CN111665719B - Supply ship synchronous control algorithm with timeliness and stability - Google Patents
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Abstract
The invention provides a tender vessel synchronous control algorithm with timeliness and stability, which comprises a terminal cost function module, a tender vessel model prediction control module and a neural dynamic optimization module. The terminal cost function module ensures the closed loop stability of the supply ship control system by using the terminal cost function; the Model prediction Control module converts the synchronous Control problem of the supply ship into a tracking Control problem following a pilot, and designs a supply ship Control algorithm based on a Model Predictive Control (MPC) algorithm, so that the anti-interference capability of the supply ship during the execution of a supply task is improved, the speed of two ships can be synchronized during the supply task, and the supply efficiency is improved; the neural dynamic optimization module solves the problems of large calculation amount and low calculation speed in the traditional model predictive control algorithm by using a parallel calculation framework of a recurrent neural network, and can enable a tender boat to better cope with emergency situations during tender.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a synchronous control algorithm for a tender boat with timeliness and stability.
Background
Chinese patent CN 201610859143.7 discloses a generalized prediction adaptive supply ship course control method based on event driving, and the invention provides an event driving-based generalized prediction adaptive supply ship course control method.A discrete event trigger working in a discrete state is selected to design a trigger judgment function under a variable threshold value, and when the trigger time is reached, the event trigger judges whether the current state meets the trigger condition through the trigger judgment function; secondly, a controlled autoregressive integral sliding average model of a rudder angle-course is obtained through a supply ship low-frequency motion mathematical model and is used as a prediction model, and parameters of the prediction model are estimated on line by adopting a forgetting factor recursion least square method; thirdly, the state to be controlled is sent to the controller by combining with the event-driven trigger, and the controller outputs rudder angle control increment and control quantity after resolving through a GPC adaptive algorithm, so that the tender vessel can quickly finish the approaching stage and the parallel stage and keep course tracking of the tender stage. The invention mainly researches the course control problem of the supply ship, but in the course of sailing supply of the supply ship, only the course tracking effect in the supply stage is not enough, the speed synchronization problem of the supply ship and the supplied ship and the position relation between the two ships are considered, and the timeliness and the stability of the algorithm are increased, so that the supply ship can efficiently and safely complete the supply task.
Disclosure of Invention
According to the technical problems provided by the invention, a supply ship synchronous control algorithm with timeliness and stability is provided. The invention mainly utilizes a tender boat synchronous control algorithm with timeliness and stability, and is characterized by comprising the following steps: the system comprises a terminal cost function module, a supply ship model prediction control module and a neural dynamic optimization module.
For the tracking control problem of the supply ship, a three-degree-of-freedom ship motion model is adopted:
in the formula, eta = [ x, y, psi =] T X represents the lateral displacement of the vessel, y represents the longitudinal displacement of the vessel, ψ represents the yaw angle; upsilon = [ u, v, r] T U represents the advancing speed of the vessel, v represents the lateral speed of the vessel, and r represents the yaw rate of the vessel; j (ψ) represents a rotation matrix,
the tender vessel is typically operated at low speed, and therefore the dynamic model of vessel motion is summarized as:
in the formula,
a matrix of the inertia is represented and,
a damping matrix is represented which,
representing the Coriolis and central centripetal force matrix, τ T ＝[τ u τ v τ r ] T Indicating control force and moment, X (·) ,Y (·) ,N (·) Are hydrodynamic parameters.
The leader ship serves as a reference of a following ship, and a mathematical model of the leader ship is defined as:
coordinate conversion is performed on equations (1) and (3) by the following equation (4):
z 1 ＝xcosψ+ysinψ
z 2 ＝-xsinψ+ycosψ (4)
z 3 ＝ψ
offset (x) of displacement o ,y o ) In combination with equation (4) above, equation (4) can be converted to:
z 1r ＝(x r -x o )cosψ r +(y r -y o )sinψ r
z 2r ＝-(x r -x o )sinψ r +(y r -y o )cosψ r
z 3r ＝ψ r (5)
defining a synchronous control error system for supplying the dynamic positioning ship as follows:
z ie ＝z i -z ir i＝1,2,3
u e ＝u-u r (6)
v e ＝v-v r
r e ＝r-r r
the formula (6) is differentiated and linearized to obtain:
in the formula, x t ＝y t ＝[z 1e z 2e z 3e u e v e r e ] T ，
Wherein,
d 11 ＝-X u ,d 22 ＝-Y v ,d 33 ＝-N r .
according to the actual requirement, selecting proper sampling time, the equation (8) can be converted into discrete form:
x(k+1)＝Ax(k)+Bτ(k) (9)
wherein x, y ∈ R 6×1 ,A∈R 6×6 ,B∈R 6×3 K denotes sampling time points, and A and B are discrete system parameter matrixes.
In the invention, the stability of the control system is ensured by designing a secondary terminal cost function, and in the terminal cost function module, a linear state feedback law is firstly designed for the control system:
τ＝Kx (10)
in the formula, K represents a vector for controlling the gain. The state matrix P of the terminal cost is obtained by solving the lyapunov equation (11)):
(A k +κI) T P+P(A k +κI)＝-(Q lq +K T R lq K) (11)
in the formula, A k ＝A+BK，Q lq And R lq A weight matrix representing the outputs and inputs, κ is selected by equation (12):
κ＜-λ max (A k ) (12)
thereby ensuring A k The real part of all eigenvalues of + kappa I is negative, where lambda is max (A k ) Is represented by A k Maximum eigenvalue of the real part.
Further, in order to improve the robustness and the anti-interference capability of the system, a tender vessel control algorithm is designed based on a model prediction control algorithm. Defining a prediction time domain as N in the supply ship model prediction control module p Control time domain of N c In the prediction calculation process, let τ (k + N) c )＝τ(k+N c +1)＝...＝τ(k+N c +N p ) Then, the future state information of the system can be calculated sequentially by a certain prediction model (x (k + 1) = Ax (k) + B τ (k)):
wherein x (k + i | k) i =1,2 p Represents future state information x (k + i) i =1,2, N, predicted from the state information at the sampling time point k p 。
According to the above formula (13), the following definitions are made:
the above formula (13) is rewritten into a matrix form as shown in the formula (15):
X＝Fx(k)+ΦΓ (15)
in the formula,
then, the synchronous multivariable control problem of the supply ship is converted into an optimal control problem with terminal cost:
the constraint conditions are as follows:
Γ min ≤Γ≤Γ max (17)
in the formula, Q mpc And R mpc Is an output weight matrix and an input weight matrix,
PX p is the terminal cost, X p Is the terminal state of X and P is the state matrix of the terminal cost function determined by equation (11).
Furthermore, in order to solve the problems of large calculation amount and low calculation speed in the traditional model predictive control algorithm, in the neural dynamic optimization system module, the parallel calculation architecture of the recurrent neural network is utilized to accelerate the calculation speed, so that the proposed algorithm has timeliness. In the neural dynamics optimization system module, substituting equation (15) into equation (16) yields:
by definition
Equation (18) is simplified to:
J＝Γ T HΓ+WΓ+ξ (20)
the objective function (equation (20)) is solved iteratively by establishing a neural dynamic optimization system (equation (21)), so that the calculation speed is increased:
in the formula,
is the convergence speed, Ω (Γ) is taken as:, P Ω Is the projection operator, and the projection operator,
compared with the prior art, the invention has the following advantages:
(1) The method is based on a model prediction control algorithm, has robustness, and can excellently complete the replenishment task under the condition that the ship has external interference;
(2) The method solves the problems of large calculation amount and low calculation speed in the traditional model predictive control algorithm by utilizing the parallel calculation architecture of the recurrent neural network, can ensure that the proposed algorithm has timeliness, and ensures that the supply vessel adopting the method can better cope with changeable external environments;
(3) The invention ensures the closed loop stability of the control system by using the terminal cost function technology, so that the proposed algorithm has stability;
(4) The technology provided by the invention is used for controlling the supply ship, so that the supply ship can automatically follow the leader ship from different initial positions under the condition of interference and achieve the expected target of synchronous speed, the working strength of a rudder during supply can be effectively reduced, the supply ship can reach a supply state more quickly, the anti-interference capability of the supply ship is increased, the speed of the two ships can be ensured to be synchronous during supply, the influence of waves on supply is reduced, and the supply ship can finish the supply task efficiently.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a block diagram of an MPC design with timeliness and stability of the present invention.
FIG. 2 is a performance diagram of the synchronization control at different starting points according to the present invention.
FIG. 3 is a schematic diagram of the velocity synchronization process at different initial points according to the present invention.
FIG. 4 is a graphical representation of the response of the control input to various initiation points of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1-4, the present invention provides a tender vessel synchronization control algorithm with timeliness and stability, which includes: the system comprises a terminal cost function module, a supply ship model prediction control module and a neural dynamic optimization module.
In the application, (1) in a terminal cost function module, the closed loop stability of a control system is guaranteed by designing a secondary terminal cost function; (2) In a model prediction control module of the supply ship, converting a synchronous control problem of the supply ship into a tracking control problem following a pilot, and solving the problem based on a model prediction control algorithm, so that the anti-interference capability of the supply ship is improved, the speed of two ships can be synchronized when a supply task is carried out, and the supply efficiency and the safety are improved; (3) In the neural dynamic optimization module, a parallel computing architecture of a recurrent neural network is used for quickly solving an objective function in the tender vessel model prediction control module, so that the ship can quickly react to a changeable external environment.
For the tracking control problem of the supply vessel, a three-degree-of-freedom vessel motion model is adopted:
in the formula, eta = [ x, y, psi =] T X represents the lateral displacement of the vessel, y represents the longitudinal displacement of the vessel, ψ represents the yaw angle; upsilon = [ u, v, r] T U represents the forward speed of the vessel, v represents the lateral speed of the vessel, and r represents the yaw rate of the vessel; j (ψ) represents a rotation matrix,
tender vessels are typically operated at low speeds, thus, the vessel is movedThe dynamic model of the ship motion is summarized as follows:
in the formula,
a matrix of the inertia is represented and,
a damping matrix is represented which is,
representing the Coriolis and central centripetal force matrix, τ T ＝[τ u τ v τ r ] T Indicating control force and moment, X (·) ,Y (·) ,N (·) Is a hydrodynamic parameter.
The leader ship serves as a reference of a following ship, and a mathematical model of the leader ship is defined as:
coordinate conversion is performed on equations (1) and (3) by the following equation (4):
offset (x) of displacement o ,y o ) In combination with equation (4) above, equation (4) can be converted to:
z 1r ＝(x r -x o )cosψ r +(y r -y o )sinψ r
z 2r ＝-(x r -x o )sinψ r +(y r -y o )cosψ r
z 3r ＝ψ r (5)
defining a synchronous control error system for the replenishment of a dynamically positioned vessel as:
z ie ＝z i -z ir i＝1,2,3
u e ＝u-u r (6)
v e ＝v-v r
r e ＝r-r r
the differential and linearization processing of equation (6) yields:
in the formula, x t ＝y t ＝[z 1e z 2e z 3e u e v e r e ] T ，
Wherein
d 11 ＝-X u ,d 22 ＝-Y v ,d 33 ＝-N r ；
According to the actual requirement, selecting a proper sampling time, the equation (8) can be converted into a discrete form:
x(k+1)＝Ax(k)+Bτ(k) (9)
wherein x, y ∈ R 6×1 ,A∈R 6×6 ,B∈R 6×3 K denotes sampling time points, and A and B are discrete system parameter matrixes.
In the invention, the stability of the control system is ensured by designing a secondary terminal cost function, and in the terminal cost function module, a linear state feedback law is firstly designed for the control system:
τ＝Kx (10)
in the formula, K represents a vector for controlling the gain. The state matrix P of the terminal cost is obtained by solving the lyapunov equation (11)):
(A k +κI) T P+P(A k +κI)＝-(Q lq +K T R lq K) (11)
in the formula, A k ＝A+BK，Q lq And R lq A weight matrix representing the output and input, κ being selected by equation (12):
κ＜-λ max (A k ) (12)
thereby ensuring A k The real part of all eigenvalues of + kappa I are negative values, where lambda is max (A k ) Is represented by A k Maximum eigenvalue of the real part.
Further, in order to improve the robustness and the anti-interference capability of the system, a tender vessel control algorithm is designed based on a model prediction control algorithm. Defining a prediction time domain as N in the supply ship model prediction control module p Control time domain as N c In the prediction calculation process, let τ (k + N) c )＝τ(k+N c +1)＝...＝τ(k+N c +N p ) Then, the future state information of the system can be calculated sequentially by a certain prediction model (x (k + 1) = Ax (k) + B τ (k)):
wherein x (k + i | k) i =1,2 p Represents future state information x (k + i) i =1,2, N, predicted from the state information at the sampling time point k p 。
According to the above formula (13), the following definitions are made:
rewriting the above formula (13) into a matrix form as shown in formula (15):
X＝Fx(k)+ΦΓ (15)
in the formula,
then, the synchronous multivariable control problem of the supply ship is converted into an optimal control problem with terminal cost:
the constraint conditions are as follows:
Γ min ≤Γ≤Γ max (17)
in the formula, Q mpc And R mpc Is an output weight matrix and an input weight matrix,
PX p is the terminal cost, X p Represents the terminal state of X, and P is the state matrix of the terminal cost function determined by equation (11).
Furthermore, in order to solve the problems of large calculation amount and low calculation speed in the traditional model predictive control algorithm, in the neural dynamic optimization system module, the parallel calculation architecture of the recurrent neural network is utilized to accelerate the calculation speed, so that the proposed algorithm has timeliness. In the neural dynamic optimization system module, substituting equation (15) into equation (16) yields:
by definition
Equation (18) is simplified to:
J＝Γ T HΓ+WΓ+ξ (20)
the objective function (equation (20)) is solved iteratively by establishing a neural dynamic optimization system (equation (21)), so that the calculation speed is accelerated:
in the formula,
is the convergence speed, taking Ω (Γ) as ^ J, P Ω Is the projection operator, and the projection operator,
example 1
The embodiment shows the synchronous control performance of the dynamically positioned ship when the novel replenishment ship synchronous control algorithm with timeliness and stability provided by the invention is adopted to finish the tracking replenishment task from different starting points. Fig. 2 shows the tracking performance of a dynamic positioning vessel when the replenishment task is performed from a different starting point, fig. 3 shows the synchronization process of the speed, and fig. 4 shows the response of the control input. In this embodiment, it can be seen from fig. 1 that although the starting point is at a different starting position, the following ship can still automatically follow the leader ship for replenishment, and it can be seen from fig. 2 that the synchronization of the speeds is automatically achieved in a steady state.
In addition, in the embodiment, the calculation time is compared, the comparison result is shown in the following table, and according to the data in the table, the novel supply ship synchronous control algorithm with timeliness and stability provided by the invention can be obtained, so that the calculation time of the traditional MPC algorithm can be effectively reduced, and the timeliness of the designed algorithm can be improved.
TABLE 1 calculated time comparison
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
In the above embodiments of the present invention, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
In the embodiments provided in the present application, it should be understood that the disclosed technology can be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units may be a logical division, and in actual implementation, there may be another division, for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, units or modules, and may be in an electrical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on a plurality of units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and these modifications or substitutions do not depart from the spirit of the corresponding technical solutions of the embodiments of the present invention.
Claims (3)
1. A tender ship synchronous control algorithm with timeliness and stability is characterized in that: the system comprises a terminal state matrix module, a model prediction control module and a neural dynamic optimization module;
for the tracking control problem of the supply ship, a three-degree-of-freedom ship motion model is adopted:
wherein eta = [ x, y, psi =] T X represents the transverse displacement of the vessel, y represents the longitudinal displacement of the vessel, ψ represents the yaw angle; upsilon = [ u, v, r] T U represents the forward speed of the vessel, v represents the lateral speed of the vessel, and r represents the yaw rate of the vessel; j (ψ) represents a rotation matrix,
the tender vessel is usually operated at low speed, and therefore the dynamic model of the vessel motion is summarized as:
in the formula,
a matrix of the inertia is represented and,
a damping matrix is represented which is,
representing the Coriolis and central centripetal force matrix, τ T ＝[τ u τ v τ r ] T Representing control force and moment; wherein X (·) ,Y (·) ,N (·) All represent hydrodynamic parameters;
the leader ship serves as a reference of a following ship, and a mathematical model of the leader ship is defined as:
the formula (1) is converted into by coordinate conversion of the formula (1) and the formula (3) by the following formula (4):
offset (x) of displacement o ,y o ) In combination with equation (4) above, equation (4) can be converted to:
z 1r ＝(x r -x o )cosψ r +(y r -y o )sinψ r
z 2r ＝-(x r -x o )sinψ r +(y r -y o )cosψ r
z 3r ＝ψ r ； (5)
defining a synchronous control error system for the replenishment of a dynamically positioned vessel as:
the formula (6) is obtained by differentiation and linearization:
in the formula, x t ＝y t ＝[z 1e z 2e z 3e u e v e r e ] T ，
Wherein,
d 11 ＝-X u ,d 22 ＝-Y v ,d 33 ＝-N r ；
by actually giving a suitable sampling time, said equation (8) is converted into a discrete form:
x(k+1)＝Ax(k)+Bτ(k)； (9)
wherein x, y ∈ R 6×1 ,A∈R 6×6 ,B∈R 6×3 K represents a sampling time point, A and B represent a dispersed system parameter matrix;
the closed loop stability of the control system is guaranteed through a secondary terminal cost function, in a terminal cost function module, a linear state feedback law is firstly designed for the control system:
τ＝Kx； (10)
wherein K represents a vector of control gains; the state matrix P of the terminal cost function is obtained by solving the Lyapunov equation, namely the formula (11):
(A k +κI) T P+P(A k +κI)＝-(Q lq +K T R lq K)； (11)
in the formula, A k ＝A+BK，Q lq And R lq A weight matrix representing the output and input, κ being selected by equation (12):
κ＜-λ max (A k )； (12)
A k the real part of all eigenvalues of + kappa I are negative values, where lambda is max (A k ) Is represented by A k Maximum eigenvalue of the real part.
2. The tender vessel synchronization control algorithm with timeliness and stability of claim 1, wherein:
in the prediction control module of the supply ship model, a prediction time domain is defined as N p Control time domain as N c In the prediction calculation process, it is assumed that:
τ(k+N c )＝τ(k+N c +1)＝...＝τ(k+N c +N p )；
the future state information of the system can be calculated sequentially by a certain prediction model x (k + 1) = Ax (k) + B τ (k):
wherein x (k + i | k) i =1,2 p Represents future state information x (k + i) i =1,2, N, predicted from the state information at the sampling time point k p ；
According to the above formula (13), the following definitions are made:
rewriting the above formula (13) into a matrix form as shown in formula (15):
X＝Fx(k)+ΦΓ； (15)
in the formula,
then, the synchronous multivariable control problem of the supply ship is converted into an optimal control problem with terminal cost:
the constraint conditions are as follows:
Γ min ≤Γ≤Γ max ； (17)
in the formula, Q mpc And R mpc Is an output weight matrix and an input weight matrix,
is the terminal cost, X p Is the terminal state of X, P is the terminal generation determined by equation (11)A state matrix of the cost function.
3. The tender vessel synchronization control algorithm with timeliness and stability of claim 1, wherein:
in the neural dynamic optimization system module, the proposed algorithm has timeliness through a parallel computing architecture of a recurrent neural network; in the neural dynamic optimization system module, substituting equation (15) into equation (16) yields:
by definition
Equation (18) is simplified to:
J＝Γ T HΓ+WΓ+ξ； (20)
the method comprises the following steps of (1) iteratively solving an objective function, namely the formula (20), by establishing a neural dynamic optimization system, namely the formula (21), so that the calculation speed is accelerated:
where, θ is the convergence speed,Ω(Γ)is taken as
P Ω Is a projection operator, which is a function of the projection operator,
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