CN110687794A - Nonlinear unbiased prediction control method of ship dynamic positioning system based on disturbance observer - Google Patents

Nonlinear unbiased prediction control method of ship dynamic positioning system based on disturbance observer Download PDF

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CN110687794A
CN110687794A CN201911064682.1A CN201911064682A CN110687794A CN 110687794 A CN110687794 A CN 110687794A CN 201911064682 A CN201911064682 A CN 201911064682A CN 110687794 A CN110687794 A CN 110687794A
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何燕
邓芳
杨化林
王龙金
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Qingdao University of Science and Technology
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Abstract

The invention provides a nonlinear unbiased prediction control method of a ship dynamic positioning system based on an interference observer. The method comprises the following steps: the method comprises the steps of considering low-frequency environment interference influence caused by wind, wave and flow, and establishing a dynamic positioning ship motion mathematical model; estimating unknown environmental interference based on interference observer to obtain interference estimation value
Figure DDA0002258961580000011
The feedback signal is used as a feedback signal to act on an outer loop control link, so that the influence of the feedback signal on a control object can be counteracted; defining an NMPC optimization problem based on a nominal model of a dynamic positioning system without interference, solving to obtain an optimal control input sequence in a control time domain, and enabling a first element of the sequence
Figure DDA0002258961580000012
Acting on the system to obtain control input at the current time

Description

Nonlinear unbiased prediction control method of ship dynamic positioning system based on disturbance observer
Technical Field
The invention relates to the field of ship dynamic positioning control, in particular to a nonlinear unbiased prediction control method of a ship dynamic positioning system based on an interference observer.
Background
The Dynamic Positioning (DP) system of a ship is a "system that automatically controls the course and position of a ship depending on its own propulsion system". Because the positioning cost of the dynamic positioning system is not increased along with the increase of water depth, the dynamic positioning system has strong adaptability to extremely deep sea areas and severe sea conditions and has strong positioning capability, the system is increasingly and widely used in offshore ship operations such as deep sea oil drilling, marine investigation, offshore supply/loading and unloading, submarine cable laying and the like, and becomes a key technology for deep sea development. The core of the dynamic positioning system is a control system consisting of a computer.
In the positioning and tracking process of the dynamic positioning ship, the dynamic positioning ship is often influenced by low-frequency interference caused by wind, second-order waves and currents, so that the ship deviates from a preset position, and a steady-state error occurs. Therefore, it is important to design a dynamic positioning unbiased control system.
The unbiased control means that the controlled variable is enabled to asymptotically track a set value through the action of a control system under the condition that external interference exists in a controlled system, so that the steady-state error of the system approaches zero. An unbiased control system is designed, which can be analyzed from two aspects. Firstly, the controlled variable is ensured to reach a set value, the steady-state error is eliminated, and the asymptotic unbiased tracking is realized. In addition, the anti-interference capability of the control system should be improved as much as possible to reduce the influence of disturbance on the system and realize robust control.
In recent years, more and more advanced control methods such as sliding mode control, neural network control and the like are used in the design of the dynamic positioning control system, and the control effect of the dynamic positioning system is improved to a certain extent. However, in practical application, the control force generated by the dynamic positioning thrust system is limited by the physical characteristics of the propeller, and has upper and lower limits. However, in the above control algorithm, the input constraint of the system cannot be considered explicitly, and the part beyond the limit in the control instruction is generally cut off in the form of a saturation nonlinear constraint.
Model Predictive Control (MPC), also known as rolling time domain Control, predicts future dynamics through a predefined prediction Model using a current state as an initial state, online solves a finite time domain open-loop optimization problem at each time step to obtain an optimal Control sequence in a Control time domain, and acts a first group in the sequence on a system. The MPC has the characteristics of low requirement on the model, capability of processing system constraint on line, strong robustness, good control effect and the like, so that the MPC becomes an advanced control technology which is widely applied to industrial processes after PID control.
With the continuous and deep research on the MPC, the MPC is researched and applied more and more in a dynamic positioning control system, but the application research on the MPC in a DP system in China is still more and more in a linear stage. However, the dynamic positioning system is a complex Nonlinear system, and a Model Predictive controller is designed by adopting a linear Model, so that the Control effect may be influenced, and a Nonlinear Model Predictive Control (NMPC) algorithm and application thereof need to be researched.
Based on the Control (DOBC) of a Disturbance Observer, the Observer is used as the inner ring of the Control system, model uncertainties such as unknown external Disturbance, model mismatch, model parameter perturbation, unmodeled dynamic state and the like are estimated by using Control input and output signals, and compensation is performed in an outer ring controller, so that the robustness of the closed-loop Control system is ensured. In the system, the external disturbance of the actual controlled object and the model mismatch between the actual controlled object and the nominal model are regarded as equivalent disturbance acting on the nominal model, the equivalent disturbance is estimated through a disturbance observer, the estimated value of the disturbance is compensated in a closed-loop system, the actual object is compensated to the nominal model, and the controller is only needed to be designed for the nominal model. DOBC is considered to be one of the most effective methods for implementing robust control, since it can well compensate for the effects of system model mismatch and external interference. Combining the advantages of DOBC and NMPC control, more and more research is beginning to focus on combining the two to achieve unbiased tracking control.
Disclosure of Invention
The invention aims to solve the problems and provides a nonlinear unbiased prediction control method of a ship dynamic positioning system based on an interference observer.
The purpose of the invention can be realized by the following technical scheme:
(1) the method comprises the steps of considering low-frequency environment interference influence caused by wind, wave and flow, and establishing a dynamic positioning ship motion mathematical model;
(2) estimating unknown environmental interference based on interference observer to obtain interference estimation value
Figure BDA0002258961560000021
The feedback signal is used as a feedback signal to act on an outer loop control link, so that the influence of the feedback signal on a control object can be counteracted;
(3) defining an NMPC optimization problem based on a nominal model of a dynamic positioning system without interference, solving to obtain an optimal control input sequence in a control time domain, and enabling a first element of the sequence
Figure BDA0002258961560000022
Acting on the system to obtain control input at the current time
The method comprises the following steps that (1) the low-frequency interference influence caused by wind, wave and flow environments is considered, and the established nonlinear motion mathematical model of the dynamic positioning system is as follows:
Figure BDA0002258961560000024
Figure BDA0002258961560000025
in the formula: eta ═ x, y, psi]TRepresenting the vessel position and heading vector, v ═ u, v, r]TRepresenting linear and angular velocity vectors, tau, of a vesselc＝[τ1,τ2,τ3]TRepresenting the vector of the control force, d ═ d1,d2,d3]TThe vector of the external environmental interference represents the influence of wind, wave, flow environmental interference, unmodeled dynamics and model mismatch.
Figure BDA0002258961560000026
Is an inertial matrix with an additional mass,
Figure BDA00022589615600000210
is a linear damping coefficient matrix, and R (psi) is a rotation matrix, defined as:
Figure BDA0002258961560000028
the disturbance d to the ship is due to the constantly changing marine environment and the limited energy provided by the wind, wave and current environmental forcesiThe variation in (i ═ 1,2,3) and interference is considered to be time-varying and finite, i.e. for some unknown normal epsilon, there are:
Figure BDA0002258961560000029
it is further assumed that all vessel state variables, including vessel position, heading, and speed, are measurable or accurately estimable.
Designing a disturbance observer to estimate the unknown environment disturbance, and rewriting a DP ship motion mathematical model into the following form:
Figure BDA0002258961560000031
Figure BDA0002258961560000032
in the formula: f. ofη(η,v)＝R(ψ)v，fv(v,u)＝M-1(-Dv+τc)，g1(η)＝M-1RT(ψ)。
Thus, a non-linear disturbance observer (NDO) of the time-varying disturbance d (t) can be designed as:
Figure BDA0002258961560000033
in the formula:
Figure BDA0002258961560000034
for the estimation of the disturbance d (t), p (t) is an auxiliary state variable of the disturbance observer, L0Is a positive fixed observer gain matrix. Will f isv(v, u) and g1(η) substituting to obtain DP system NDO as follows:
Figure BDA0002258961560000035
designing an NMPC controller, firstly considering a nominal system without interference, and writing a ship motion mathematical model into a state space form:
Figure BDA0002258961560000036
y＝Hx
in the formula:
Figure BDA0002258961560000037
in the form of a state vector, the state vector,
Figure BDA0002258961560000038
in order to control the input vector,
Figure BDA0002258961560000039
for the output vector, each matrix in the equation is defined as follows:
Figure BDA00022589615600000310
H＝[I3×303×3]
discretizing the continuous time model to obtain a discrete state space model of the DP system as follows:
xk+1＝f(xk,uk)＝Axk+Buk
yk＝Hxk
defining an NMPC rolling horizon optimization problem:
Figure BDA00022589615600000311
in the formula:
Figure BDA00022589615600000312
wy≥0，wu> 0 is the diagonal penalty matrix for the output and control inputs, rkFor reference to the input signal, NpTo predict the time domain, Nc＜NpTo control the time domain. The subscript k + i | k denotes the predicted state or input at a future time i, Uk＝[uk|k；uk+1|k；...；uk+N-1|k]The input sequence is controlled for the future in the time domain for time k.
Assuming that the control quantity is not changed outside the control time domain, i.e. when j equals Nc,Nc+1,…,N p1 hour uk+j|k＝uk+j-1|k. Solving the NMPC optimization problem to obtain an optimal control input sequence in a control time domain:
Figure BDA0002258961560000041
the first element of the sequence
Figure BDA0002258961560000042
Acting on the system and estimating the interference
Figure BDA0002258961560000043
Acting as a feedback signal in an outer loop control link, obtaining the control input of the current moment:
the invention considers the influence of external time-varying environment interference and input constraint, designs the nonlinear interference observer to estimate the unknown environment interference, and uses the interference estimation value as a feedback signal to act in an outer loop control link to directly offset the influence of the interference, thereby designing the NMPC optimal controller according to a nominal model without interference, enabling the system to track the set target without deviation, and improving the control precision of the dynamic positioning system and the robustness of the response to the interference.
Drawings
Fig. 1 is a control schematic diagram of the present invention.
Fig. 2 is a comparison graph of the actual and estimated disturbance values.
FIG. 3 is a ship output response curve.
Fig. 4 is a graph of the trajectory of the output berth in the horizontal plane.
Detailed Description
The invention is further described below with reference to the figures and examples.
A nonlinear unbiased prediction control method of a ship dynamic positioning system based on an interference observer is characterized in that the influence of external time-varying environment interference and input constraint are considered, the nonlinear interference observer is designed to estimate unknown environment interference, the interference estimation value is used as a feedback signal to act in an outer loop control link, and the influence of the interference is directly offset, so that an NMPC optimal controller is designed according to a nominal model without the interference, the system can track a set target in an unbiased mode, and the control precision of the dynamic positioning system and the robustness of interference response are improved.
As shown in FIG. 1, the method comprises the following steps:
(1) the method comprises the steps of considering low-frequency environment interference influence caused by wind, wave and flow, and establishing a dynamic positioning ship motion mathematical model;
(2) estimating unknown environmental interference based on interference observer to obtain interference estimation value
Figure BDA0002258961560000045
The feedback signal is used as a feedback signal to act on an outer loop control link, so that the influence of the feedback signal on a control object can be counteracted;
(3) defining an NMPC optimization problem based on a nominal model of a dynamic positioning system without interference, solving to obtain an optimal control input sequence in a control time domain, and enabling a first element of the sequence
Figure BDA0002258961560000046
Acting on the system to obtain control input at the current time
Figure BDA0002258961560000047
The method comprises the following steps that (1) the low-frequency interference influence caused by wind, wave and flow environments is considered, and the established nonlinear motion mathematical model of the dynamic positioning system is as follows:
Figure BDA0002258961560000051
Figure BDA0002258961560000052
in the formula: eta ═ x, y, psi]TRepresenting the vessel position and heading vector, v ═ u, v, r]TRepresenting linear and angular velocity vectors, tau, of a vesselc＝[τ1,τ2,τ3]TRepresenting the vector of the control force, d ═ d1,d2,d3]TThe vector of the external environmental interference represents the influence of wind, wave, flow environmental interference, unmodeled dynamics and model mismatch.
Figure BDA0002258961560000053
Is an inertial matrix with an additional mass,
Figure BDA00022589615600000516
is a linear damping coefficient matrix, and R (psi) is a rotation matrix, defined as:
Figure BDA0002258961560000055
the disturbance d to the ship is due to the constantly changing marine environment and the limited energy provided by the wind, wave and current environmental forcesi(i ═ 1,2,3) and the variation in interference is considered to be time-varying and finite, i.e. for some unknown normal number epsilon, there is：
Figure BDA0002258961560000056
It is further assumed that all vessel state variables, including vessel position, heading, and speed, are measurable or accurately estimable.
Designing a disturbance observer to estimate the unknown environment disturbance, and rewriting a DP ship motion mathematical model into the following form:
Figure BDA0002258961560000057
Figure BDA0002258961560000058
in the formula: f. ofη(η,v)＝R(ψ)v，fv(v,u)＝M-1(-Dv+τc)，g1(η)＝M-1RT(ψ)。
Thus, a non-linear disturbance observer (NDO) of the time-varying disturbance d (t) can be designed as:
Figure BDA0002258961560000059
in the formula:
Figure BDA00022589615600000510
for the estimation of the disturbance d (t), p (t) is an auxiliary state variable of the disturbance observer, L0Is a positive fixed observer gain matrix. Will f isv(v, u) and g1(η) substituting to obtain DP system NDO as follows:
Figure BDA00022589615600000511
designing an NMPC controller, firstly considering a nominal system without interference, and writing a ship motion mathematical model into a state space form:
Figure BDA00022589615600000512
y＝Hx
in the formula:
Figure BDA00022589615600000513
in the form of a state vector, the state vector,
Figure BDA00022589615600000514
in order to control the input vector,
Figure BDA00022589615600000515
for the output vector, each matrix in the equation is defined as follows:
Figure BDA0002258961560000061
H＝[I3×303×3]
discretizing the continuous time model to obtain a discrete state space model of the DP system as follows:
xk+1＝f(xk,uk)＝Axk+Buk
yk＝Hxk
defining an NMPC rolling horizon optimization problem:
Figure BDA0002258961560000062
in the formula:
Figure BDA0002258961560000063
wy≥0，wu> 0 is the diagonal penalty matrix for the output and control inputs, rkFor reference to the input signal, NpTo predict the time domain, Nc＜NpTo control the time domain. The subscript k + i | k denotes the predicted state or input at a future time i, Uk＝[uk|k；uk+1|k；...；uk+N-1|k]The input sequence is controlled for the future in the time domain for time k.
Assuming that the control quantity is not changed outside the control time domain, i.e. when j equals Nc,Nc+1,…,N p1 hour uk+j|k＝uk+j-1|k. Solving the NMPC optimization problem to obtain an optimal control input sequence in a control time domain:
Figure BDA0002258961560000064
the first element of the sequence
Figure BDA0002258961560000065
Acting on the system and estimating the interferenceActing as a feedback signal in an outer loop control link, obtaining the control input of the current moment:
the following examples are provided to illustrate and explain the present invention, and it should be understood that the examples described herein are only for the purpose of illustration and explanation and are not intended to limit the present invention.
Fig. 1 is a control schematic diagram of a nonlinear unbiased prediction control method of a ship dynamic positioning system based on a disturbance observer according to the present invention.
A CyberShip II (CSII) ship model in a Marine System Simulation (MSS) toolbox of a Marine control laboratory of Norwegian science and technology university is taken as a Simulation object, the CSII is a 1:70 proportion ship model of a certain Marine supply ship, and an inertia matrix and a damping matrix of the ship are respectively as follows:
Figure BDA0002258961560000068
establishing a simulation model by Matlab \ Simulink, setting the simulation time to be 500s, and setting the initial ship position of the ship to be eta0＝[0m,0m,0°]TThe control aim being to make the vessel follow the reference railThe trace r reaches the desired ship position etad＝[1m,0.5m,20°]TThe reference inputs are set to:
a first order Markov interference model was used, namely:wherein T isdD is an initial value of interference, 1 ═ diag {10,10,10}, q ═ diag (0.25,0.25,0.1)0＝[0N,0N,0N.m]T。
The MPC optimal regulator penalty matrix is set to: w is ay＝diag{100,100,100}，wuCorresponding to the control time domain N, 1,1cPredicting time domain N10pThe sampling time is set to 0.1s, 100. Gain matrix L of nonlinear disturbance observer0With respect to diag {1,1,1}, the initial state of the ship is x0＝[0m,0m,0deg,0m/s,0m/s,0°deg/s]T。
Fig. 2 to 4 are graphs of simulation results. Wherein fig. 2 shows the actual interference value d ═ d1,d2,d3]TAnd its estimated value
Figure BDA0002258961560000073
The comparison curve shows that the designed nonlinear disturbance observer can accurately estimate the disturbance of the external environment. Fig. 3 is an output response curve of a ship, wherein NDO-NMPC represents an inventive non-linear Disturbance Observer based NMPC method (Nonlinear Disturbance Observer-based NMPC), and fig. 4 is an output berth trajectory curve of the ship in a horizontal plane. As can be seen from fig. 3 and 4, under the condition of external environmental interference, the ship position can be set by the method provided by the invention by gradual unbiased tracking, so that the method has a good control effect and the system has strong stability and robustness.

Claims (3)

1. The invention provides a nonlinear unbiased prediction control method of a ship dynamic positioning system based on an interference observer, which is characterized by comprising the following steps of:
(1) the method comprises the steps of considering low-frequency environment interference influence caused by wind, wave and flow, and establishing a dynamic positioning ship motion mathematical model;
(2) estimating unknown environmental interference based on interference observer to obtain interference estimation value
Figure FDA0002258961550000011
The feedback signal is used as a feedback signal to act on an outer loop control link, so that the influence of the feedback signal on a control object can be counteracted;
(3) defining an NMPC optimization problem based on a nominal model of a dynamic positioning system without interference, solving to obtain an optimal control input sequence in a control time domain, and enabling a first element of the sequence
Figure FDA0002258961550000012
Acting on the system to obtain control input at the current time
Figure FDA0002258961550000013
2. The nonlinear unbiased prediction control method of a vessel dynamic positioning system based on a disturbance observer according to claim 1, characterized in that, according to a vessel motion mathematical model, the nonlinear disturbance observer is designed as follows:
Figure FDA0002258961550000014
in the formula: in the formula:
Figure FDA0002258961550000015
for the estimation of the disturbance d (t), p (t) is an auxiliary state variable of the disturbance observer, L0Is a positive fixed observer gain matrix.
3. The method of claim 1, wherein an NMPC optimization problem is defined as follows:
Figure FDA0002258961550000016
s.t.xk+j|k＝f(xk+j-1|k,uk+j-1|k),j＝1,2,...,Np
yk+j|k＝Hxk+j|k,j＝1,2,...,Np
umin≤uk+j|k≤umax,j＝0,1,...,Nc-1
Figure FDA0002258961550000017
in the formula:wy≥0，wu> 0 is the diagonal penalty matrix for the output and control inputs, rkFor reference to the input signal, NpTo predict the time domain, Nc＜NpTo control the time domain. The subscript k + i | k denotes the predicted state or input at a future time i, Uk＝[uk|k；uk+1|k；...；uk+N-1|k]The input sequence is controlled for the future in the time domain for time k.
Assuming that the control quantity is not changed outside the control time domain, i.e. when j equals Nc,Nc+1,…,Np1 hour uk+j|k＝uk+j-1|k. Solving the NMPC optimization problem to obtain an optimal control input sequence in a control time domain:
Figure FDA0002258961550000019
the first element of the sequence
Figure FDA00022589615500000110
Acting on the system and estimating the interferenceActing as a feedback signal in an outer loop control link, obtaining the control input of the current moment:
Figure FDA00022589615500000112
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CN113296499A (en) * 2021-04-15 2021-08-24 哈尔滨工程大学 FPSO (Floating production storage and offloading) anchoring dynamic positioning control method for optimal heading polar region based on acceleration feedforward
CN113296499B (en) * 2021-04-15 2022-10-28 哈尔滨工程大学 Optimal polar region FPSO (Floating production storage and offloading) anchoring dynamic positioning control method based on acceleration feedforward
CN116819950A (en) * 2023-08-25 2023-09-29 中国海洋大学 Ship and floating ocean platform dynamic positioning control method and system
CN116819950B (en) * 2023-08-25 2023-11-07 中国海洋大学 Ship and floating ocean platform dynamic positioning control method and system

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