A method and system for adaptive rudder and track-keeping integral optimal control of ships

Abstract

This invention relates to an integral optimal control method and system for ship adaptive rudder track holding, belonging to the field of ship adaptive rudder track control technology. It is proposed to address the problems of low track tracking accuracy and poor performance in indirect track control, as well as yaw issues encountered by wind, waves, and currents during straight track tracking. Key technical points: Based on the ship's speed u0 and the target heading deviation ψ... r Update system matrix A; select accuracy and energy consumption balance parameter matrices, solve the ILQR Riccati equation to obtain the optimal control variance matrix; calculate the ILQR controller proportional differential coefficient matrix, and calculate the integral coefficient matrix according to the critical damping principle; set the noise variance matrix, solve the GESO Riccati equation to obtain the observation equation matrix; calculate the GESO observation gain, and calculate the observation integral gain matrix according to the critical damping principle; calculate the GESO state observation result x and the ILQG control law; repeat the above steps to control the ship to travel along the set straight track. This invention can effectively solve the yaw problem encountered by wind, waves and current interference when tracking a straight track, making the closed-loop system have good robust stability, while reducing the number of steering operations per unit time and reducing steering energy consumption; after extensive testing, it has advanced performance.

Description

Technical Field

[0001] This invention belongs to the field of ship adaptive rudder trajectory control technology, specifically relating to a ship adaptive rudder trajectory maintenance integral optimal control method and system. Background Technology

[0002] Adaptive steering is a ship maneuvering motion control system based on advanced control theory and rudder technology, widely used in the course and track control of ocean-going and coastal merchant ships. Adaptive steering has three operating modes: servo steering, course rudder, and track rudder. Straight track control is a crucial component of adaptive steering navigation technology. Traditional steering systems typically require manual control, while adaptive steering systems can automatically adjust the rudder angle according to the ship's motion state and environmental conditions to achieve better maneuvering control, improve ship handling performance, reduce fuel consumption, and minimize the impact of environmental disturbances on navigation performance. The most important task in ship track control is designing a stable, accurate, energy-efficient, and convenient track control algorithm. This algorithm calculates the course and track errors from the ship's current position, course, and a given planned route, and then issues rudder angle control commands based on these errors to guide the ship along the predetermined planned route.

[0003] Track tracking control refers to the process by which a ship, driven by a control system, enters a pre-planned route from any initial position and eventually reaches its destination. Currently, adaptive rudder straight-line track control algorithms are mainly divided into two categories: indirect control and direct control. Indirect control methods consist of a heading guide and a heading controller. The heading guide calculates a desired heading based on the ship's track deviation, and the heading controller tracks this desired heading to reduce track error until it catches up with the desired track. Indirect control methods are simple and easy to implement, but their performance is poor, mainly due to insufficient control accuracy and weak disturbance rejection capabilities. The most commonly used heading guide is the line-of-sight (LOS) method. Direct control, on the other hand, directly calculates steering commands based on track error to control the ship to track the desired track, and typically offers higher track control accuracy compared to indirect methods.

[0004] The LQG controller is a linear quadratic Gaussian controller widely used in control systems. It consists of a linear quadratic regulator (LQR) and a Kalman filter. The LQR is an optimal controller for linear systems, minimizing the sum of squared errors between the system output and the reference signal while limiting the magnitude of the control input. The Kalman filter, based on Bayesian statistical principles, estimates the system state and eliminates the influence of measurement noise. Combining the LQR and Kalman filter results in the LQG controller. This controller can achieve optimal control of the system state and output under conditions of uncertainty and noise. Therefore, it is widely used in industrial control, aerospace, robotics, and other fields.

[0005] To address the issues of low accuracy and poor performance of indirect track control in existing technologies, no one has proposed applying the LQG control method to ship adaptive rudder track holding control and introducing integral improvements to the algorithm to obtain an adaptive rudder ILQG track holding controller for indirect track control track tracking. Summary of the Invention

[0006] The technical problem that this invention aims to solve is:

[0007] To address the problems of low tracking accuracy and poor performance of indirect track control, as well as yaw caused by wind, waves, and current interference encountered during straight track tracking, this invention proposes an integral optimal control method and system for ship adaptive rudder track maintenance.

[0008] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0009] An integral optimal control method for ship adaptive rudder track maintenance includes the following steps:

[0010] Step 1: Based on the ship's speed u0 and the target heading deviation ψ r Update system matrix A;

[0011] Step 2: Select the accuracy and energy consumption balance parameter matrix, and solve the ILQR Riccati equation to obtain the optimal control variance matrix;

[0012] Step 3: Calculate the proportional-derivative coefficient matrix of the ILQR controller, and calculate the integral coefficient matrix based on the critical damping principle;

[0013] Step 4: Set the noise variance matrix V, and solve the GESO Riccati equation to obtain the observation equation matrix;

[0014] Step 5: Calculate the GESO observation gain and calculate the observation integral gain matrix based on the critical damping principle;

[0015] Step 6: Calculate the GESO state observation result x and the ILQG control law δ;

[0016] Step 7: Repeat steps 1 to 6 to control the ship to travel along the set straight track.

[0017] Furthermore, in step one, the method for updating the system matrix A is as follows:

[0018] When a ship travels at a constant speed along a straight path, it can be rewritten as

[0019]

[0020] In the formula, x=(e ψ r vr) T ψ is the vertical distance between the ship and the desired straight path. r =ψ-ψ d The heading tracking error can be calculated using the following formula:

[0021]

[0022] Where A is the system state transition matrix, B is the control transition matrix, u = δ is the rudder angle, which is the input value of the system and the optimal control quantity that the algorithm needs to solve in the end. ω is the noise interference during the ship's motion, u0 is the initial speed of the ship, v is the ship's sway speed, and r is the ship's bow roll rate.

[0023] Furthermore, in step two, based on the ship motion model and the ship's motion state, a corresponding positive definite matrix P is set. c Q c Consider the state variables e and ψ r For optimal convergence, select R. c For a unit array, Q c =diag{q1,q2,0,0}, the quadratic performance index of the ship's adaptive rudder ILQG control system is J=∫x T Q c x+u T R c The optimal control variance matrix P is obtained by solving the following optimal control Riccati equation u dt. c ;

[0024] AP c +P c A T -P c BR -1 B T P c +Q=0

[0025] The matrix Q must be positive definite and the real symmetric matrix P calculated from it must be a matrix Q. c If the equation is positive definite and has real solutions, there may be cases where there are no solutions during the process of solving the equation. In such cases, it is necessary to adjust the parameter values ​​of the Q matrix until the equation has a solution and the conditions are met.

[0026] Furthermore, in step three, the proportional-differential coefficient matrix K of the ILQR controller is calculated. r =R -1 B T P c Based on P obtained in step two c The equation matrix corresponds to the optimal control rudder angle input value for this system, which should be:

[0027]

[0028] Furthermore, in step four, the noise variance matrix V is set to the actual measured noise variance, and the observation equation matrix P is solved according to the following GESO Riccati equation. o ;

[0029] AP o +P o A T -P o C T V -1 CP o +W=0

[0030] The matrix W must be positive definite and the real symmetric matrix P calculated from it must be a matrix that is also positive definite. o If the equation is positive definite and has real solutions, then similarly, in the process of solving the equation, there may be no solution or no solution that meets the requirements. In this case, the value of the W matrix needs to be adjusted so that the equation has a solution and meets the conditions.

[0031] Further, in step five, the GESO observation gain K is calculated. f =P o C T V -1 Calculate the observation integral gain matrix K based on the critical damping principle. fi .

[0032] Furthermore, in step six, the GESO state observation results are calculated based on the following extended state system equations. And calculate the ILQG control rate δ;

[0033]

[0034]

[0035] Furthermore, during navigation, the ship has a certain error in its distance from the desired track line and the desired track angle, with a vertical distance of e from the desired track.

[0036] A system for an adaptive rudder trajectory-keeping integral optimal control method for ships is provided. This system has program modules corresponding to the steps of the above-described technical solution, and executes the steps of the above-described adaptive rudder trajectory-keeping integral optimal control method for ships during runtime.

[0037] A computer-readable storage medium storing a computer program configured to implement the steps of the ship adaptive rudder track-keeping integral optimal control method when invoked by a processor.

[0038] The present invention has the following beneficial technical effects:

[0039] This invention is an Integral Gaussian Linear Quadratic Optimal Control (ILQG) method, which uses a Gaussian Optimal Extended State Observer (GESO) and an Integral Linear Quadratic Optimal Control (ILQR) controller in a joint design to achieve ship trajectory model state estimation and ship straight trajectory maintenance control under marine environmental disturbances.

[0040] This invention applies the LQG control method to ship adaptive rudder track-keeping control and introduces integral improvements to the algorithm to obtain an adaptive rudder ILQG track-keeping controller. Utilizing relevant theories of optimal control algorithms, an optimal controller and optimal observer are designed to ensure the ship navigates along the desired track. If the ship deviates from its course due to wind, waves, or current disturbances, the system controls the ship to return to the desired track and ultimately reach the target track point.

[0041] The critical damping integral of ILQG control effectively solves the yaw problem encountered by wind, waves, and current interference during straight-line track tracking, giving the closed-loop system good robust stability. GESO effectively removes high-frequency interference and noise from waves and sensors, reducing the number of steering maneuvers per unit time during the ship's track-keeping control process, resulting in good steering performance, reduced energy consumption, and extended steering system lifespan. Due to its fast convergence speed, the ship can recover more quickly after deviating from the target track due to disturbances, with smaller overshoot during the recovery process.

[0042] This invention designs an Integral Gaussian Linear Quadratic Optimal Control (ILQG) algorithm for ship adaptive rudder trajectory control. This invention effectively solves the yaw problem encountered by wind, waves, and current interference when tracking a straight trajectory, resulting in good robust stability of the closed-loop system. It also reduces the number of steering maneuvers per unit time, lowering steering energy consumption. Extensive testing has demonstrated its advanced performance. This invention is primarily applied in the field of ship adaptive rudder trajectory control. Attached Figure Description

[0043] Figure 1 This is a basic schematic diagram of the ship's adaptive rudder track maintenance principle in this invention;

[0044] Figure 2 This is a graph showing the trajectory tracking results in this invention;

[0045] Figure 3 This is a graph of the trajectory tracking error function in this invention;

[0046] Figure 4 This is a block diagram of the ship adaptive rudder ILQG track-keeping control system in the invention. Detailed Implementation

[0047] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the invention will be described below in conjunction with the accompanying drawings. Figures 1 to 4 This implementation method will be described in detail.

[0048] like Figure 1 As shown, the ship has a certain error in its distance from the desired track line and the desired track angle during navigation, and the vertical distance from the desired track is e. The angle between the ship's current heading angle and the desired trajectory is the trajectory angle error ψ. r =ψ-ψ d The ship adaptive rudder track-keeping integral optimal control method of the present invention mainly includes the following steps:

[0049] Step 1: Based on the ship's speed u0 and the target heading deviation ψ r Update system matrix A;

[0050] The specific method for updating system matrix A is as follows:

[0051] The basic principle diagram of ship adaptive rudder track maintenance is as follows: Figure 1 As shown, when the ship travels at a constant speed along a straight path, the model can be rewritten as follows:

[0052]

[0053] In the formula, x=(e ψ r vr) T ψ is the vertical distance between the ship and the desired straight path. r =ψ-ψ d For heading tracking error, e and ψ r The main control parameters in the straight-line trajectory control of ships using this method are calculated using the following formula: system matrix A.

[0054]

[0055] Where: A is the system state matrix, also known as the system matrix (system state transition matrix); B is the system input matrix (control transition matrix); ω is the noise interference experienced by the system (noise interference during ship motion); u = δ is the rudder angle, which serves as the input value of the system and is the optimal control quantity that the algorithm ultimately needs to solve; u0 is the initial speed of the ship; v is the ship's sway speed; and r is the ship's bow roll rate.

[0056] Step 2: Select the accuracy and energy consumption balance parameter matrix, and solve the ILQR Riccati equation to obtain the optimal control variance matrix;

[0057] Based on the ship motion model and ship motion state listed in the above steps, set the corresponding positive definite matrix P. c Q c In the process of controlling a ship's motion trajectory, it is necessary to comprehensively control the ship's position deviation and heading deviation, while other state variables such as v and r can be ignored. Therefore, we only need to consider e and ψ among the state variables. r The convergence effect is negligible; the effects of v and r can be ignored. Therefore, choose R. c For a unit array, Q c =diag{q1,q2,0,0}, is a constant that can be selected by the user. The quadratic performance index of the ship's adaptive rudder ILQG control system is J=∫x T Q c x+u T R c The optimal control variance matrix P is obtained by solving the following optimal control Riccati equation u dt. c ;

[0058] AP c +P c A T -P c BR -1 B T P c +Q=0

[0059] Where A is the state matrix of the system, i.e., the system matrix, B is the input matrix of the system, and the matrix Q is chosen to be positive definite and a real symmetric matrix P calculated from it. c If the equation is positive definite and has real solutions, there may be cases where there are no solutions during the solution process. In such cases, the parameter values ​​of the Q matrix need to be adjusted until the equation has a solution and the conditions are met.

[0060] Step 3: Calculate the proportional-derivative coefficient matrix of the ILQR controller, and calculate the integral coefficient matrix based on the critical damping principle;

[0061] The previous step of solving the equation allows us to calculate the real symmetric positive definite P. cMatrix, calculate the proportional-differential coefficient matrix K of the ILQR controller. r =R -1 B T P c Based on P obtained in step two c The equation matrix corresponds to the optimal control rudder angle input value for this system, which should be:

[0062]

[0063] Step 4: Set up the noise variance matrix and solve the GESO Riccati equation to obtain the observation equation matrix;

[0064] Subsequently, the Gaussian Optimal Extended State Observer (GESO) was designed, with the noise variance matrix V set as the actual measured noise variance. The observation equation matrix P was then solved according to the following GESO Riccati equation. o ;

[0065] AP o +P o A T -P o C T V -1 CP o +W=0

[0066] The matrix W must be positive definite and the real symmetric matrix P calculated from it must be a matrix that is also positive definite. o If the equation is positive definite and has real solutions, then similarly, in the process of solving the equation, there may be no solution or no solution that meets the requirements. In this case, the value of the W matrix needs to be adjusted so that the equation has a solution and meets the conditions.

[0067] Step 5: Calculate the GESO observation gain and calculate the observation integral gain matrix based on the critical damping principle;

[0068] Based on P calculated in the previous step o Matrix, calculate GESO observation gain K f =P o C T V -1 Calculate the observation integral gain matrix K based on the critical damping principle. fi ;

[0069] Step 6: Calculate the GESO state observation result x and the ILQG control law δ;

[0070] Use step three to obtain K r K obtained in step five f and K fi In step two, P is obtained. c Calculate the GESO state observation results based on the following extended state system equations. And calculate the ILQG control rate δ;

[0071]

[0072]

[0073] Step 7: Repeat steps 1 through 6 above to control the ship to travel along the set straight track.

[0074] Repeat steps 1 through 6 until the process of maintaining the ship's straight course ends.

[0075] Practical application effects such as Figure 2 and Figure 3 As shown in the figure, the ship track tracking result curve is as follows: Figure 2 As shown in the figure, the ship track tracking error result curve is as follows: Figure 3 As shown. (Through) Figure 2 Figure 3 It can be seen that the algorithm has good control effect in straight-line trajectory control, the control error can quickly converge to zero, and the control accuracy is high.

[0076] Parameters not defined in this invention are common knowledge in the art, or whose meaning can be derived from the context, or are within the scope of existing technology.

[0077] The embodiments or examples described above are merely some, not all, of the embodiments or examples of this invention. The above content of this invention is only a preferred embodiment and is not intended to limit the implementation of this invention. Those skilled in the art can easily make corresponding modifications or alterations based on the main concept and spirit of this invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of this invention without creative effort should fall within the scope of protection of this invention.

Claims

1. A ship adaptive rudder track-keeping integral optimal control method, characterized in that, Includes the following steps: Step 1: Based on the ship's speed Deviation from target heading Update the system state transition matrix ; Step 2: Select the accuracy and energy consumption balance parameter matrix, and solve the ILQR Riccati equation to obtain the optimal control variance matrix; Step 3: Calculate the proportional-derivative coefficient matrix of the ILQR controller, and calculate the integral coefficient matrix based on the critical damping principle; Step 4: Set the noise variance matrix V, and solve the GESO Riccati equation to obtain the observation equation matrix; Step 5: Calculate the GESO observation gain and calculate the observation integral gain matrix based on the critical damping principle; Step Six: Calculate the GESO state observation results and ILQG control rate δ; Step 7: Repeat steps 1 to 6 to control the ship to travel along the set straight track; In step six, the GESO state observation results are calculated based on the following extended state system equations. And calculate the ILQG control rate. ; in, As a unit array, Here is the system state transition matrix. To control the transition matrix, This is the proportional-differential coefficient matrix of the ILQR controller. For GESO observation gain, To observe the integral gain matrix, The optimal control variance matrix is... , This is the vertical distance between the ship and the desired straight path. Here, v represents the heading tracking error, v represents the ship's sway speed, and r represents the ship's bow roll rate.

2. The ship adaptive rudder trajectory maintenance integral optimal control method according to claim 1, characterized in that, In step one, the system state transition matrix is ​​updated. The specific method is as follows: When a ship travels at a constant speed along a straight path, it can be rewritten as In the formula, , This is the vertical distance between the ship and the desired straight path. For the heading tracking error, the system state transition matrix can be calculated using the following formula. ; in, Here is the system state transition matrix. To control the transition matrix, Let be the rudder angle, be the input value of the system, and be the optimal control variable that needs to be solved. Noise interference during ship movement. Let v be the initial speed of the ship, v be the yaw speed, and r be the bow roll rate.

3. The ship adaptive rudder track-keeping integral optimal control method according to claim 1, characterized in that, In step two, based on the ship motion model and the ship's motion state, the corresponding positive definite matrix is ​​set. , Considering the state variables and The convergence effect, select As a unit array, The quadratic performance index of the ship adaptive rudder ILQG control system is: Solving the following optimal control Riccati equation yields the optimal control variance matrix. ; Among them, matrix The chosen matrix must be positive definite and be a real symmetric matrix calculated from the given matrix. If the equation is positive definite and has real solutions, but you encounter a situation where there is no solution during the solution process, then adjustments are needed. The parameter values ​​of the matrix are determined until the equation has a solution and the conditions are met.

4. The ship adaptive rudder track-keeping integral optimal control method according to claim 1, characterized in that, In step three, the proportional-derivative coefficient matrix of the ILQR controller is calculated. According to the result obtained in step two The equation matrix corresponds to the optimal control rudder angle input value, which should be: 。 5. The ship adaptive rudder track-keeping integral optimal control method according to claim 1, characterized in that, In step four, the noise variance matrix is ​​set. To actually measure the noise variance, the observation equation matrix is ​​solved according to the following GESO Riccati equation. ; Among them, matrix The chosen matrix must be positive definite and be a real symmetric matrix calculated from the given matrix. If the equation is positive definite and has real solutions, then similarly, in the process of solving the equation, there may be no solution or no solution that meets the requirements. In this case, the value of the W matrix needs to be adjusted so that the equation has a solution and meets the conditions.

6. The ship adaptive rudder track-keeping integral optimal control method according to claim 5, characterized in that, In step five, the GESO observation gain is calculated. Calculate the observation integral gain matrix based on the critical damping principle. .

7. The ship adaptive rudder track-keeping integral optimal control method according to claim 2, characterized in that, During navigation, the ship will have certain errors in its distance from the desired track line and desired track angle, and the vertical distance from the desired track will be... , .

8. A system for ship adaptive rudder track-keeping integral optimal control, characterized in that: The system has a program module corresponding to the steps of any one of the claims 1-7 above, and executes the steps in the above-described ship adaptive rudder track-keeping integral optimal control method when running.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the ship adaptive rudder track-keeping integral optimal control method according to any one of claims 1-7.

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