CN113110519A - Non-incremental model-free adaptive heading control method for ships - Google Patents

Non-incremental model-free adaptive heading control method for ships Download PDF

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CN113110519A
CN113110519A CN202110578219.XA CN202110578219A CN113110519A CN 113110519 A CN113110519 A CN 113110519A CN 202110578219 A CN202110578219 A CN 202110578219A CN 113110519 A CN113110519 A CN 113110519A
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廖煜雷
裴华仁
杜廷朋
王博
贾琪
谷秋实
李晔
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Harbin Engineering University
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Abstract

A non-incremental model-free adaptive heading control method for ships relates to the technical field of automatic motion control of ships. The invention aims to solve the problem that when the MFAC is directly applied to a non-self-balancing system, the stability of the system is reduced. The invention introduces an input-output coupling self-adaptive compensation term on the basis of the original MFAC criterion function, thereby redesigning the control law, offsetting the integral influence of the controlled system and enabling the improved algorithm to be applied to non-self-balance systems such as ship heading control and the like. Meanwhile, related coefficient terms introduced into the control law are used for self-adaptively adjusting the weight ratio of the coefficient terms in the control law, so that the capacity of the system for resisting external large disturbance interference and model mutation is improved. And, the weight coefficient k of the adaptive compensation termrThe introduction of (2) also increases the algorithm adjustability flexibility.

Description

Non-incremental model-free adaptive heading control method for ships
Technical Field
The invention belongs to the technical field of automatic motion control of ships.
Background
Good heading control is one of the necessary conditions for ships to complete various tasks, but because the movement of the ships generally has the characteristics of underactuation, large time lag and the like, and is easily interfered by wind, wave and flow and the like in navigation, and the great change of self hydrodynamic characteristics when the tasks are executed, the conventional movement control strategy taking a mathematical model as a guide is not applicable.
Model-Free Adaptive Control (MFAC) is a method for performing Control by using only dynamic input/output (I/O) data of a system, without depending on a mathematical Model of a controlled object. However, the ship heading control belongs to a non-self-balancing system and comprises an integral link which can reduce the stability of the system, and the specific expression is that the output of a controlled object cannot reach a stable state but is infinitely increased or reduced under the action of step input.
Disclosure of Invention
The invention provides a non-incremental model-free adaptive heading control method for ships and warships, aiming at solving the problem that the stability of a system is reduced when MFAC is directly applied to a non-self-balanced system.
A non-incremental model-free adaptive heading control method for ships comprises the following steps:
the method comprises the following steps: introducing an input-output coupling adaptive compensation term into a model-free adaptive control input resolving rule function of the ship control system to obtain a non-incremental control input resolving rule function;
step two: substituting the dynamic linearized data model into a non-incremental control input resolving rule function to enable the derivative of input information u (k) to be equal to 0, and obtaining a non-incremental model-free self-adaptive control law;
step three: estimating an estimated value of a dynamic linearized data model parameter phi (k) at the moment k according to historical input and output information of a ship control system
Figure BDA0003085084610000011
Step four: according to the estimated value obtained in the third step
Figure BDA0003085084610000012
And calculating input information u (k) of the ship control system at the moment k according to the non-incremental model-free adaptive control law obtained in the step two, and executing the input information u (k) by the ship control system to obtain output information y (k +1) of the ship at the moment k + 1.
Further, after the second step, a judging step is further included, where the judging step is:
obtaining a heading deviation e (k) at the time k by differentiating an expected heading angle y (k) of the ship at the time k with a heading angle y (k),
and (e), (k) judging whether the deviation is smaller than a preset deviation threshold value, if so, ending the control on the ship, and if not, executing the step three.
Further, after the fourth step, k is made k +1, and the process returns to the determination step.
Further, in the first step, the non-incremental control input calculation criterion function is recorded as J [ · [ ]]The input of the function is u (k), krΔ y (k +1) · u (k-1) is an input-output coupling adaptive compensation term, and then:
J[u(k)]＝[y*(k+1)-y(k+1)]2+λ[u(k)-u(k-1)]2+krΔy(k+1)·u(k-1)，
wherein u (k) and y (k) are respectively a rudder angle and a heading angle at the time k and are respectively used as input information and output information of the ship control system, Δ y (k +1) ═ y (k +1) -y (k), y ═ k +1) is an expected heading angle at the time k +1, λ is a step factor of u (k), and k (k) is a step factor of k (k)rThe weight coefficients of the adaptive compensation term are coupled for input and output.
Further, in the second step, the expression of the dynamic linearized data model is as follows:
y(k+1)＝y(k)+ΦT(k)ΔH(k)，
wherein phiT(k)＝[φy,φu]Is a transposition of phi (k), phiyAnd phiuModel parameters for the heading angle and rudder angle at time k, respectively, [ Δ h (k) ═ Δ y (k), Δ u (k)]T，Δu(k)＝u(k) U (k-1), Δ y (k) y (k-1), u (k) and y (k) are respectively the rudder angle and the heading angle at time k, and are respectively input information and output information.
Further, in the second step, the expression of the non-incremental model-free adaptive control law is as follows:
Figure BDA0003085084610000021
wherein the content of the first and second substances,
Figure BDA0003085084610000022
and
Figure BDA0003085084610000023
are respectively phiuAnd phiyλ is the step size factor of u (k), krWeight coefficient, y, for input-output coupling of adaptive compensation terms*(k +1) is the desired heading angle, ρ, at time k +11Step-size factor, p, for the desired output deviation2Is a step factor of the actual output deviation.
Further, in the third step, the historical input and output information of the ship control system includes: input information u (k-1) at time k-1, output information y (k-1) at time k-1, input information u (k-2) at time k-2, output information y (k-2) at time k-2, and estimated values of dynamic linearized data model parameters at time k-1
Figure BDA0003085084610000024
Further, in the third step, the estimated value of the dynamic linearized data model parameter Φ (k) at time k is estimated according to the following formula
Figure BDA0003085084610000025
Figure BDA0003085084610000026
Wherein eta belongs to (0, 1) as a penalty factor, mu is a weight coefficient for limiting the change of the model parameter,
ΔH(k-1)＝[Δy(k-1),Δu(k-1)]T，
Δu(k-1)＝u(k-1)-u(k-2)，
Δy(k-1)＝y(k-1)-y(k-2)。
further, the estimated value obtained in the third step
Figure BDA0003085084610000031
And substituting the non-incremental model-free self-adaptive control law obtained in the step two to obtain the input information of the ship control system at the moment k.
The invention provides a non-incremental model-free adaptive heading control method for ships, which introduces an input-output coupling adaptive compensation term on the basis of an original MFAC (Mel frequency transfer coefficient) criterion function, further redesigns a control law, offsets integral influence of a controlled system, and enables an improved algorithm to be applied to non-self-balanced systems such as ship heading control and the like. And meanwhile, a coefficient term related to u (k-1) is introduced into the control law, and the weight ratio of the coefficient term in the control law is self-adaptively adjusted, so that the capacity of the system for resisting external large disturbance interference and model mutation is improved. And, the weight coefficient k of the adaptive compensation termrThe introduction of (2) also increases the algorithm adjustability flexibility.
Drawings
Fig. 1 is a flowchart of a non-incremental model-free adaptive heading control method for a ship according to an embodiment;
fig. 2 is a schematic diagram of a non-incremental model-free adaptive heading control method for ships according to an embodiment.
Detailed Description
The patent document with the publication date of 10 and 4 in 2020 and the application patent number of CN112034858A named as 'a model-free adaptive heading control method for fusing weak observation high-order output data' provides an improved MFAC method, and introduces a first-order difference term into a control law by improving a control input criterion function
Figure BDA0003085084610000032
And second order difference term
Figure BDA0003085084610000033
The reset heading control law accelerates the on-line identification, learning and control process of the controller, and solves the problems of oscillation and divergence when the MFAC is directly applied to the control of the non-self-balancing system.
The publication date is 5 and 17 in 2019, the application patent number is 201910163383.7, and the patent document named as PID model-free adaptive course control algorithm for ships applies adaptive proportion terms
Figure BDA0003085084610000034
And adaptive differential term
Figure BDA0003085084610000041
Introducing a control law of MFAC, providing a PID-MFAC algorithm, solving the problems of serious overshoot, oscillation and even instability when the MFAC algorithm is directly applied to the heading control of a ship.
The patent document with the publication date of 12 and 4 in 2020 and the application patent number of 202010863628.X named as 'improved method for model-free adaptive control' introduces a proportional control term beta K [ y ] aiming at the problems of slow response and oscillation phenomenon of the original control law*(k+1)-y(k)]-βK[y*(k)-y(k-1)](ii) a And an anti-saturation algorithm is introduced into the original MFAC controller part, so that the system control precision is improved.
The three patent documents aiming at the improvement of the MFAC make up the defects of variable integral control structures such as the MFAC by introducing a proportional term, an adaptive proportional term or an adaptive differential term related to the control output y (-) from the perspective of the control output y (-) and solve the oscillation problem when the MFAC is directly applied to non-self-balanced systems such as ship heading control.
In the embodiment, from the angle of the control input u (·), an adaptive compensation term is introduced to adaptively adjust the weight of the system input u (k-1) in the control law at the previous moment, so that the stable control of the non-self-balanced system is realized. The method comprises the following specific steps:
the first embodiment is as follows: the embodiment is specifically described with reference to fig. 1 and fig. 2, and the non-incremental model-free adaptive heading control method for ships in the embodiment includes the following steps:
the method comprises the following steps: and introducing an input-output coupling adaptive compensation term into a model-free adaptive control input calculation criterion function of the ship control system to obtain a non-incremental control input calculation criterion function.
Specifically, the non-incremental control input solver criterion function is denoted as J [ ·]The input of the function is u (k), krΔ y (k +1) · u (k-1) is an input-output coupling adaptive compensation term, and then:
J[u(k)]＝[y*(k+1)-y(k+1)]2+λ[u(k)-u(k-1)]2+krΔy(k+1)·u(k-1)，
wherein u (k) and y (k) are respectively a rudder angle and a heading angle at the time k and are respectively used as input information and output information of the ship control system, and delta y (k +1) ═ y (k +1) -y (k), and y*(k +1) is the desired heading angle at time k +1, λ is the step size factor of u (k), krThe weight coefficients of the adaptive compensation term are coupled for input and output.
Step two: the expression for the dynamic linearized data model is as follows:
y(k+1)＝y(k)+ΦT(k)ΔH(k)，
wherein phiT(k)＝[φy,φu]Is a transposition of phi (k), phiyAnd phiuModel parameters for y (k) and u (k), respectively, [ Δ h (k) ═ Δ y (k), Δ u (k)]，Δu(k)＝u(k)-u(k-1)，Δy(k)＝y(k)-y(k-1)。
Substituting the dynamic linearized data model into a non-incremental control input resolving rule function to enable the derivative of input information u (k) to be equal to 0, and then obtaining a non-incremental model-free adaptive control law:
Figure BDA0003085084610000051
wherein the content of the first and second substances,
Figure BDA0003085084610000052
and
Figure BDA0003085084610000053
are respectively phiuAnd phiyEstimate of (c), p1Step-size factor, p, for the desired output deviation2Is a step factor of the actual output deviation.
Step three: the expected heading angle y of the ship at the moment k*(k) Obtaining a heading deviation e (k) at the time k (k) by taking the difference with the heading angle y (k)*(k) -y (k) determining whether e (k) is less than a predetermined deviation threshold e1If yes, ending the control of the ship, otherwise, executing the step four.
Step four: selecting input and output information of the ship control system at the first two moments, namely: input information u (k-1) at time k-1, output information y (k-1) at time k-1, input information u (k-2) at time k-2, output information y (k-2) at time k-2, and estimated values of dynamic linearized data model parameters at time k-1
Figure BDA0003085084610000054
Estimating an estimated value of a dynamic linearized data model parameter phi (k) at time k according to the following formula
Figure BDA0003085084610000055
Figure BDA0003085084610000056
Wherein eta belongs to (0, 1) as a penalty factor, mu is a weight coefficient for limiting the change of the model parameter,
ΔH(k-1)＝[Δy(k-1),Δu(k-1)]，
Δu(k-1)＝u(k-1)-u(k-2)，
Δy(k-1)＝y(k-1)-y(k-2)。
when in use
Figure BDA0003085084610000057
Or
Figure BDA0003085084610000058
When the temperature of the water is higher than the set temperature,
Figure BDA0003085084610000059
k is 1, i.e. the initial time. Wherein sign [ ·]Denotes a sign function, and ε is a very small positive number, and has a value of 10 in this embodiment-3。
Step five: the estimated value obtained in the fourth step
Figure BDA00030850846100000510
Substituting the non-incremental model-free self-adaptive control law obtained in the step two, calculating input information u (k) of the ship control system at the moment k, controlling the ship by using u (k), executing instructions by the ship control system, changing the heading to obtain output information y (k +1) at the moment k +1 of the ship, then enabling k to be k +1, and returning to the step three.
The embodiment introduces the input-output coupling adaptive compensation item in the model-free adaptive control input resolving rule function, solves the problem that the MFAC method cannot be directly applied to the non-self-balance system such as ship heading control, and avoids output oscillation. Meanwhile, the coefficient term about u (k-1) introduced in the control law in the embodiment self-adaptively adjusts the weight ratio of the coefficient term in the control law, so that the capacity of resisting external large disturbance of the system is improved. Weight coefficient krThe adjustable flexibility of the algorithm is increased, so that the algorithm has generality.

Claims (9)

1. A non-incremental model-free adaptive heading control method for ships is characterized by comprising the following steps:
the method comprises the following steps: introducing an input-output coupling adaptive compensation term into a model-free adaptive control input resolving rule function of the ship control system to obtain a non-incremental control input resolving rule function;
step two: substituting the dynamic linearized data model into a non-incremental control input resolving rule function to enable the derivative of input information u (k) to be equal to 0, and obtaining a non-incremental model-free self-adaptive control law;
step three: estimating an estimated value of a dynamic linearized data model parameter phi (k) at the moment k according to historical input and output information of a ship control system
Figure FDA0003085084600000011
Step four: according to the estimated value obtained in the third step
Figure FDA0003085084600000012
And calculating input information u (k) of the ship control system at the moment k according to the non-incremental model-free adaptive control law obtained in the step two, and executing the input information u (k) by the ship control system to obtain output information y (k +1) of the ship at the moment k + 1.
2. The non-incremental model-free adaptive heading control method for the ship according to claim 1, wherein a judging step is further included after the second step, and the judging step is as follows:
the expected heading angle y of the ship at the moment k*(k) Making a difference with a heading angle y (k), obtaining a heading deviation e (k) at the moment k, judging whether e (k) is less than a preset deviation threshold value, if so, ending the control of the ship, otherwise, executing a step three.
3. The non-incremental model-free adaptive heading control method for the ship according to claim 2, wherein after the fourth step, k is k +1, and then the judging step is returned.
4. The non-incremental model-free adaptive heading control method for ships according to claim 1, 2 or 3, wherein in the step one, the non-incremental control input calculation criterion function is recorded as J [ · in the step one]The input of the function is u (k), krΔ y (k +1) · u (k-1) is an input-output coupling adaptive compensation term, and then:
J[u(k)]＝[y*(k+1)-y(k+1)]2+λ[u(k)-u(k-1)]2+krΔy(k+1)·u(k-1)，
wherein u (k) and y (k) are respectively a rudder angle and a heading angle at the time k and are respectively used as input information and output information of the ship control system, and delta y (k +1) ═ y (k +1) -y (k), and y*(k +1) is the desired heading angle at time k +1, λ is the step size factor of u (k), krThe weight coefficients of the adaptive compensation term are coupled for input and output.
5. The non-incremental model-free adaptive heading control method for the ship according to claim 1, 2 or 3, wherein in the second step, the expression of the dynamic linearized data model is as follows:
y(k+1)＝y(k)+ΦT(k)ΔH(k)，
wherein phiT(k)＝[φy,φu]Is a transposition of phi (k), phiyAnd phiuModel parameters for the heading angle and rudder angle at time k, respectively, [ Δ h (k) ═ Δ y (k), Δ u (k)]TΔ u (k) (u) (k) -u (k-1), Δ y (k) (y (k) -y (k-1), u (k) and y (k) are the rudder angle and heading angle at time k, respectively, as input information and output information, respectively.
6. The non-incremental model-free adaptive heading control method for the ship according to claim 5, wherein in the second step, the expression of the non-incremental model-free adaptive control law is as follows:
Figure FDA0003085084600000021
wherein the content of the first and second substances,
Figure FDA0003085084600000022
and
Figure FDA0003085084600000023
are respectively phiuAnd phiyλ is the step size factor of u (k), krWeight coefficient, y, for input-output coupling of adaptive compensation terms*(k +1) is the desired heading angle, ρ, at time k +11Step-size factor, p, for the desired output deviation2Is a step factor of the actual output deviation.
7. The non-incremental model-free adaptive heading control method for the ship according to claim 1, 2 or 3, wherein in step three, historical input and output information of a ship control system comprises: input information u (k-1) at time k-1, output information y (k-1) at time k-1, input information u (k-2) at time k-2, output information y (k-2) at time k-2, and estimated values of dynamic linearized data model parameters at time k-1
Figure FDA0003085084600000024
8. The non-incremental model-free adaptive heading control method for ships according to claim 7, wherein in the third step, the estimated value of the dynamic linearized data model parameter phi (k) at the time k is estimated according to the following formula
Figure FDA0003085084600000025
Figure FDA0003085084600000026
Wherein eta belongs to (0, 1) as a penalty factor, mu is a weight coefficient for limiting the change of the model parameter,
ΔH(k-1)＝[Δy(k-1),Δu(k-1)]T，
Δu(k-1)＝u(k-1)-u(k-2)，
Δy(k-1)＝y(k-1)-y(k-2)。
9. the non-incremental model-free adaptive heading control method for ships according to claim 1, 2 or 3, wherein the estimated value obtained in the third step
Figure FDA0003085084600000027
And substituting the non-incremental model-free self-adaptive control law obtained in the step two to obtain the input information of the ship control system at the moment k.
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