CN110687793A - Input increment-based nonlinear unbiased prediction control method for ship dynamic positioning system - Google Patents

Input increment-based nonlinear unbiased prediction control method for ship dynamic positioning system Download PDF

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CN110687793A
CN110687793A CN201911064678.5A CN201911064678A CN110687793A CN 110687793 A CN110687793 A CN 110687793A CN 201911064678 A CN201911064678 A CN 201911064678A CN 110687793 A CN110687793 A CN 110687793A
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邓芳
何燕
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 input increment. The method comprises the following steps: establishing a state space model of the dynamic positioning system and carrying out discretization treatment to obtain a discrete time model of the dynamic positioning system by considering low-frequency environment interference influence caused by wind, wave and flow; taking the input increment as a state variable, taking the control input as an extended state, establishing an extended state observation model containing the input increment, and estimating an unknown state and the control input by adopting an unscented Kalman filtering algorithm; and defining an unbiased NMPC optimization problem with input constraint based on a nominal model of the dynamic positioning system without interference, solving to obtain an optimal control input increment sequence in a control time domain, and acting a first element of the sequence on the system to obtain the control input at the current moment. The method can enable the dynamic positioning ship interfered by the environment to set the ship position or the air route in an unbiased tracking way, and improve the control precision and the robustness of the dynamic positioning system.

Description

Input increment-based nonlinear unbiased prediction control method for ship dynamic positioning system
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 input increment.
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.
Therefore, the influence of low-frequency environment interference caused by wind, second-order waves and flow needs to be considered, under the control force saturation constraint, a nonlinear model predictive control algorithm capable of tracking and setting a ship position or a ship route in an unbiased mode is researched, and the control accuracy and robustness of the dynamic positioning system are improved.
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 input increment.
The purpose of the invention can be realized by the following technical scheme:
(1) considering the low-frequency environment interference influence caused by wind, wave and flow, establishing a dynamic positioning system state space model and carrying out discretization treatment to obtain a discrete time model;
(2) taking the input increment as a state variable, taking the control input as an extended state, establishing an extended state observation model containing the input increment, and estimating an unknown state and the control input by adopting an Unscented Kalman Filtering (UKF) algorithm;
(3) defining an unbiased NMPC optimization problem with input constraint based on a nominal model of a dynamic positioning system without interference, solving to obtain an optimal control input increment sequence in a control time domain, and carrying out a first element of the sequence
Figure BDA0002258958950000021
Acting on the system to obtain control of the current timeInput device
Figure BDA0002258958950000022
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 discrete time state space model of the dynamic positioning system is as follows:
xk+1＝Axk+Buk+Edk+Gwk
yk＝Hxk+υk
in the formula: the index k indicates the current time step,
Figure BDA0002258958950000023
in the form of a state vector, the state vector,
Figure BDA0002258958950000024
in order to control the vector, the vector is controlled,
Figure BDA0002258958950000025
in order to measure the vector, the vector is measured,
Figure BDA0002258958950000026
in order to be a vector of the process noise,to measure the noise vector, wkAnd upsilonkAre all white gaussian noise with zero mean value,
Figure BDA0002258958950000028
the vector is an external environmental interference vector and represents the influence of wind, wave and flow environmental interference, unmodeled dynamics and model mismatch, and A, B, E, G and H are corresponding matrixes.
And (2) taking the input increment as a state variable, taking the control input as an extended state, and establishing an extended state observation model containing the input increment as follows:
Figure BDA0002258958950000029
Figure BDA00022589589500000210
estimating state and control input based on unscented Kalman filtering UKF algorithm:
in the formula:
Figure BDA00022589589500000212
the filter gain matrix for the corresponding state and control inputs is determined by the UKF algorithm.
Step (3) based on the non-interference nonlinear discrete time nominal model:
xk+1＝f(xk,uk)＝Axk+Buk
yk＝Hxk
defining an NMPC rolling horizon optimization problem:
in the formula:
Figure BDA0002258958950000032
wy≥0，wΔu> 0 is the diagonal penalty matrix for the output and input deltas, respectively, 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, Δ U, at a future time i from the current time kk＝[Δuk|k；Δuk+1|k；...；Δuk+N-1|k]A sequence of increments is input for future control in the control time domain at time k.
Assuming that the control quantity is not changed outside the control time domain, i.e. when j equals Nc,Nc+1,…,NpTime-1. delta. uk+j|k0. Solving the NMPC optimization problem to obtain the optimal control in the control time domainInputting a sequence:
the first element of the sequence
Figure BDA0002258958950000034
Acting on the system, namely obtaining the control input of the current moment:
Figure BDA0002258958950000035
the invention considers the external time-varying environmental interference influence and input constraint, takes the control input as an expansion state, establishes an expansion state observation model containing input increment, and estimates the unknown state and the control input based on the UKF algorithm, thereby designing the NMPC optimal controller, 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 interference response.
Drawings
Fig. 1 is a control schematic diagram of the present invention.
Fig. 2 is a ship output response curve.
Fig. 3 is a plot of the trajectory of the outgoing boat position in the horizontal plane.
Detailed Description
The invention is further described below with reference to the figures and examples.
A ship dynamic positioning system nonlinear unbiased prediction control method based on input increment is characterized in that control input is used as an expansion state, an expansion state observation model containing the input increment is established, and an unknown state and the control input are estimated based on a UKF algorithm, so that an NMPC optimal controller is designed, a 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) considering the low-frequency environment interference influence caused by wind, wave and flow, establishing a dynamic positioning system state space model and carrying out discretization treatment to obtain a discrete time model;
(2) taking the input increment as a state variable, taking the control input as an extended state, establishing an extended state observation model containing the input increment, and estimating an unknown state and the control input by adopting a UKF algorithm;
(3) defining an unbiased NMPC optimization problem with input constraint based on a nominal model of a dynamic positioning system without interference, solving to obtain an optimal control input increment sequence in a control time domain, and carrying out a first element of the sequence
Figure BDA0002258958950000041
Acting on the system to obtain control input at the current time
Figure BDA0002258958950000042
Firstly, considering the low-frequency interference influence caused by wind, wave and flow environments, establishing a continuous time ship nonlinear motion state space model:
Figure BDA0002258958950000043
y＝Hx+υ
in the formula:
Figure BDA0002258958950000044
is a state vector, η ═ x, y, ψ]TFor the low-frequency motion vector of the ship, v ═ u, v, r]TAs are the vessel velocity and the angular velocity vector,
Figure BDA0002258958950000045
in order to control the vector, the vector is controlled,
Figure BDA0002258958950000046
in order to measure the vector, the vector is measured,
Figure BDA0002258958950000047
in order to be a vector of the process noise,
Figure BDA0002258958950000048
to measure the noise vector, w and υ are zero-mean gaussian white noise. 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.
Wherein each matrix is defined as follows:
Figure BDA0002258958950000049
H＝[I3×303×3]
in the formula:
Figure BDA00022589589500000410
is an inertial matrix with an additional mass,
Figure BDA00022589589500000411
is a linear damping coefficient matrix, and R (psi) is a rotation matrix, defined as:
Figure BDA00022589589500000412
under the influence of marine environmental changes, environmental disturbances are usually slowly changing, and in the simulation process of the DP control system, d is usually expressed as a first-order Markov process:
Figure BDA00022589589500000413
in the formula: t isd＝diag{Td1,Td2,Td3The time constant is the self-defined time,
Figure BDA00022589589500000414
is a zero-mean gaussian white noise vector,
Figure BDA00022589589500000415
a diagonal scale factor matrix of ξ.
Discretizing the continuous time model to obtain a discrete state space model of the DP system as follows:
xk+1＝Axk+Buk+Edk+Gwk
yk＝Hxk+υk
and (2) considering a DP system state observation model without external interference:
xk+1＝Axk+Buk+Gwk
yk＝Hxk+υk
replacing the control input with the input increment, and taking the control input as an extended state to obtain an extended state model containing the input increment:
Figure BDA0002258958950000051
Figure BDA0002258958950000052
estimating state and control inputs based on the UKF algorithm:
Figure BDA0002258958950000053
in the formula:
Figure BDA0002258958950000054
the filter gain matrix for the corresponding state and control inputs is determined by the UKF method.
The UKF filtering algorithm is as follows:
the extended state observation model is first written as the following general form:
Figure BDA0002258958950000055
yk＝h(χk)+υk
in the formula: chi shapekFor an n-dimensional extended state vector, fχ(. cndot.) is an extended process model, h (. cndot.) is an extended measurement model,
Figure BDA0002258958950000056
and upsilonkThe covariance matrices corresponding to the zero-mean white gaussian noise process and the measurement noise are Q and R, respectively. And:
Figure BDA0002258958950000057
fχ(χk,uk)＝Auχk+BuΔuk，h(χk)＝Huχk，G＝Gu，
Figure BDA0002258958950000058
i.e. the process noise covariance matrix Q ═ Qw。
Based on UKF algorithm, for a given state mean
Figure BDA0002258958950000059
And its variance initial value P02n +1 sigma points will be generated around the mean, represented by the matrix:
Figure BDA00022589589500000510
and (3) carrying out unscented transformation on each sigma point by using a process and a measurement model of the system to obtain:
Figure BDA00022589589500000512
therefore, based on the Kalman filtering basic principle, the predicted value of the state mean value and the variance thereof can be calculated
Figure BDA00022589589500000513
And Pk|k-1And a measurement vectorInnovation covariance prediction
Figure BDA00022589589500000515
And state-measurement vector cross covariance prediction
Figure BDA00022589589500000516
And finally, obtaining the state and variance estimation value of the current moment:
Figure BDA00022589589500000517
Figure BDA0002258958950000061
in the formula: kkFor the UKF filter gain matrix, it is calculated by:
Figure BDA0002258958950000062
step (3) based on the non-interference nonlinear discrete time nominal model:
xk+1＝f(xk,uk)＝Axk+Buk
yk＝Hxk
defining an NMPC rolling horizon optimization problem based on state and control input estimates:
Figure BDA0002258958950000063
in the formula:wy≥0，wΔu> 0 is the diagonal penalty matrix for the output and input deltas, respectively, rkFor reference to the input signal, NpTo predict the time domain, Nc＜NpTo control the time domain, usDerived from the input increment. The subscript k + i | k denotes the predicted state or input, Δ U, at a future time i from the current time kk＝[Δuk|k；Δuk+1|k；...；Δuk+N-1|k]A sequence of increments is input for future control in the control time domain at 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|kI.e. Δ u k+j|k0. Solving the NMPC optimization problem to obtain an optimal control input increment sequence in a control time domain:
the first element of the sequence
Figure BDA0002258958950000066
Acting on the system, namely 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 shows a control schematic diagram of a nonlinear unbiased prediction control method of a ship dynamic positioning system based on input increment.
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 BDA0002258958950000068
establishment by Matlab \ SimulinkThe simulation time of the simulation model is set to 500s, and the initial ship position of the ship is set to eta0＝[0m,0m,0°]TThe control objective is to make the ship reach the expected ship position eta along the reference track rd＝[1m,0.5m,20°]TThe reference inputs are set to:
Figure BDA0002258958950000071
a first order Markov interference model was used, namely:
Figure BDA0002258958950000072
wherein T isdD is an initial value of interference, d, and 1 is set as diag {10,10,10}, and Ω is set as diag {0.2,0.2,0.05}0＝[0N,0N,0N.m]T。
Setting parameters: the UKF filter parameters are set to Q ═ diag {10,10,10}, and R ═ diag {1,1,1 }. The MPC optimal regulator penalty matrix is set to: w is ay＝diag{100,100,1}，wΔuCorresponding to the control time domain N, 1,1cPredicting time domain N10pThe sampling time is set to 0.1s, 100.
Fig. 2 and 3 are graphs of simulation results. Wherein, fig. 2 is an output response curve of the ship, and fig. 3 is an output berth track curve of the ship in a horizontal plane. As can be seen from fig. 2 and 3, 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 (4)

1. The invention provides a nonlinear unbiased prediction control method of a ship dynamic positioning system based on input increment, which is characterized by comprising the following steps of:
(1) establishing a state space model of the dynamic positioning system and carrying out discretization treatment to obtain a discrete time model of the dynamic positioning system by considering low-frequency environment interference influence caused by wind, wave and flow;
(2) taking the input increment as a state variable, taking the control input as an extended state, establishing an extended state observation model containing the input increment, and estimating an unknown state and the control input by adopting a UKF algorithm;
(3) defining an unbiased NMPC optimization problem with input constraint 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 solving a first element of the sequence
Figure FDA0002258958940000011
Acting on the system to obtain control input at the current time
Figure FDA0002258958940000012
2. The nonlinear unbiased predictive control method of a vessel dynamic positioning system based on input increments as recited in claim 1, characterized in that the control input is replaced by the input increments, the control input is taken as an extended state, and an extended state model containing the input increments is established as follows:
Figure FDA0002258958940000013
in the formula: the index k indicates the current time step,
Figure FDA0002258958940000014
in the form of a state vector, the state vector,
Figure FDA0002258958940000015
in order to control the input vector,
Figure FDA0002258958940000016
in order to input the increment vector, the increment vector is input,
Figure FDA0002258958940000017
in order to measure the vector, the vector is measured,
Figure FDA0002258958940000018
in order to be a vector of the process noise,
Figure FDA0002258958940000019
to measure the noise vector, wkAnd upsilonkAll are zero mean white Gaussian noise, and A, B, G and H are corresponding matrixes.
3. The nonlinear unbiased predictive control method for a vessel dynamic positioning system based on input increments as recited in claim 1, characterized by estimating the state and disturbance using the UKF algorithm:
Figure FDA00022589589400000110
in the formula:
Figure FDA00022589589400000111
the filter gain matrix for the corresponding state and control inputs is determined by the UKF method.
4. The method of claim 1, wherein the NMPC optimization problem is defined as follows:
Figure FDA00022589589400000112
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
in the formula: in the formula:wy≥0，wΔu> 0 are the diagonal penalty matrices for the output and input deltas, respectively. N is a radical ofpTo predict the time domain, Nc＜NpTo control the time domain, usDerived from the input increment. The subscript k + i | k denotes the predicted state or input, Δ U, at a future time i from the current time kk＝[Δuk|k；Δuk+1|k；...；Δuk+N-1|k]A sequence of increments is input for future control in the control time domain at 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|kI.e. Δ uk+j|k0. Solving the NMPC optimization problem to obtain an optimal control input increment sequence in a control time domain:
Figure FDA0002258958940000021
the first element of the sequence
Figure FDA0002258958940000022
Acting on the system, namely obtaining the control input of the current moment:
Figure FDA0002258958940000023
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