CN115903807B - Dynamic event triggering-based dynamic positioning ship track tracking control method - Google Patents

Dynamic event triggering-based dynamic positioning ship track tracking control method Download PDF

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CN115903807B
CN115903807B CN202211434409.5A CN202211434409A CN115903807B CN 115903807 B CN115903807 B CN 115903807B CN 202211434409 A CN202211434409 A CN 202211434409A CN 115903807 B CN115903807 B CN 115903807B
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positioning ship
ship
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triggering
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CN115903807A (en
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王海滨
赵锐
尤波
谢文博
李鸣阳
孙明晓
栾添添
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Harbin University of Science and Technology
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Abstract

A dynamic event triggering-based dynamic positioning ship track tracking control method relates to the technical field of ship motion control. The invention aims to solve the problems of energy waste and actuator abrasion caused by frequent update of an actuator when the DPV is controlled by adopting a PPC method in the prior art. According to the invention, decoupling is carried out according to a decoupling principle, and a design sliding mode surface provides a foundation for the design of a subsequent controller. The integral interference observer is designed, and the second-order preset performance function can not only meet the transient steady-state performance of the system, but also provide better initial performance inclusion degree and reduce the pressure of an actuating mechanism. Considering all states in the execution process, taking the change of all states as a factor of a dynamic event triggering strategy, introducing a performance safety evaluation factor into a triggering condition, designing an all-state event triggering controller, improving the triggering accuracy, reducing the triggering frequency and ensuring the accuracy of a track tracking task.

Description

Dynamic event triggering-based dynamic positioning ship track tracking control method
Technical Field
The invention belongs to the technical field of ship motion control, and particularly relates to track tracking control of a dynamic positioning ship.
Background
With the gradual exhaustion of oil and gas resources at landlands, ocean resources have become a major goal of world-wide development. With the continuous improvement and perfection of technologies such as computers, cloud processing, remote terminals, artificial intelligence, big data computing and the like, reliable technical support and theoretical support of software and hardware are provided for the control research of the full-drive surface ship, and meanwhile, the practical application of the full-drive surface ship is also more and more extensive, wherein the dynamic positioning ship is used as a representative of the full-drive surface ship and is particularly valued by scientific researchers.
Since marine engineering operations are often long-term continuous operations, especially during the course of performing trajectory tracking tasks, power positioning vessels (Dynamic positioning vessel, DPV) inevitably remain in operation for a long period of time, achieving high-precision trajectory tracking throughout complex deep-sea environments is a significant challenge. The main reasons for its difficulty are two broad categories: firstly, the environmental interference changes along with time, and the performance of a control system is difficult to guarantee at any time; another problem is the energy consumption and actuator wear caused by long-term continuous operation in complex deep sea environments.
The preset performance control (Prescribed performance control, PPC) is an effective solution to ensure that the trajectory tracking performance meets the task requirements, and provides a new design concept for ensuring the transient steady state performance of the control system. Currently, the PPC method has been successfully applied to trajectory tracking control of various practical systems, such as robots, spacecraft, unmanned aerial vehicles, etc., and in recent years, the technology has been gradually applied to the DPV field. Clearly, all of these prior works demonstrate that PPC schemes can keep the tracking error within the performance envelope constructed by the performance function, and then ensure that the tracking error converges to within a preset arbitrarily small set of residuals at a prescribed convergence rate and steady state value, while the overshoot is less than a preset constant. In long-term continuous engineering operation, DPV is used to collect system state and adjust actuator state at each sampling instant, but this process may result in unnecessary energy waste and actuator wear due to frequent actuator updates.
Disclosure of Invention
The invention aims to solve the problems of energy waste and actuator abrasion caused by frequent updating of an actuator when a PPC method is adopted to control a DPV in the prior art, and provides a dynamic event triggering-based dynamic positioning ship track tracking control method.
A dynamic event triggering-based dynamic positioning ship track tracking control method comprises the following steps:
step one: designing an integral interference observer according to a kinematic model and a dynamic model of the dynamic positioning ship:
Figure BDA0003946260040000021
wherein, xi 1 (t) and ζ 2 (t) integrating two state variables of the disturbance observer at time t respectively,
Figure BDA0003946260040000022
and->
Figure BDA0003946260040000023
Respectively is xi 1 (t) and ζ 2 First derivative of (t), l 1 And l 2 For integrating two gain parameters of the disturbance observer and being constants greater than 0, M is the inertial matrix of the dynamic positioning ship, M -1 Is the inverse matrix of M>
Figure BDA0003946260040000024
For the external environment interference estimated value generated by the t moment integral interference observer, τ (t) is the control input vector of the t moment dynamic positioning ship, x (t) is the t moment tracking error vector and x (t) = [ x ] 1 (t),x 2 (t),x 3 (t)] T ，H 1 Is an intermediate variable, t is the running time of the control system of the dynamic positioning ship,
x(t)＝γ 1 η e +υ e ，
Figure BDA0003946260040000025
γ 1 constant, eta, greater than 0 e To track the position error value, v e For tracking the speed error value, R is a conversion matrix between a north-east coordinate system and a ship body coordinate system, v is speed information of the power positioning ship, D is a damping coefficient matrix of the power positioning ship, and eta is a damping coefficient matrix of the power positioning ship d To track the position expectation value, v d In order to track the desired value of the velocity,
Figure BDA0003946260040000026
and->
Figure BDA0003946260040000027
Respectively are provided withIs eta d And v d Is the first derivative of (a);
step two: a tracking error constraint is applied in the tracking error vector x (t) at time t, said tracking error constraint being as follows:
Figure BDA0003946260040000028
wherein i=1, 2,3,δ i and
Figure BDA0003946260040000029
p respectively i Lower and upper coefficients of (t), ρ i (t) is a performance function and satisfies the following formula:
Figure BDA00039462600400000210
Figure BDA00039462600400000211
Figure BDA00039462600400000212
and->
Figure BDA00039462600400000213
P respectively i First and second derivatives of (t), ω being a parameter adjusting the rate of change of the transient constrained boundary curve, ρ ∞i For ρ i A steady state value of (t), Y being a positive constant, sign (&) being a sign function;
step three: converting x (t) according to the tracking error constraint condition of x (t) to obtain a converted t moment tracking error s (t), and obtaining a first derivative of s (t):
Figure BDA00039462600400000214
wherein s (t) = [ s ] 1 (t),s 2 (t),s 3 (t)] T ，
Figure BDA0003946260040000031
And->
Figure BDA0003946260040000032
First derivatives of x (t) and ρ (t), respectively, ρ (t) = [ ρ ] 1 (t),ρ 2 (t),ρ 3 (t)] T ，θ(t)＝[θ 1 (t),θ 2 (t),θ 3 (t)] T ，μ(t)＝[μ 1 (t),μ 2 (t),μ 3 (t)] T ，
Figure BDA0003946260040000033
μ i (t)＝x i (t)/ρ i (t)；
Step four: setting a measurement vector
Figure BDA0003946260040000034
Then the measurement vector error e at the time t is obtained according to the measurement vector 2 (t)：
Figure BDA0003946260040000035
Wherein delta is x ＝x(t k )-x(t)，Δ ν ＝υ(t k )-υ(t)，
Figure BDA0003946260040000036
Step five: constructing a full-state event trigger controller and event trigger conditions of a power positioning ship control system:
Figure BDA0003946260040000037
wherein t is k To trigger the occurrence time, t k+1 For triggering the next moment in time τ FETC (t) is a control signal output by the full state event trigger controller, and alpha and beta are bothIs a normal number of times, and the number of times is equal to the normal number,
Figure BDA0003946260040000038
Y 1 ＝M(γ 1 R-M -1 D)，
Figure BDA0003946260040000039
Figure BDA00039462600400000310
l (t) is a dynamic threshold variable, lambda s And lambda (lambda) ξ The gain parameters are given, and Q is a positive definite symmetric matrix;
step six: and calculating and obtaining a control signal of the dynamic positioning ship by using the full-state event trigger controller, controlling the dynamic positioning ship to move, and completing the track tracking control of the dynamic positioning ship based on the dynamic event trigger.
Further, in the first step, a point O is located on the water surface E Establishing a north-east coordinate system X of motion of a dynamic positioning ship for an origin E Y E Z E Positioning the centre of gravity O of the ship by power B Establishing a hull coordinate system X of a dynamic positioning ship for an origin B Y B Z B According to the north-east coordinate system X E Y E Z E And a hull coordinate system X B Y B Z B A kinematic model and a dynamic model of the dynamic positioning ship are constructed,
the kinematic model expression of the dynamic positioning ship is as follows:
Figure BDA0003946260040000041
the dynamic model expression of the dynamic positioning ship is as follows:
Figure BDA0003946260040000042
in the above, eta is the actual position and attitude angle of the dynamic positioning ship under the north-east coordinate system,
Figure BDA0003946260040000043
is the first derivative of eta, eta= [ n, e, phi ]] T N is the north position, e is the east position, ψ is the heading angle of the power positioning ship,
Figure BDA0003946260040000044
υ＝[u,v,r] T u is the longitudinal speed of the power positioning ship, v is the transverse speed of the power positioning ship, and r is the Z-winding speed of the power positioning ship B Angular velocity of shaft rotation, Z B The axis is the axis perpendicular to the plane of the hull in the hull coordinate system, τ w And tau is the control input vector of the dynamic positioning ship for the actual value of the external environment interference.
Further, in the third step, the following steps:
Figure BDA0003946260040000045
further, the measurement vector in the above step four can be described by the following equation:
Figure BDA0003946260040000046
further, in the fifth step, the first derivative L (t) of the dynamic threshold variable L (t) is:
Figure BDA0003946260040000047
wherein alpha is l And beta l All are normal numbers, N p Is a performance safety assessment factor.
Aiming at the control of frequent triggering of the actuating mechanism of the dynamic positioning ship under the condition of marine time-varying wind and wave interference, the invention provides a dynamic event triggering-based track tracking control method of the dynamic positioning ship, which has the following advantages compared with the prior art:
(1) The invention provides a novel Second-order preset performance function (SOPPF). In contrast to conventional performance functions, the law of change of the SOPPF is a process of going from a smooth transition to rapid convergence and then gradually reaching a steady state. Due to the characteristics of the proposed performance function, the contradiction between the performance constraint and the control input when the initial tracking error is large can be smartly relieved, so that a more stable control effect is obtained.
(2) In order to simplify the design of the event triggering mechanism, the invention designs an auxiliary sliding mode surface by means of a sliding mode control theory and introduces the auxiliary sliding mode surface into a DPV event triggering controller. In addition, the invention provides a decoupling method for analyzing and proving the rationality of the proposed auxiliary sliding mode surface design.
(3) The invention provides a full-state event trigger controller which is used for meeting preset performance constraint in a track tracking process. In addition, the performance safety evaluation factors are introduced into the dynamic threshold event trigger control strategy, and based on the performance safety evaluation factors, the proposed event trigger mechanism not only ensures the accuracy of track tracking, but also greatly reduces the trigger frequency of an executing mechanism and saves more communication resources.
In summary, the invention can complete the track tracking task with less trigger frequency and traffic on the premise of ensuring the DPV to perform constraint and time-varying disturbance. In the presence of unknown sea loads, a full state event triggered control scheme based on an integrated disturbance observer (Integral Disturbance Observer, IDO) and PPC strategy is proposed for DPV. The invention can be applied to a ship dynamic positioning system with system model coupling, limited communication and time-varying environment interference in the marine operation process.
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FIG. 1 is a schematic block diagram of a dynamic positioning ship track tracking control method based on dynamic event triggering;
FIG. 2 is a schematic diagram showing comparison of preset performance functions;
FIG. 3 is a schematic diagram of a North east coordinate system and a hull coordinate system;
FIG. 4 is a graph of time triggered and event triggered control effects.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
Because the time-varying wind and wave interference power positioning ship exists in the deep sea environment, the problem of frequent triggering of an executing mechanism can exist in the track tracking process. To solve this problem, the present embodiment introduces an event trigger mechanism into the trajectory tracking task, which indirectly reduces the operating frequency of the actuator by reducing the transmission frequency of the control input signal. Specifically, the method is realized by the following embodiments.
Referring to fig. 1 to 4, a track tracking control method for a dynamic positioning ship based on dynamic event triggering according to the present embodiment specifically illustrates the present embodiment, including the following steps:
step one: at a point O on the water surface E Establishing a north-east coordinate system X of motion of a dynamic positioning ship for an origin E Y E Z E Positioning the centre of gravity O of the ship by power B Establishing a hull coordinate system X of a dynamic positioning ship for an origin B Y B Z B . According to the north-east coordinate system X E Y E Z E And a hull coordinate system X B Y B Z B And constructing a kinematic model and a dynamic model of the dynamic positioning ship.
The kinematic model expression of the dynamic positioning ship is as follows:
Figure BDA0003946260040000061
the dynamic model expression of the dynamic positioning ship is as follows:
Figure BDA0003946260040000062
in the above, eta is the actual position and attitude angle of the dynamic positioning ship under the north-east coordinate system,
Figure BDA0003946260040000063
is the first derivative of eta, eta= [ n, e, phi ]] T N is the north position, e is the east position, ψ is the heading angle of the power positioning ship,
v is the speed information of the dynamic positioning ship, and v= [ u, v, r ]] T U is the longitudinal speed of the power positioning ship, v is the transverse speed of the power positioning ship, and r is the Z-winding speed of the power positioning ship B Angular velocity of shaft rotation, Z B The axis is the axis perpendicular to the hull plane in the hull coordinate system,
r is a conversion matrix between a north-east coordinate system and a ship body coordinate system, M is an inertia matrix of the dynamic positioning ship, D is a damping coefficient matrix of the dynamic positioning ship, and the specific values are as follows:
Figure BDA0003946260040000064
Figure BDA0003946260040000065
Figure BDA0003946260040000066
τ w and tau is the control input vector of the dynamic positioning ship for the actual value of the external environment interference.
Meanwhile, a tracking error vector x is designed:
x＝γ 1 η e +υ e ，
γ 1 the constant is larger than 0, and the specific value is as follows: gamma ray 1 ＝diag([0.035,0.6,0.6])；
η e To track the position error value, v e Is the tracking speed error value.
First derivative of tracking error vector x
Figure BDA0003946260040000071
The method meets the following conditions:
Figure BDA0003946260040000072
wherein H is 1 As an intermediate variable, the number of the variables,
Figure BDA0003946260040000073
M -1 is the inverse matrix of M, eta d To track the position expectation value, v d In order to track the desired value of the velocity,
Figure BDA0003946260040000074
and->
Figure BDA0003946260040000075
Respectively eta d And v d The specific values are as follows:
η d ＝[800cos(0.005t),800sin(0.005t),0] T ，υ d ＝[2,2,0] T 。
step two: given an initial state: η (0) = [0m,0 ]] T And v (0) = [0m/s,0m/s,0deg/s] T 。
In order to eliminate the influence of unknown ocean loads on the tracking performance of the system, an integral interference observer is designed according to a kinematic model and a dynamic model of the dynamic positioning ship:
Figure BDA0003946260040000076
wherein, xi 1 (t) and ζ 2 (t) integrating two state variables of the disturbance observer at time t respectively,
Figure BDA0003946260040000077
and->
Figure BDA0003946260040000078
Respectively is xi 1 (t) and ζ 2 (t) a first derivative; l (L) 1 And l 2 The specific values of the two gain parameters of the integral interference observer are: l (L) 1 ＝6，l 2 ＝5；/>
Figure BDA0003946260040000079
For the external environment interference estimated value generated by the t moment integral interference observer, τ (t) is the control input vector of the t moment dynamic positioning ship, x (t) is the t moment tracking error vector and x (t) = [ x ] 1 (t),x 2 (t),x 3 (t)] T T is the running time of the control system of the dynamic positioning ship.
Step three: the track following task of the control system of the dynamic positioning ship is required to strictly ensure the following effect. Therefore, transient and steady state performance in tracking is equally important and prescribed performance control must be ensured.
A tracking error constraint is applied in the tracking error vector x (t) at time t, said tracking error constraint being as follows:
Figure BDA00039462600400000710
if x i (0) > 0 then
Figure BDA00039462600400000711
If x i (0) If the weight is less than or equal to 0->
Figure BDA00039462600400000712
And both cases can be used with zero initial conditions. Thus giving the following second order performance function ρ i (t) (i=1, 2, 3), defined as:
Figure BDA0003946260040000081
Figure BDA0003946260040000082
in the above-mentioned method, the step of,δ i and
Figure BDA0003946260040000083
p respectively i Lower and upper coefficients of (t),>
Figure BDA0003946260040000084
and->
Figure BDA0003946260040000085
P respectively i First and second derivatives of (t), ω being a parameter adjusting the rate of change of the transient constrained boundary curve, ρ ∞i For ρ i Steady state value of (t), Y is a positive constant and sign (·) is a sign function.
To further illustrate the effectiveness of the performance function presented in this section, the effect of its constraints is verified by comparison with a conventional performance function, as shown in FIG. 2.
The specific settings of the second-order performance function parameters are shown in table 1:
TABLE 1 Performance function parameters
Figure BDA0003946260040000086
Step four: converting x (t) according to the tracking error constraint condition of x (t) to obtain a converted t moment tracking error s (t), and obtaining a first derivative of s (t):
Figure BDA0003946260040000087
wherein s (t) = [ s ] 1 (t),s 2 (t),s 3 (t)] T ，
Figure BDA0003946260040000088
Figure BDA0003946260040000089
And->
Figure BDA00039462600400000810
First derivatives of x (t) and ρ (t), respectively, ρ (t) = [ ρ ] 1 (t),ρ 2 (t),ρ 3 (t)] T ，θ(t)＝[θ 1 (t),θ 2 (t),θ 3 (t)] T ，μ(t)＝[μ 1 (t),μ 2 (t),μ 3 (t)] T ，/>
Figure BDA00039462600400000811
μ i (t)＝x i (t)/ρ i (t)。
Step five: setting a measurement vector
Figure BDA00039462600400000812
Then the measurement vector error e at the time t is obtained according to the measurement vector 2 (t)：
Figure BDA0003946260040000091
Wherein delta is x ＝x(t k )-x(t)，Δ ν ＝υ(t k )-υ(t)，
Figure BDA0003946260040000092
The measurement vector can be described by the following equation:
Figure BDA0003946260040000093
step six: in order to ensure that the system output can quickly and accurately track the expected track under the condition of uncertain output constraint and parameters, the reliability and the effectiveness of the operation of the dynamic positioning ship are further improved, and a full-state event trigger controller and an event trigger condition of a control system of the dynamic positioning ship are constructed based on an interference observer and a second-order performance function:
Figure BDA0003946260040000094
wherein t is k To trigger the occurrence time, t k+1 The next moment occurs for triggering; τ FETC (t) is a control signal output by the full state event trigger controller; alpha and beta are positive constants, and specific values are as follows: α=0.02, β=10; k (k) 2 ＝diag([5,5,1])；
Figure BDA0003946260040000095
Y 1 ＝M(γ 1 R-M -1 D)，
Figure BDA0003946260040000096
Figure BDA0003946260040000097
L (t) is a dynamic threshold variable; lambda (lambda) s And lambda (lambda) ξ All are given gain parameters, and the specific values are as follows: lambda (lambda) s ＝λ ξ =1; q is a positive definite symmetric matrix;
first derivative of dynamic threshold variable L (t)
Figure BDA0003946260040000098
The method comprises the following steps:
Figure BDA0003946260040000099
wherein alpha is l And beta l All are positive constants, and the specific values are as follows: alpha l ＝0.1，β l ＝0.001。
N p Is of the performanceSecurity assessment factor (performance safety evaluation factor, PSEF), N p ＝||θ||，N p The function of (2) is to evaluate the effect of the current system state on the performance constraint at the next time, i.e. N when the tracking error approaches the performance constraint boundary p Will become larger, on the contrary, N p Will be relatively small. On the basis, N is as follows p Introducing a full state event trigger mechanism and assigning weights to it will better achieve the effect of dynamic trigger threshold triggering.
Step seven: and calculating and obtaining a control signal of the dynamic positioning ship by using the full-state event trigger controller, controlling the dynamic positioning ship to move, and completing the track tracking control of the dynamic positioning ship based on the dynamic event trigger.
In this embodiment, first, a simple decoupling process is performed on the model of the system according to the principle of decoupling, and the sliding surface is designed and proved to be reasonable, so as to provide a foundation for the design of the following controller. Secondly, in order to ensure accurate estimation of time-varying interference, an integral interference observer is designed, so that time-varying wind and wave interference can be accurately estimated, and the demonstration of system stability can be simplified by combining with the design of a sliding mode surface. Then, a second order preset performance function is provided, which not only can also meet the transient steady state performance of the system, but also can provide better initial performance inclusion degree compared with the traditional performance function, and reduces the pressure of an actuating mechanism. And then taking all states in the system executing process into consideration, taking the change of all states as factors of a dynamic event triggering strategy, introducing a Performance Safety Evaluation Factor (PSEF) into a triggering condition, designing an all-state event triggering controller, better improving the triggering accuracy, more efficiently reducing the triggering frequency and simultaneously ensuring the accuracy of a track tracking task.
Through Matlab simulation, the proposed full-state event trigger control method can ensure the rapid convergence of track tracking errors under the conditions of time-varying external interference and performance constraint, so that the smooth completion of tracking tasks can be ensured, and meanwhile, the simulation result verifies the effectiveness and accuracy of a control algorithm, namely the realization of the designed full-state event trigger controller based on a second-order preset performance function, so that the signal trigger frequency in the track tracking process can be effectively reduced, namely the loss and communication cost of an actuator are reduced, and meanwhile, the accurate track tracking and performance constraint are realized. In addition, the proper control design parameters are selected so that all signals in the closed loop system are bounded, and the Zeno phenomenon triggered by the full state event is completely avoided.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.

Claims (5)

1. The dynamic event triggering-based dynamic positioning ship track tracking control method is characterized by comprising the following steps of:
step one: designing an integral interference observer according to a kinematic model and a dynamic model of the dynamic positioning ship:
Figure FDA0004271983430000011
wherein, xi 1 (t) and ζ 2 (t) integrating two state variables of the disturbance observer at time t respectively,
Figure FDA0004271983430000012
and->
Figure FDA0004271983430000013
Respectively is xi 1 (t) and ζ 2 First derivative of (t), l 1 And l 2 Is an integralTwo gain parameters of the disturbance observer are constants larger than 0, M is an inertia matrix of the dynamic positioning ship, and M is a constant of the dynamic positioning ship -1 Is the inverse matrix of M>
Figure FDA00042719834300000113
For the external environment interference estimated value generated by the t moment integral interference observer, τ (t) is the control input vector of the t moment dynamic positioning ship, x (t) is the t moment tracking error vector and x (t) = [ x ] 1 (t),x 2 (t),x 3 (t)] T ，H 1 Is an intermediate variable, t is the running time of the control system of the dynamic positioning ship,
x(t)＝γ 1 η e +υ e ，
Figure FDA0004271983430000014
γ 1 constant, eta, greater than 0 e To track the position error value, v e For tracking the speed error value, R is a conversion matrix between a north-east coordinate system and a ship body coordinate system, v is speed information of the power positioning ship, D is a damping coefficient matrix of the power positioning ship, and eta is a damping coefficient matrix of the power positioning ship d To track the position expectation value, v d In order to track the desired value of the velocity,
Figure FDA0004271983430000015
and->
Figure FDA0004271983430000016
Respectively eta d And v d Is the first derivative of (a);
step two: a tracking error constraint is applied in the tracking error vector x (t) at time t, said tracking error constraint being as follows:
Figure FDA0004271983430000017
wherein i=1, 2,3, - δ i And
Figure FDA0004271983430000018
p respectively i The lower bound of the coefficient of (t) and the upper bound of the coefficient, ρ i (t) is a performance function and satisfies the following formula:
Figure FDA0004271983430000019
Figure FDA00042719834300000110
Figure FDA00042719834300000111
and->
Figure FDA00042719834300000112
P respectively i First and second derivatives of (t), ω being a parameter adjusting the rate of change of the transient constrained boundary curve, ρ ∞i For ρ i A steady state value of (t), Y being a positive constant, sign (&) being a sign function;
step three: converting x (t) according to the tracking error constraint condition of x (t) to obtain a converted t moment tracking error s (t), and obtaining a first derivative of s (t):
Figure FDA0004271983430000021
wherein s (t) = [ s ] 1 (t),s 2 (t),s 3 (t)] T ，
Figure FDA0004271983430000022
And->
Figure FDA0004271983430000023
First derivatives of x (t) and ρ (t), respectively, ρ (t) = [ ρ ] 1 (t),ρ 2 (t),ρ 3 (t)] T ，θ(t)＝[θ 1 (t),θ 2 (t),θ 3 (t)] T ，μ(t)＝[μ 1 (t),μ 2 (t),μ 3 (t)] T ，
Figure FDA0004271983430000024
Step four: setting a measurement vector
Figure FDA0004271983430000025
Then the measurement vector error e at the time t is obtained according to the measurement vector 2 (t)：
Figure FDA0004271983430000026
Wherein delta is x ＝x(t k )-x(t)，Δ ν ＝υ(t k )-υ(t)，
Figure FDA0004271983430000027
Step five: constructing a full-state event trigger controller and event trigger conditions of a power positioning ship control system:
Figure FDA0004271983430000028
wherein t is k To trigger the occurrence time, t k+1 For triggering the next moment in time τ FETC (t) is a control signal output by the full-state event trigger controller, alpha and beta are both normal numbers,
Figure FDA0004271983430000029
k 2 ＝diag([5,5,1])，N p in order to be a performance safety assessment factor,
Y 1 ＝M(γ 1 R-M -1 D)，
Figure FDA00042719834300000210
Figure FDA00042719834300000211
l (t) is a dynamic threshold variable, lambda s And lambda (lambda) ξ The gain parameters are given, and Q is a positive definite symmetric matrix;
step six: and calculating and obtaining a control signal of the dynamic positioning ship by using the full-state event trigger controller, controlling the dynamic positioning ship to move, and completing the track tracking control of the dynamic positioning ship based on the dynamic event trigger.
2. The dynamic event triggering-based dynamic positioning ship track tracking control method as claimed in claim 1, wherein in the first step, a point O on the water surface is used E Establishing a north-east coordinate system X of motion of a dynamic positioning ship for an origin E Y E Z E Positioning the centre of gravity O of the ship by power B Establishing a hull coordinate system X of a dynamic positioning ship for an origin B Y B Z B According to the north-east coordinate system X E Y E Z E And a hull coordinate system X B Y B Z B A kinematic model and a dynamic model of the dynamic positioning ship are constructed,
the kinematic model expression of the dynamic positioning ship is as follows:
Figure FDA0004271983430000031
the dynamic model expression of the dynamic positioning ship is as follows:
Figure FDA0004271983430000032
in the above description, eta is the actual power positioning ship under the north-east coordinate systemThe position and the attitude angle of the device,
Figure FDA0004271983430000033
is the first derivative of eta, eta= [ n, e, phi ]] T N is a north position, e is an east position, ψ is a heading angle of the dynamic positioning ship, ++>
Figure FDA0004271983430000034
υ＝[u,v,r] T U is the longitudinal speed of the power positioning ship, v is the transverse speed of the power positioning ship, and r is the Z-winding speed of the power positioning ship B Angular velocity of shaft rotation, Z B The axis is the axis perpendicular to the plane of the hull in the hull coordinate system, τ w And tau is the control input vector of the dynamic positioning ship for the actual value of the external environment interference.
3. The dynamic event triggering-based dynamic positioning ship track tracking control method as set forth in claim 1, wherein in the third step:
Figure FDA0004271983430000035
4. the dynamic event triggering-based trajectory tracking control method of a dynamic positioning ship according to claim 1, wherein the measurement vector in the fourth step can be described by the following equation:
Figure FDA0004271983430000036
5. the dynamic event triggering-based dynamic positioning ship track tracking control method as claimed in claim 1, wherein in the fifth step, the first derivative of the dynamic threshold variable L (t)
Figure FDA0004271983430000041
The method comprises the following steps:
Figure FDA0004271983430000042
wherein alpha is l And beta l All are normal numbers.
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