear state space equation:
Figure BDA0002439706310000041
in the formula: a ═ T-1A1，B＝T-1B1，u＝[F M]T，
Figure BDA0002439706310000042
This equation can be used for controller design.
In some embodiments, designing the conventional active disturbance rejection controller for the catamaran longitudinal motion model specifically includes:
(1) in order to obtain good wave resistance, the ideal state is that the ship does not heave and pitch in sea waves, namely the expected input of the active disturbance rejection controller is zero, and then the output of the tracking differentiator is also zero, so that the active disturbance rejection controller for longitudinal stabilization omits a differential tracking link, and only needs to design an extended state observer and a nonlinear error feedback control law;
(2) the longitudinal motion of the ship, namely the heave and pitch, has a coupling relation, and two active disturbance rejection controllers need to be designed and a static decoupling matrix needs to be designed, so that the decoupling control of the heave and pitch motion is realized.
In some embodiments, an extended state observer and a nonlinear error feedback control law of the active disturbance rejection controller designed in step three are improved by combining a sliding mode variable structure control law, specifically:
(1) according to the advantages of sliding mode control, selecting a nonsingular terminal sliding mode control law to perform variable structure operation on a traditional active disturbance rejection controller, respectively introducing the sliding mode control law into an extended state observer and a nonlinear error feedback control law, and enabling a system error to approach the system origin along a sliding mode surface to obtain a composite controller;
(2) the control effect of the composite controller is adjusted by adjusting the parameters, so that the effect of longitudinal stabilization is achieved.
The invention discloses a high-speed catamaran longitudinal rolling reduction method based on variable structure active disturbance rejection control, which is characterized in that a flow chart is shown in figure 1, and the specific flow is as follows:
(1) establishing a coordinate system and a random sea wave model:
firstly, a right-hand rectangular motion coordinate system Oxyz is selected, the ship moves forwards along with the ship in a translation mode according to a ship coordinate system, and the speed of the right-hand rectangular motion coordinate system is the same as that of the ship. The coordinate origin O of the coordinate system is on the still water level where the vessel is located, and the xOy plane coincides with the still water level. Wherein the x-axis points in the forward direction of motion of the ship. The xOz plane coincides with the longitudinal mid-section of the vessel, with the z-axis passing vertically up through the center of gravity G of the vessel and the y-axis pointing to the port side of the vessel.
Secondly, the motion conditions of the sea waves are complex and changeable, and for the convenience of research, only the influence of random sea waves on the longitudinal motion of the high-speed catamaran is considered. The harmonics of the various orders combine to form a random wave, and the corresponding harmonics are also randomly generated resulting in phase and wavelength.
Figure BDA0002439706310000051
Wherein: ζ (t) is the random amplitude; n is the total number of times of superposition; zetaaiAmplitude of the ith wave; k is a radical ofiIs the number of waves in the period, and ki＝2π/λi；iThe phase of the ith harmonic wave takes a value range of [0,2 pi ].
The wave energy spectral density function varies with respect to changes in sea conditions, and can be determined from actual sea conditions or derived from theoretical formulas, depending on the particular sea condition.
Using the ITTC spectrum, i.e.
Figure BDA0002439706310000052
The relationship between encounter frequency and natural frequency is:
Figure BDA0002439706310000053
wherein: omega is the natural wave frequency, U is the ship speed, mueHeading and wave heading angle, the condition studied here for a ship travelling in the waves, i.e. mue＝0。
Substituting formula (3) into formula (2) to obtain a spectral density function as:
Figure BDA0002439706310000054
will Sζ(ωe) Set as a function of spectral density and divide the spectrum into wavelets, so the wavetime-domain function is:
Figure BDA0002439706310000055
a simulation graph of random sea waves can be obtained through matlab, and a sea wave environment foundation is provided for a subsequent simulation experiment.
(2) Establishing a catamaran control model with T-shaped wings:
firstly, separating a heave and pitch related motion equation set from a six-degree-of-freedom coupled motion equation set of a catamaran with T-shaped wings:
Figure BDA0002439706310000056
the meaning of each symbol in the formula is: m is the mass of the catamaran; i isyIs the moment of inertia of the vessel relative to the y-axis; x is the number of3、
Figure BDA0002439706310000057
Figure BDA0002439706310000058
Heave displacement, heave velocity and heave acceleration respectively; x is the number of5、
Figure BDA0002439706310000059
The pitch angle, the pitch angular velocity and the pitch angular acceleration; a isijAn additional mass coefficient of representation; bijRepresents a damping coefficient; c. CijThe score represents the coefficient of restitution; fwaveAnd MwaveRespectively the force and moment of the sea wave, FAnti-rolling accessory bodyAnd MAnti-rolling accessory bodyRespectively representing the lifting force and the moment provided by the anti-rolling attachment;
then, the system of equations is simplified to a linear state space equation:
Figure BDA0002439706310000061
in the formula: a ═ T-1A1，B＝T-1B1，u＝[F M]T，
Figure BDA0002439706310000062
This equation can be used for controller design.
Wherein the content of the first and second substances,
Figure BDA0002439706310000063
the lift force and lift moment calculation model of the anti-rolling appendage is as follows:
Figure BDA0002439706310000064
M＝da·FT-foil＝da·kα (9)
wherein rho is the water density and is 1.0 × 103kg/m3(ii) a A is the surface area (m) of the appendage2) U is the ship's speed (kn), α is the angle of attack (deg.)LIs the coefficient of lift, daIndicating T-shaped wingOr the distance between the corrugated board and the center of gravity of the ship body.
The state space equation is rewritten into a general matrix form, and then:
Figure BDA0002439706310000065
at this point, the random sea wave model is subjected to hydrodynamic analysis by using ANSYS software to obtain a coefficient, the stress model of the ship body under the action of the sea waves is fitted under the conditions of the navigational speed of 40 knots and the sea condition of 4 levels, and a function ss2tf is used in a MAT L AB platform to realize the model, so that the model of the heave force and the pitching moment of the ship body under the action of the sea waves is obtained and is shown in FIG. 2.
(3) Designing an active disturbance rejection controller with a decoupling matrix:
it is known that the Active Disturbance Rejection Controller (ADRC) mainly consists of a Tracking Differentiator (TD), an Extended State Observer (ESO), a nonlinear state error feedback control law (N L SEF), since the invention is studying the longitudinal motions of the vessel, i.e. heave and pitch, in order to get a good wave endurance, we always expect the vessel to have no heave and pitch in the sea, i.e. the desired input of the active disturbance rejection controller is 0, and TD is used for the tracking and acquisition of the desired input signal, and in case the desired input is 0, the output must also be 0, so for the active disturbance rejection controller of the invention, no TD link is needed.
For a second order system as follows:
Figure BDA0002439706310000071
the ESO links are as follows:
Figure BDA0002439706310000072
z1and z2Differential of tracking y, z3Is an estimate of the total disturbance unknown to the system, β01，β02，β03Are variable parameters, and when they are chosen reasonably, the ESO isThe system state including the total interference can be estimated, and fal (e, a,) is a non-linear function as shown in equation (13):
Figure BDA0002439706310000073
n L SEF used:
control law: u. of0＝β1fal(e1,a1,)+β2fal(e2,a2,) (14)
Wherein 0 < a1＜1＜a2，β1，β2Is the gain of the non-linear element.
The heave and pitch models of the ship are both of the second order, so the designed ADRC controller is also of the second order, wherein the ESO is a third-order link, and the pitch and the heave of the ship need to be controlled as well as the ship need to be controlled, so two ADRC controllers are needed to respectively control the pitch and the heave of the ship body, the pitch motion and the heave motion in the longitudinal motion of the high-speed catamaran are coupled, and both the two anti-roll bodies can generate force and moment, and if only the heave feedback control anti-roll body is adopted, the pitch can be increased; if only pitch feedback is used to control the anti-roll appendage, heave will increase. The heave and pitch of the high-speed catamaran can not be reduced simultaneously by adopting any one of the decoupling devices, so that the decoupling step is added, and the input-output coupling relation of the system is offset.
The schematic diagram of the decoupling design of the active disturbance rejection controller is shown in fig. 3, and the ith control of the system leads to the following input-output relationship:
Figure BDA0002439706310000074
this makes the entire coupled system a single input single output system.
The motion equation of the ship system with the added anti-rolling attachment is as follows:
Figure BDA0002439706310000081
wherein:
Figure BDA0002439706310000082
Figure BDA0002439706310000083
in the formula m33Is the ship mass, m55Are the pitch moments of inertia and these hydrodynamic coefficients are simulated on an ANSYS platform according to the dimensional parameters of the ship.
The heave amount of the ship and the pitch of the ship respectively enable the corresponding ADRC to generate an output, and the output is transmitted to the T-shaped wing and the wave suppression plate through the decoupling matrix, and the derivation process is as follows:
Figure BDA0002439706310000084
decoupling matrix:
Figure BDA0002439706310000085
can find B-1(t) if present, determining a virtual control quantity U1、U2(i.e., U)heave、Upitch) The actual control quantities required are then:
Figure BDA0002439706310000086
the system (12) was introduced and the system was returned to a two-integrator tandem type for simulation.
The ESO and N L SEF algorithms of the entire active disturbance rejection controller using the virtual control quantity are as follows:
Figure BDA0002439706310000087
Figure BDA0002439706310000088
NLSEF1：U1＝b1u1-z13(16)
NLSEF2：U2＝b2u2-z23(17)
note: wherein z isijI 1 and 2 represent the reference numerals of the two controllers, and j 1, 2 and 3 represent the third-order outputs.
(4) Aiming at a designed active disturbance rejection controller, sliding mode control is introduced for improvement to obtain a composite controller:
the sliding mode variable structure control is introduced into the ADRC controller, the ESO and N L SEF modules are improved, the system error approaches to the system origin along the sliding mode surface, the parameters are improved, the controller can ensure the characteristics of the original ADRC control, and the adjustable parameters can be smoothly transited during switching, so that the system error is reduced.
① first, a variable structure extended state observer (VSC-ESO) design is performed:
appropriate equivalent changes are made to the top three-level ESO (here, taking an ESO as an example, so the corner mark is removed i that distinguishes the two controllers), and we can obtain:
Figure BDA0002439706310000091
order to
Figure BDA0002439706310000092
Let | a0(t) is less than or equal to A and is bounded,
order to
Figure BDA0002439706310000093
The system error expansion state observation equation is as follows:
Figure BDA0002439706310000094
the VSC-ESO is stabilized by selecting the proper g (e) function, thereby ensuring the stability of the ESO.
Firstly, taking a sliding mode switching function:
s＝c1e1+c2e2+e3,c1＞0,c2＞0 (20)
constant c1,c2The value of (2) should satisfy that the characteristic root of the characteristic equation (21) has a negative real part, so that the system (19) is gradually stable and has a larger margin.
s3+c2s2+c1s＝0 (21)
When s (t) is 0, the system (19) is in a sliding mode state, and the state space equation is as follows:
Figure BDA0002439706310000095
in order to satisfy the existence and accessibility of the system (19) in the s ≠ 0 sliding mode approach stage,
Figure BDA0002439706310000096
introducing smooth-k theta(s) constraint to deviate from sliding mode surface to replace ksgn(s) function to reduce buffeting and enable
Figure BDA0002439706310000097
Figure BDA0002439706310000101
Wherein k is1Is a positive number, and the number of the positive number,1is a small positive number. The following conditions were confirmed:
taking L yapunov function
Figure BDA0002439706310000102
To obtain the following formula:
Figure BDA0002439706310000103
if k is guaranteed to satisfy: k is a radical of1> A, then
Figure BDA0002439706310000104
The presence and accessibility are satisfied, the sliding form system (19) is stable, and the result (18) is also stable.
Whether the system (19) is in the approaching or sliding mode state, there are:
Figure BDA0002439706310000105
so that g (e) ═ c1e2-c2e3-k1θ(s), the system (19) can in turn be written as:
Figure BDA0002439706310000106
the VSC-ESO model is obtained as follows:
Figure BDA0002439706310000107
② then designing variable structure nonlinear state error feedback control law (VSC-N L SEF)
The state error signal e is formed by the output v of a differential Tracker (TD) and a reconstructed signal z of a variable structure extended state observer to the system state quantity, and the TD link is omitted in the invention, so that the e is equal to v-z1＝-z1，e2＝-z2And because of the expanded state in the observer
Figure BDA0002439706310000108
So there is N L SEF:
Figure BDA0002439706310000109
referring to the variable structure design above, a sliding mode switching function is taken: s (t) ═ c1e1+e2，c1More than 0, introducing smooth-k theta(s) constraint to deviate from the sliding mode surface to replace ksgn(s) function to reduce buffeting and enable
Figure BDA0002439706310000111
Figure BDA0002439706310000112
Wherein k is2Is a positive number, and the number of the positive number,2is a small positive number. Get u0＝-c1e1-k2θ(s) can ensure the system to be stable, so the control law:
Figure BDA0002439706310000113
(5) the variable-structure active-disturbance-rejection composite controller can be obtained, the structural block diagram of the controller is shown in fig. 4, and the composite controller is subjected to parameter adjustment to achieve an ideal control effect.
In summary, the invention provides a high-speed catamaran longitudinal stabilization method based on sliding mode variable structure principle improved active disturbance rejection control, which maintains the characteristics of an original active disturbance rejection controller, and the sliding mode control is added to ensure that adjustable parameters are in stable transition in the switching process, so that the system error is reduced, the control performance is improved, and the burden of parameter adjustment is reduced. Firstly, establishing a coordinate system and establishing a simulated sea wave model; establishing a high-speed catamaran model based on the anti-rolling attachment; the heave and pitch of the high-speed catamaran are fed back to the controller, and the attack angle of the anti-rolling attachment is changed through the controller, so that the anti-rolling attachment generates corresponding force and moment to inhibit or counteract disturbance force and moment generated by sea waves; designing a self-disturbance rejection controller which comprises an extended state observer and a nonlinear feedback control law; then designing and selecting a nonsingular terminal sliding mode control law; and finally, improving the observer and control law of active disturbance rejection control according to the selected sliding mode control law to obtain the composite controller of the high-speed catamaran longitudinal anti-rolling control system. The method can be applied to the stability control aspect of military and civil high-speed multi-hull ships, can effectively weaken the influence of sea waves on the stability of longitudinal motion of the ships, and improves the comfort level of passengers.

Claims (5)

1. The high-speed catamaran longitudinal rolling reduction method based on variable structure active disturbance rejection control is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a coordinate system and a random sea wave model;
step two: establishing a longitudinal motion model of the high-speed catamaran with the anti-rolling attachment and carrying out linearization processing on the longitudinal motion model to obtain a state space equation for designing a controller;
step three: aiming at the high-speed catamaran longitudinal motion model established in the step two, designing an active disturbance rejection controller for controlling the longitudinal motion of the catamaran, wherein the active disturbance rejection controller comprises an extended state observer and a nonlinear error feedback control law, and designing a static decoupling matrix aiming at the longitudinal motion with a coupling relation of heave and pitch;
step four: and (4) combining a sliding mode variable structure control law, and improving the extended state observer and the nonlinear error feedback control law of the active disturbance rejection controller designed in the third step to obtain the variable structure active disturbance rejection controller of the high-speed catamaran longitudinal stabilization control system.
2. The high-speed catamaran longitudinal rolling reduction method based on variable structure active disturbance rejection control according to claim 1, characterized in that: the first step specifically comprises the following steps: the establishment of the coordinate system and the random sea wave model comprises the following steps:
(1) selecting a coordinate system, namely selecting a fixed coordinate system and a moving coordinate system;
(2) and a random sea wave model is established to simulate a sea wave environment, so that a foundation is provided for a simulation experiment.
3. The high-speed catamaran longitudinal rolling reduction method based on variable structure active disturbance rejection control according to claim 1 or 2, characterized in that: the establishment of the high-speed catamaran longitudinal motion model with the anti-rolling attachment in the second step is specifically as follows:
(1) separating a heave motion equation set and a pitch motion equation set related to the six-degree-of-freedom coupling of the catamaran with the anti-rolling attachment from the motion equation set:
Figure FDA0002439706300000011
Figure FDA0002439706300000012
in the formula: m is the mass of the catamaran; i isyIs the moment of inertia of the vessel relative to the y-axis; x is the number of3、
Figure FDA0002439706300000013
Heave displacement, heave velocity and heave acceleration respectively; x is the number of5、
Figure FDA0002439706300000014
The pitch angle, the pitch angular velocity and the pitch angular acceleration; a isijAn additional mass coefficient of representation; bijRepresents a damping coefficient; c. CijThe score represents the coefficient of restitution; fwaveAnd MwaveRespectively the force and moment of the sea wave, FAnti-rolling accessory bodyAnd MAnti-rolling accessory bodyRespectively representing the lifting force and the moment provided by the anti-rolling attachment;
(2) obtaining a linear state space equation:
Figure FDA0002439706300000015
in the formula: a ═ T-1A1，B＝T-1B1，u＝[F M]T，
Figure FDA0002439706300000016
4. The high-speed catamaran longitudinal rolling reduction method based on variable structure active disturbance rejection control according to claim 3, characterized in that: the design of the traditional active disturbance rejection controller aiming at the longitudinal motion model of the catamaran specifically comprises the following steps:
(1) omitting a differential tracking link of an active disturbance rejection controller for longitudinal stabilization, and designing an extended state observer and a nonlinear error feedback control law;
(2) the ship longitudinal motion, namely the heave and pitch, has a coupling relation, two active disturbance rejection controllers are designed, a static decoupling matrix is designed, and decoupling control on the heave and pitch motion is realized.
5. The high-speed catamaran longitudinal rolling reduction method based on variable structure active disturbance rejection control according to claim 4, wherein the method comprises the following steps: the fourth step of combining the sliding mode variable structure control law specifically comprises the following steps:
(1) selecting a nonsingular terminal sliding mode control law to perform variable structure operation on a traditional active disturbance rejection controller, respectively introducing the sliding mode control law into an extended state observer and a nonlinear error feedback control law, and enabling a system error to approach the original point of a system along a sliding mode surface to obtain a composite controller for longitudinal stabilization of a catamaran;
(2) the control effect of the composite controller is adjusted by adjusting the parameters, so that the effect of longitudinal stabilization is achieved.
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