A wave compensation system control method based on LQR-LADRC

Abstract

This invention discloses a wave compensation system control method based on LQR-LADRC. The control method includes: Step 1) performing kinematic modeling on a shipborne Stewart six-DOF platform to obtain the motion relationships and velocity Jacobian matrices of the upper platform, lower platform, and drive chains; Step 2) establishing a dynamic model of the drive chains using the Newton-Euler method within a natural orthogonal compensation framework; Step 3) measuring the six-dimensional attitude of the ship's deck using a pose sensor, calculating the link lengths of each drive chain using inverse kinematics, and obtaining the rotation angles of each drive chain based on the linear relationship between link lengths and rotation angles; Step 4) establishing a position loop control model for a permanent magnet synchronous servo motor; wherein a three-loop control strategy is adopted for the permanent magnet synchronous servo motor, and the outer position loop uses a controller combining LQR-LADRC. This invention has the advantages of easy adjustment of controller parameters, high compensation accuracy, and strong decoupling and anti-disturbance performance.

Description

Technical Field

[0001] This invention relates to the field of wave compensation, and more specifically to a wave compensation system control method based on LQR-LADRC. Background Technology

[0002] Offshore oil extraction, marine lifting equipment maintenance, and wind power maintenance are susceptible to disturbances caused by ocean waves, resulting in six degrees of freedom of roll, pitch, yaw, swell, roll, and heave. These disturbances severely impact resource extraction windows, personnel safety, and equipment accessibility, leading to low work efficiency. To address this issue, an active shipboard wave compensation platform controls the length of six branch actuators on the Stewart platform to isolate disturbances encountered during ship operation and improve work efficiency in complex sea conditions.

[0003] With the continuous development of marine technology, shipborne equipment has placed higher demands on wave compensation accuracy and load-bearing capacity. In recent years, some research has emerged on shipborne Stewart platform controllers. For example, a complete shipborne dynamics model is established by fully considering the load inertia of the branch actuators, and a modal space is introduced, adopting a sliding mode controller scheme. Another example is the use of a fuzzy controller based on the inverse kinematics of a hybrid system to solve the motion redundancy problem of the Stewart platform and the 3-DOF gangway hybrid system. Yet another example is the use of a beetle search algorithm controller based on the task space to eliminate the coupling error of parallel mechanisms, and the design of an adaptive control strategy based on radial basis function neural networks (RBFNN) to compensate for external disturbances. Still another example is the use of a new velocity feedforward compensator and a sliding mode reverse thrust controller based on command filtering to solve the disturbances caused by ship motion.

[0004] Currently, the main control strategies for active shipborne wave compensation systems include PI control, sliding mode control, fuzzy control, and active disturbance rejection control. However, PI control, based on classical control theory, does not require a precise controlled object, but it is difficult to achieve effective tracking for multiple-input multiple-output (MIMO), nonlinear, and strongly coupled systems. Sliding mode control and fuzzy control, based on modern control theory, require a precise model of the controlled object. Once the system model is uncertain, external disturbances may lead to poor control performance. Although active disturbance rejection control can resist external disturbances well and does not require a precise model of the controlled object, it suffers from the problem of difficulty in tuning the controller bandwidth and extended state observer bandwidth.

[0005] Active shipborne wave compensation platforms typically face low-frequency heavy load conditions when operating at sea. At the same time, the upper platform is susceptible to eccentric loads from the gangway, while the lower platform is susceptible to external time-varying wave disturbances and strong coupling between internal branches. This leads to common problems such as the difficulty in parameter adjustment in existing control methods. Summary of the Invention

[0006] To at least partially address the shortcomings of existing technologies, the main objective of this invention is to provide a wave compensation system control method based on LQR-LADRC. This invention, building upon the Extended State Observer (LESO) of traditional LADRC, designs and replaces the original proportional derivative (PD) gain with a linear quadratic regulator (LQR). This effectively solves the adjustment problem of the original channel parameters in LADRC, ensures suppression of unknown interference, and also offers advantages such as high compensation accuracy and strong decoupling performance. This invention enables high-precision control of active shipborne wave compensation devices, providing assurance for maritime operations and improving operational efficiency in complex sea conditions.

[0007] To achieve the aforementioned main objectives, this invention discloses a wave compensation system control method based on LQR-LADRC. The wave compensation system includes an active shipborne wave compensation device, which comprises a six-degree-of-freedom Stewart platform and a three-degree-of-freedom gangway. The Stewart platform includes an upper platform, a lower platform, and six drive chains. The drive chains are connected to the upper and lower platforms via ball joints. The lower platform is mounted on the ship's deck, and the gangway is mounted on the upper platform. All six drive chains are controlled by permanent magnet synchronous servo motors. The control method includes the following steps:

[0008] Step 1: Perform kinematic modeling on the shipborne Stewart six-DOF platform to obtain the kinematic relationships of the upper platform, lower platform, and drive chain, as well as the velocity Jacobian matrix;

[0009] Step 2: Establish a dynamic model of the driving branch using the Newton-Euler method within the natural orthogonal complement framework;

[0010] Step 3: Measure the six-dimensional attitude of the ship's deck using a pose sensor, calculate the link length of each drive chain using inverse kinematics, and obtain the rotation angle of each drive chain based on the linear relationship between link length and rotation angle.

[0011] Step 4: Establish the position loop control model of the permanent magnet synchronous servo motor; a three-loop control strategy is adopted for the permanent magnet synchronous servo motor. The outer position loop uses a controller combining LQR-LADRC to estimate and compensate for the total disturbance of external parameter disturbances and internal disturbances that are not modeled. The inner and outer speed loops and current loops both use PI control to stabilize and regulate speed and load.

[0012] According to a specific embodiment of the present invention, step 1 specifically includes the following steps:

[0013] Step 1.1: Establish the world coordinate system, the first coordinate system for the lower platform and ship deck, and the second coordinate system for the upper platform and gangway;

[0014] Step 1.2: Based on the geometric parameters of the active shipborne wave compensation device, calculate the positions of the upper platform hinge point and the lower platform hinge point in their respective coordinate systems;

[0015] Step 1.3: Transform the hinge points of the upper platform and the lower platform to the world coordinate system respectively, and calculate the velocity Jacobian matrix between the upper platform, the lower platform and the driving branch;

[0016] Step 1.4: In the first coordinate system, the position vector of the driving branch is derived using the closed-loop vector method, and the velocity-motion relationship between the upper platform, the lower platform and the driving branch is obtained according to the principle of spiral reciprocity.

[0017] According to a specific embodiment of the present invention, the specific process of step 4 is as follows:

[0018] Step 4.1: Establish the mechanical motion equations of the permanent magnet synchronous servo motor to obtain the relationship between the input angle and the output current;

[0019] Step 4.2: Construct a control law estimate of the total disturbance of the system using a linear extended observer, and design linear feedback to eliminate the total disturbance so that the controller is transformed into a second-order cascade integrator;

[0020] Step 4.3: For the second-order cascade integrator, set the LQR control law and provide proof of the controller's stability;

[0021] Step 4.4: Integrate the LADRC and LQR controllers and verify the controller performance.

[0022] According to a specific embodiment of the present invention, the mechanical motion equation established in step 4.1 is as follows: Among them, T e It is electromagnetic torque, T L This is the load torque of the Stewart platform, J r It is the equivalent moment of inertia ω of the driving branch in the Stewart platform. r It is the angular velocity of the motor, B r It is the friction damping coefficient; among them, the permanent magnet synchronous servo motor adopts a surface-mounted rotor structure, and its DC shaft inductance L d and AC shaft inductance L q Based on the conservation of motor energy, vector control is adopted, with the direct-axis current i... d =0, so the electromagnetic torque equation in the synchronously rotating dq coordinate system can be obtained: Combining the two formulas above, we can obtain the relationship between the input rotation angle and the output current:

[0023] According to a specific embodiment of the present invention, the second-order cascade integrator converted in step 4.2 can be expressed as:

[0024] Step 4.3 is for The specific process for setting the LQR control law using a second-order cascade integrator is as follows:

[0025] In an LQR controller, the state variables are selected as the reference value and the output error e = y. r If -y is used, then when the system asymptotically stabilizes as e→0, the target output becomes the tracking reference value y. r Additionally, y = x1 = θ r , Load T L =0, and the following state-space equation can be obtained:

[0026] in, C r =[1 0],u * =i q ;

[0027] The performance indicators of the quadratic form are:

[0028] The optimal control rate can be obtained as: u * =-K r x+κ;

[0029] Among them, the control rate K r =R -1 B r T P, κ = R -1 B r T (PB r R -1 B r T -A r T ) -1 C r T Qy r It is derived from the reference input y r The feedforward compensation caused by this matrix, P, is a symmetric positive definite constant matrix that satisfies the following Riccati algebraic matrix equation:

[0030] PA r +A r T P-PB r R -1 B r T P+Cr T QC r =0;

[0031] Therefore, the closed-loop system equations are:

[0032] According to a specific embodiment of the present invention, step 5 is further included: establishing a simulation model to simulate and analyze the performance of the controller combined with LQR-LADRC; wherein, the simulation model uses the Stewart platform in the active shipborne wave compensation device as the compensation platform and another Stewart platform installed below the compensation platform as the simulation platform, the simulation platform is used to simulate wave motion, and the compensation platform is used to perform motion compensation.

[0033] According to a specific embodiment of the present invention, the specific analysis process of step 5 is as follows:

[0034] Step 5.1: When evaluating the compensation effect, select a set of sinusoidal ocean wave signals with fixed frequency and amplitude for single-degree-of-freedom simulation, and compare the residual motion errors of the three controllers: PI, LQR, and LQR-LADRC.

[0035] Step 5.2: When evaluating the anti-disturbance effect, simulation analysis was performed on the compensation platform with fixed and sinusoidal time-varying load forces and torques respectively, and the residual motion errors of the three controllers PI, LQR, and LQR-LADRC were compared respectively.

[0036] Step 5.3: When evaluating the decoupling performance, in a six-degree-of-freedom simulation of ocean waves with minimal mutual interference, multi-degree-of-freedom simulation analysis is performed, and the residual motion errors of the three controllers, namely PI, LQR, and LQR-LADRC, are compared respectively.

[0037] According to a specific embodiment of the present invention, a comparative experiment is set up in step 5.2. Specifically, no load is applied in the first half of the experiment and a load is applied in the second half, and then the residual motion errors of the three controllers, namely PI, LQR, and LQR-LADRC, are compared.

[0038] According to one specific embodiment of the present invention, white noise signal is introduced in step 5.3 to simulate system noise.

[0039] This invention offers the following advantages: it provides a wave compensation system control method based on LQR-LADRC that is easy to develop and allows for data visualization. By establishing a dynamic model of the driving branch using the Newton-Euler method within a natural orthogonal compensation framework, the dynamic equations of the achievable device no longer contain coupling information, improving system decoupling. Furthermore, the LQR-LADRC position loop control model proposed in the joint space offers advantages over traditional PI control strategies, including faster response and no overshoot. Simulation verification shows that the proposed control method's parameters are easily adjustable, and while achieving optimal control by tracking the wave curve, it also possesses good anti-disturbance and decoupling capabilities. This provides guidance for the high-precision control of active shipborne wave compensation platforms.

[0040] To more clearly illustrate the purpose, technical solution, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0041] Figure 1 This is an installation diagram of the shipborne wave compensation device of the present invention;

[0042] Figure 2 This is a model diagram of the shipborne wave compensation device of the present invention;

[0043] Figure 3 This is a structural diagram of the dual Stewart platform in the simulation model;

[0044] Figure 4 This is a schematic diagram of the gangway being installed on the simulation model;

[0045] Figure 5 This is a simplified structural diagram and coordinate system diagram of the Stewart platform;

[0046] Figure 6 This is the control flowchart of the shipborne wave compensation device;

[0047] Figure 7 This is a flowchart of the position loop control of the PMSM;

[0048] Figure 8 This is the LQR-LADRC control block diagram;

[0049] Figure 9 This is a block diagram of LQR servo tracking control;

[0050] Figure 10 This is a schematic diagram of the Matlab simulation experimental platform. Detailed Implementation

[0051] Many specific details are set forth in the following description in conjunction with embodiments in order to provide a full understanding of the invention. However, it should be understood that the following embodiments and detailed description are for illustrative purposes only and do not limit the scope of protection of the invention.

[0052] This invention discloses a wave compensation system control method based on LQR-LADRC. The wave compensation system includes an active shipborne wave compensation device 1, which is installed on the deck 2 of the ship. Figure 1-3 As shown, it includes a six-DOF Stewart platform 3 and a three-DOF gangway 4. The Stewart platform 3 comprises an upper platform 301, a lower platform 302, and six drive chains 303. The drive chains 303 are connected to the upper platform 301 and the lower platform 302 via ball joints 304. The lower platform 302 is mounted on the ship's deck 2, and the gangway 4 is mounted on the upper platform 301. All six drive chains 303 are controlled by permanent magnet synchronous servo motors (PMSM). Specifically, the lower platform 302 is mounted on the ship's deck 2, and the gangway 4 is mounted on the upper platform 301. The mechanical feedback of the six drive chains 303 in the Stewart platform 3 adjusts the motion amplitude to counteract the six-DOF disturbances (roll, pitch, yaw, surge, sway, and heave) generated by the ship in waves.

[0053] The control method includes the following steps:

[0054] Step 1: Perform kinematic modeling on the shipborne Stewart six-DOF platform to obtain the motion relationships and velocity Jacobian matrices of the upper platform, lower platform, and drive chain; specifically including:

[0055] Step 1.1: Establish the world coordinate system, the first coordinate system for the lower platform and ship deck, and the second coordinate system for the upper platform and gangway;

[0056] Step 1.2: Based on the geometric parameters of the active shipborne wave compensation device, calculate the positions of the upper platform hinge point and the lower platform hinge point in their respective coordinate systems;

[0057] Step 1.3: Transform the hinge points of the upper platform and the lower platform to the world coordinate system respectively, and calculate the velocity Jacobian matrix between the upper platform, the lower platform and the driving branch;

[0058] Step 1.4: In the first coordinate system, the position vector of the driving branch is derived using the closed-loop vector method, and the velocity-motion relationship between the upper platform, the lower platform and the driving branch is obtained according to the principle of spiral reciprocity.

[0059] The calculation process for step 1 above is as follows:

[0060] To clearly describe the movement of the Stewart platform at sea, such as Figure 5 As shown, three coordinate systems were established; among them, O w -x w y w z w Representing the world coordinate system, it remains fixed at all times; O B -x B y B z B (First coordinate system) represents the connection between the lower platform and the deck, and is the coordinate system for ship navigation; the inertial measurement unit (IMU) is installed on the deck to measure the ship's pose coordinates under wave disturbances; O T -x T y T z T (Second coordinate system) represents the coordinate system connecting the upper platform and the gangway.

[0061] Please continue reading. Figure 5 Kinematic and dynamic analyses were performed on the shipborne Stewart platform, defining the parameters between various coordinates of the Stewart platform. Among these, B... i T represents the i-th hinge point of the lower platform. i Let represent the i-th hinge point of the upper platform. The i-th hinge is 120° away from the (i-2)-th hinge. The radius of the upper platform is r. T The included angle between the mounting hinge points is θ1, and the radius of the lower platform is R. b The included angle between the hinge points is θ2. By establishing mathematical and geometric relationships, the position coordinates of the hinge points on the upper platform and each hinge point on the lower platform in their respective coordinate systems can be obtained; among them, the position coordinates of the hinge points on the upper platform... The hinge point coordinates of the lower platform

[0062] To achieve a simpler representation, all six hinge points of the Stewart platform are transformed to the world coordinate system. The hinge point of the upper platform is relative to the world coordinate system O. w -x w y w z w The coordinates are:

[0063]

[0064] The lower platform hinge point relative to the world coordinate system O w -x w y w z w The coordinates are:

[0065]

[0066] in, Indicates the origin O of the lower platform coordinate system. B Relative to the origin O of the world coordinate system w displacement, O represents the center of the origin of the coordinate system on the upper platform. T Relative to the center of the origin O of the lower platform coordinate system B displacement, Let represent the rotation matrices of the lower platform relative to the world coordinate system. This represents the rotation matrix of the upper platform relative to the lower platform.

[0067] Taking the derivatives of equations (1) and (2) yields the velocity Jacobian matrices between the upper platform and the driving branch, and between the lower platform and the driving branch, respectively:

[0068]

[0069] in With J Ti These represent the Jacobian matrices for the upper and lower platforms, respectively.

[0070] When solving for the lengths of each driving branch, the kinematic analysis is based on O. B -x B y B z B In the coordinate system, the position vector of the i-th branch can be derived using the closed-loop vector method:

[0071]

[0072] The unit vector of the i-th driving branch axis is as follows:

[0073]

[0074] These are the velocity vectors of the six driving branches; where, taking the differential of formula (5) and according to the principle of spiral reciprocity, the velocity-motion relationship between the Stewart platform and the driving branches is:

[0075]

[0076] in:

[0077]

[0078] Step 2: Establish a dynamic model of the driving branch using the Newton-Euler method within the natural orthogonal complement framework; the specific dynamic model is as follows:

[0079]

[0080] Among them Ww =W A +W G +W D Decomposed into driving force W A Gravity W G Dissipation force W D M T To ensure the quality of the platform, Let θ be the velocity spinor of the upper platform. k and τ J I represents a vector of joint variables and joint moments. J To drive the moment of inertia of the branch-equivalent robotic arm, The matrix coefficients are the inertia terms with quadratic joint velocities. Multiply by the Jacobian matrix on the left. The desired dynamic equation is obtained as follows:

[0081]

[0082] Where, τ W =J T W T , By embodying the information of coupling in J T In this system, the dynamic equations no longer contain the decoupling diagonal matrix, achieving decoupling between the channels. The variables can then be represented in a more compact form:

[0083]

[0084] Step 3: Measure the six-dimensional attitude of the ship's deck using a pose sensor, calculate the length of each drive chain using inverse kinematics, and obtain the rotation angle of each drive chain based on the linear relationship between the length and the rotation angle.

[0085] The deck is equipped with an inertial measurement unit (IMU) that can measure the six degrees of freedom disturbances caused by waves. The IMU calculates the ship's attitude and position in the inertial coordinate system and uses inverse kinematics to control the length of each drive chain to counteract the disturbances in the six degrees of freedom, so as to keep the upper platform basically stationary relative to the inertial reference frame, thereby ensuring the safe transfer of personnel and cargo.

[0086] Step 4: Establish the position loop control model for the permanent magnet synchronous servo motor. A three-loop control strategy is adopted for the permanent magnet synchronous servo motor. The outer position loop uses a combined LQR-LADRC controller to estimate and compensate for the total disturbance caused by external parameter disturbances and internal disturbances not modeled. Both the inner and outer speed loops and current loops use PI control to stably regulate speed and load. The LQR-LADRC combined controller is designed based on the traditional LADRC Extended State Observer (LESO), using a linear quadratic regulator (LQR) to replace the original proportional derivative (PD) gain.

[0087] The specific process of step 4 is as follows:

[0088] Step 4.1: Establish the mechanical motion equations of the permanent magnet synchronous servo motor to obtain the relationship between the input angle and the output current;

[0089] Step 4.2: Construct a control law estimate of the total disturbance of the system using a linear extended observer (LESO), and design linear feedback to eliminate the total disturbance so that the controller is transformed into a second-order cascade integrator;

[0090] Step 4.3: For the second-order cascade integrator, set the LQR control law and provide proof of the controller's stability;

[0091] Step 4.4: Integrate the LADRC and LQR controllers and verify the controller performance.

[0092] The control method in the embodiment is based on a joint space control strategy, which can transform the MIMO problem of the Stewart platform into a SISO problem, such as... Figure 6 The control block diagram shown simplifies the controller design. A permanent magnet synchronous motor (PMSM) is chosen as the actuator (drive chain) to achieve precise control of each drive branch of the Stewart platform. First, the six-dimensional attitude of the ship's deck is measured using an IMU sensor. The rod length of each drive chain's electric cylinder is calculated using inverse kinematics, and the corresponding rotation angle θ of the electric cylinder is calculated mathematically, where ph is the lead of the ball screw.

[0093] To achieve high-precision control of the electric cylinder's rotation angle θ, a mathematical model for the PMSM position loop control is established. The PMSM employs vector control, decoupling the direct-axis and alternating-axis components by controlling the magnitude and direction of the stator current in the synchronous rotating coordinate system, thereby achieving decoupling of the magnetic field and torque control. The overall control block diagram of the PMSM is shown below. Figure 7As shown, a classic three-loop control strategy is adopted. The outer position loop uses an improved LADRC+LQR combined controller to estimate and compensate for the total disturbance of external parameter disturbances and internal unmodeled disturbances. The inner and outer speed loops and current loops both use PI control to achieve rapid and stable adjustment of speed and load force.

[0094] The specific steps of the above process are as follows:

[0095] First, the mechanical motion equations of the electric motor are established as follows:

[0096]

[0097] Among them, T e It is electromagnetic torque, T L It is the load torque of the Stewart platform, J r It is the equivalent moment of inertia ω of the driving branch in Stewart. r It is the angular velocity of the electric motor, B r It is the friction damping coefficient.

[0098] The PMSM in this embodiment adopts a surface-mount rotor structure, and its DC shaft inductance L d and AC shaft inductance L q Equal to each other, based on the law of conservation of motor energy, vector control is adopted, and the direct-axis current i d =0, so the electromagnetic torque equation in the synchronously rotating dq coordinate system can be obtained:

[0099]

[0100] Where, p n It is the number of pole pairs of the motor. It is magnetic flux, i d i q These are the currents along the direct axis and quadrature axis, respectively, L. d L q These are the direct-axis and quadrature-axis inductances, respectively.

[0101] Rearranging formulas (12) and (13), we can obtain the input motor rotation angle θ. r and output current i q Relationship:

[0102]

[0103] like Figure 8 The LQR-LADRC control block diagram shown first utilizes LESO to construct the control law, then designs linear feedback control to transform the controller into a second-order cascade integrator, and finally employs an LQR controller for the second-order cascade integrator. Specifically, internal and external disturbances are treated as the total system disturbance f. d (TL J r B r ,θ r ):

[0104]

[0105] Rewrite the system output in the following form:

[0106]

[0107] Based on the original system state, the new state variable x3 = f(T) L J r B r ,θ r If the original system becomes a third-order controlled system, then the current i q As input u, motor rotation angle θ r As the output, the state variable x1 = θ is selected. r , Position control gain b0 = k t i q ,h(T L J r B r ,θ r If is the differential of the disturbance x3, then the formula can be rewritten as the following state-space equation:

[0108]

[0109] Its state-space equations are expressed mathematically as follows:

[0110]

[0111] in, C = [1 0 0], E = [0 0 1].

[0112] After introducing the new state variable, the third-order linear LESO can be expressed as:

[0113]

[0114] Where z is the estimated value of the observer's state variable x, L is the error feedback gain matrix, and since f d The unknown term can be estimated using the correction term, therefore it is omitted in the above formula. Rewrite the observer equations:

[0115]

[0116] in,

[0117] z = [z1 z2 z3] T Where z1 is an estimate of x1, z2 is an estimate of x2, and z3 is the disturbance x3 = f d The estimation is as follows: After parameterization, the poles of the characteristic equation are placed in the left half-plane -ω0 (ω0 is the observer bandwidth) through pole placement. Then the feedback gain matrix of the observer is:

[0118] L=[3ω0 3ω0 2 ω0 3 ] (twenty one)

[0119] For a given observer, the characteristic equation is such that... The eigenvalues ​​of the matrix are less than 0:

[0120]

[0121] According to Lyapunov's first law, The characteristic equation of LESO has a negative real part, therefore LESO is asymptotically stable.

[0122] For the disturbance z3 observed by the LESO observer, a linear feedback u = -z3 + u can be designed. * / b is used for elimination, where u * It is the error feedback variable. Substituting it into formula (16) will change the disturbance f. d eliminate:

[0123]

[0124] Where z3 is the state observer's response to the disturbance f d For an ideal state observer, the estimation error is negligible, so the relationship between the input and output is rewritten as a linear second-order cascaded integrator:

[0125]

[0126] like Figure 9 The LQR servo tracking control block diagram shown is for... A second-order cascaded integrator of the form of an LQR controller is designed. In the LQR controller, the state variables are selected as the reference value and the output error e = y. r If -y is used, then when the system asymptotically stabilizes as e→0, the target output becomes the tracking reference value y. r Let y = x1 = θ r , Load T L =0, and the following state-space equation can be obtained:

[0127]

[0128] in, C r =

[10] ,u * =i q ;

[0129] The performance indicators for the quadratic form are:

[0130] The optimal control rate can be obtained as: u * =-K r x+κ (27)

[0131] Among them, the control rate K r =R -1 B r T P, κ = R -1 B r T (PB r R -1 B r T -A r T ) -1 C r T Qy r It is derived from the reference input y r The feedforward compensation caused by this matrix, P, is a symmetric positive definite constant matrix that satisfies the following Riccati algebraic matrix equation:

[0132] PA r +A r T P-PB r R -1 B r T P+C r T QC r =0 (28)

[0133] Therefore, the closed-loop system equations are:

[0134]

[0135] The control method of this embodiment further includes step 5: establishing a simulation model to simulate and analyze the performance of the LQR-LADRC combined controller; wherein, the simulation model uses the Stewart platform in the active shipborne wave compensation device as the compensation platform and another Stewart platform installed below the compensation platform as the simulation platform; for example Figure 4As shown, considering the difficulty in obtaining the required wave data for simulation and ensuring the continuity of the simulation, a two-layer Stewart platform was set up, in which the lower structure 5 is used to simulate wave motion and the upper structure 3 serves as the wave compensation system.

[0136] The specific analysis process in step 5 is as follows:

[0137] Step 5.1: When evaluating the compensation effect, select a set of sinusoidal ocean wave signals with fixed frequency and amplitude for single-degree-of-freedom simulation, and compare the residual motion errors of the three controllers: PI, LQR, and LQR-LADRC.

[0138] Step 5.2: When evaluating the anti-disturbance effect, simulation analysis is performed on the compensation platform with fixed and sinusoidal time-varying load forces and torques, and the residual motion errors of the three controllers, PI, LQR, and LQR-LADRC, are compared. In Step 5.2, a comparative experiment is set up, in which no load is applied in the first half of the experiment and a load is applied in the second half, and then the residual motion errors of the three controllers, PI, LQR, and LQR-LADRC, are compared.

[0139] Step 5.3: When evaluating the decoupling performance, a multi-degree-of-freedom simulation analysis is performed to simulate ocean waves with minimal mutual interference in a six-degree-of-freedom environment. The residual motion errors of the PI, LQR, and LQR-LADRC controllers are compared separately. White noise is introduced in Step 5.3 to simulate system noise.

[0140] The specific calculation process for step 5 above is as follows:

[0141] To evaluate the control performance of the proposed LQR-LADRC-based wave compensation system control method, a dynamic model of the Stewart shipborne compensation platform and its limb actuators (drive chains) was established in Matlab / Simulink. The simulation model is as follows: Figure 10 The diagram shows a dual Stewart platform. The lower platform uses a motion simulator to provide suitable wave motion, while the upper platform is a compensation platform. The wave signal generated by the motion simulator is transmitted to the controller via an inertial motion sensor (X-sense / Mti-300), with a signal sampling time of 1 ms. Considering that the controlled object is to keep the upper platform (compensation platform) stationary relative to the lower platform (simulation platform, inertial platform), the position and attitude deviations in the inertial frame are used to evaluate the controller's compensation performance. External loads, signal noise, and sensor signal acquisition delays are also considered to simulate the error compensation effect under real-world conditions.

[0142] When evaluating the compensation effect of the proposed control method, a set of sinusoidal ocean wave signals with fixed frequency and amplitude were selected: The residual motion errors of the three controllers, namely PI, LQR, and LQR-LADRC, are compared respectively.

[0143] To evaluate the anti-disturbance effect of the proposed control method, fixed and sinusoidal time-varying load forces and moments are applied to the upper platform, respectively. Based on the load characteristics of the upper platform, a fixed force load disturbance F is applied in the X, Y, and Z directions. x =F y =F z = -3000N, a fixed load disturbance M is applied in the RX, RY, and RZ directions. x =M y =M z = -250 N·m. Considering that the shipborne active wave compensation platform is a nonlinear time-varying system, sinusoidal time-varying loads are applied in the X, Y, Z and RX, RY, RZ directions respectively. By analyzing and comparing the residual motion error of the upper platform when a disturbance is applied using PI, LQR, and LQR-LADRC controllers, the good anti-interference effect of the control method proposed in the embodiment is highlighted.

[0144] The simulation experiment was set up for comparison. No load was applied from 0-15s, and a load was applied from 15-30s. The residual motion errors of three controllers (PI, LQR, and LQR-LADRC) were compared. To evaluate the decoupling performance of the proposed control method, a multi-degree-of-freedom simulation experiment was conducted under the mutual interference of six degrees of freedom ocean waves. Considering the noise in the IMU sensor signals, actuator response delays, and external signal interference, a white noise signal with a maximum amplitude of 0.0001 m (rad) and a frequency of 5 Hz was introduced into the controller input to simulate system noise. By analyzing and comparing the residual motion errors of the PI, LQR, and LQR-LADRC controllers, the excellent decoupling performance of the proposed control method in this embodiment is highlighted.

[0145] Although the present invention has been described above by way of embodiments, the above embodiments are only used to exemplify possible implementations of the present invention and are not intended to limit the scope of protection of the present invention. Any equivalent substitutions or changes made by those skilled in the art in accordance with the present invention should also be covered by the scope of protection defined by the claims of the present invention.

Claims

1. A control method for a wave compensation system based on LQR-LADRC, wherein the wave compensation system includes an active shipborne wave compensation device, the active shipborne wave compensation device comprising a six-degree-of-freedom Stewart platform and a three-degree-of-freedom gangway; wherein, The Stewart platform comprises an upper platform, a lower platform, and six drive chains. The drive chains connect the upper and lower platforms via ball joints. The lower platform is mounted on the ship's deck, and the gangway is mounted on the upper platform. All six drive chains are controlled by permanent magnet synchronous servo motors. The control method includes the following steps: Step 1: Perform kinematic modeling on the shipborne Stewart six-DOF platform to obtain the kinematic relationships and velocity Jacobian matrices of the upper platform, lower platform, and drive chain; Step 2: Establish a dynamic model of the driving branch using the Newton-Euler method within the natural orthogonal complement framework; Step 3: Measure the six-dimensional attitude of the ship's deck using a pose sensor, calculate the link length of each drive chain using inverse kinematics, and obtain the rotation angle of each drive chain based on the linear relationship between link length and rotation angle. Step 4: Establish the position loop control model of the permanent magnet synchronous servo motor; among which, a three-loop control strategy is adopted for the permanent magnet synchronous servo motor. The outer position loop adopts a controller combining LQR-LADRC to estimate and compensate for the total disturbance of external parameter disturbances and internal disturbances that are modeled. The inner and outer speed loops and current loops both adopt PI control to stabilize and regulate speed and load force. The specific process of step 4 is as follows: Step 4.1: Establish the mechanical motion equations of the permanent magnet synchronous servo motor to obtain the relationship between the input angle and the output current; Step 4.2: Construct a control law estimate of the total disturbance of the system using a linear extended observer, and design linear feedback to eliminate the total disturbance so that the controller is transformed into a second-order cascade integrator; Step 4.3: For the second-order cascade integrator, set the LQR control law and prove that the controller is stable; Step 4.4: Integrate the LADRC and LQR controllers and verify the controller performance.

2. The wave compensation system control method based on LQR-LADRC according to claim 1, wherein: Step 1 specifically includes the following steps: Step 1.1: Establish the world coordinate system, the first coordinate system for the lower platform and ship deck, and the second coordinate system for the upper platform and gangway; Step 1.2: Based on the geometric parameters of the active shipborne wave compensation device, calculate the positions of the upper platform hinge point and the lower platform hinge point in their respective coordinate systems; Step 1.3: Transform the hinge points of the upper platform and the lower platform to the world coordinate system respectively, and calculate the velocity Jacobian matrix between the upper platform, the lower platform and the driving branch; Step 1.4: In the first coordinate system, the position vector of the driving branch is derived using the closed-loop vector method, and the velocity-motion relationship between the upper platform, the lower platform and the driving branch is obtained according to the principle of spiral reciprocity.

3. The wave compensation system control method based on LQR-LADRC according to claim 1, wherein: The mechanical motion equations established in step 4.1 are as follows: Among them, T e It is electromagnetic torque, T L This is the load torque of the Stewart platform, J r It is the equivalent moment of inertia ω of the driving branch in the Stewart platform. r It is the angular velocity of the motor, B r It is the friction damping coefficient; among them, the permanent magnet synchronous servo motor adopts a surface-mounted rotor structure, and its DC shaft inductance L d and AC shaft inductance L q Equal to each other, based on the law of conservation of motor energy, vector control is adopted, and the direct-axis current i d =0, so the electromagnetic torque equation in the synchronously rotating dq coordinate system can be obtained: Where, p n It is the number of pole pairs of the motor. It is magnetic flux, i d i q These are the currents along the direct axis and the quadrature axis, respectively; combining the two formulas above, we can obtain the relationship between the input rotation angle and the output current:

4. The wave compensation system control method based on LQR-LADRC according to claim 3, wherein: The second-order cascaded integrator converted in step 4.2 can be expressed as: Step 4.3 is for The specific process for setting the LQR control law using a second-order cascade integrator is as follows: In an LQR controller, the state variables are selected as the reference value and the output error e = y. r If -y is used, then when the system asymptotically stabilizes as e→0, the target output becomes the tracking reference value y. r Additionally, y = x1 = θ r , Load T L =0, and the following state-space equation can be obtained: Among them, C r = [1 0],u * = i q ; The performance indicators of the quadratic form are: The optimal control rate can be obtained as: u * =-K r x+κ; Among them, K r =R -1 B r T P, κ = R -1 B r T (PB r R -1 B r T -A r T ) -1 C r T Qy r It is derived from the reference input y r The feedforward compensation caused by this matrix, P, is a symmetric positive definite constant matrix that satisfies the following Riccati algebraic matrix equation: PA r +A r T P-PB r R -1 B r T P+C r T QC r =0; Therefore, the closed-loop system equations are:

5. The wave compensation system control method based on LQR-LADRC according to claim 1, wherein: Also includes: Step 5: Establish a simulation model to simulate and analyze the performance of the LQR-LADRC combined controller; The simulation model uses the Stewart platform in the active shipborne wave compensation device as the compensation platform and another Stewart platform installed below the compensation platform as the simulation platform. The simulation platform is used to simulate wave motion, and the compensation platform is used to perform motion compensation.

6. The wave compensation system control method based on LQR-LADRC according to claim 5, wherein: The specific analysis process in step 5 is as follows: Step 5.1: When evaluating the compensation effect, select a set of sinusoidal ocean wave signals with fixed frequency and amplitude for single-degree-of-freedom simulation, and compare the residual motion errors of the three controllers: PI, LQR, and LQR-LADRC. Step 5.2: When evaluating the anti-disturbance effect, simulation analysis was performed on the compensation platform with fixed and sinusoidal time-varying load forces and torques respectively, and the residual motion errors of the three controllers PI, LQR, and LQR-LADRC were compared respectively. Step 5.3: When evaluating the decoupling performance, in a six-degree-of-freedom simulation of ocean waves with minimal mutual interference, multi-degree-of-freedom simulation analysis is performed, and the residual motion errors of the three controllers, PI, LQR, and LQR-LADRC, are compared respectively.

7. The wave compensation system control method based on LQR-LADRC according to claim 6, wherein: Step 5.2 includes a comparative experiment, in which no load is applied in the first half of the experiment and a load is applied in the second half, and then the residual motion errors of the three controllers, namely PI, LQR, and LQR-LADRC, are compared.

8. The wave compensation system control method based on LQR-LADRC according to claim 6, wherein: In step 5.3, a white noise signal is introduced to simulate system noise.

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