Sea wave trajectory simulation control method and system based on adaptive sliding mode control

Abstract

The invention provides a sea wave trajectory simulation control method and system based on adaptive sliding mode control, and relates to the technical field of ocean testing, a synchronous control part in a control strategy calculates a synchronous error of sliding of each axis on a respective single-axis trajectory, and coordinates the speed rhythm of sliding of each axis on the respective trajectory through a synchronous control matrix; a single-axis control part in the control strategy is adjusted through adaptive iteration parameters to approach real response parameters of the system, and meanwhile, an uncertain disturbance term is observed and estimated through an extended state observer; converting the single-axis system into a state equation form; designing a self-adaptive sliding mode controller to realize self-adaptive estimation; constructing an extended state equation and designing an observer, and estimating all states and interference terms of the system in the whole time period through the observer; the sliding mode control rate is optimized, the observation value of the interference term is used as an interference compensation introduction control rate, and a new sliding mode control rate is obtained; and compensating a real-time motion mode to obtain a synchronous control mode.

Description

Technical Field

[0001] This invention relates to the field of marine testing technology, specifically to a control method and system for simulating ocean wave trajectories based on adaptive sliding mode control. Background Technology

[0002] Wave sensors are core components of ocean observation. Their performance directly affects the quality of ocean data. Before being put into use, these sensors must undergo rigorous testing and calibration in a laboratory environment to verify their measurement accuracy, dynamic response characteristics, and environmental adaptability.

[0003] A six-degree-of-freedom wave simulation platform is the key equipment for completing this test. It provides a controllable and repeatable physical testing environment for wave sensors by accurately reproducing the six-dimensional wave-following motion (three-dimensional translation, two-dimensional tilt, and rotation) of the wave sensor at a real ocean wave surface point in the laboratory. Assuming the wave-following characteristics of the wave sensor are ideal, the simulated motion of the wave surface point must first ensure the realism of the wave waveform, which requires high synchronization of the simulation platform's six-axis motion. Simultaneously, the wave period varies under different sea conditions; to maximize the simulation of the characteristic motion of the waves, the simulation platform must have excellent dynamic response characteristics, capable of accurately simulating and following the set wave trajectory.

[0004] To achieve highly realistic reproduction of wave motion, the following technical challenges are faced: 1. High Synchronization Requirements: Sensor testing and calibration require the platform to strictly track given wave trajectory commands. In other words, the simulated wave motion must maintain accurate and valid waveforms and wave periods to be experimentally valuable. This necessitates that the simulation platform's six-axis motion be synchronized not only spatially but also temporally. Simultaneously, spatial synchronization is prioritized (i.e., ensuring the accuracy of the wave waveform), followed by temporal synchronization (ensuring the accuracy of the wave period).

[0005] 2. Strong coupling of multiple degrees of freedom: In order to obtain simulated motion with a large wave height, the controlled object of this patented algorithm must adopt a series joint motion simulation platform. Therefore, there is strong dynamic coupling between the six degrees of freedom of the platform. The motion of one degree of freedom will cause strong interference to other degrees of freedom. The control algorithm must have strong anti-interference ability, which ordinary PID control algorithm cannot meet.

[0006] 3. Fast dynamic response is required: Wave motion is a complex motion with multiple frequency components superimposed (including high-frequency components of small waves and low-frequency components of large waves), and the simulation platform needs to simulate motion under different sea conditions (effective period is 0.5s-30s). This requires the platform to have a high dynamic response speed (high-frequency motion of small waves) and also needs to have a wide bandwidth (ideally, it should be able to adjust parameters according to different frequency simulation conditions to adapt to different bandwidth requirements).

[0007] 4. The system exhibits nonlinearity and uncertainty: The platform itself contains nonlinear factors such as friction and dead zone of the drive cylinder, and bandwidth limitations of the servo drive. Simultaneously, dynamic adjustments to the parameters within the servo drive and changes in the load (sensor and its mounting fixture) introduce uncertainties into system parameters (such as center of mass and moment of inertia). Traditional PID control methods have limited capabilities in handling these nonlinearities, couplings, and uncertainties, often leading to large trajectory tracking errors and distortion in high-frequency reproduction, failing to meet the requirements of high-precision wave sensor testing. Summary of the Invention

[0008] This strategy aims to address the core challenges in high-precision multi-axis motion control, such as complex models, strong coupling, and high anti-interference requirements. We abandon the traditional control paradigm that relies on precisely coupled models and innovatively propose an integrated control framework that integrates decoupling, observation, compensation, and synchronization. The core breakthrough of this framework lies in transforming the complex multi-axis coupling problem into an observable and compensable disturbance, thereby significantly simplifying the complexity of system design and implementation while ensuring extremely high control performance.

[0009] The control architecture of this system consists of three core parts.

[0010] 1. Single-axis high-performance adaptive sliding mode controller Precise modeling: Establish an independent dynamic model for each servo axis as the basis for precise control.

[0011] Parameter Adaptation: Innovatively, key parameters such as system response time are used as online adjustment parameters, enabling the controller to automatically adapt to operating conditions such as load changes and parameter drift, laying the foundation for system robustness.

[0012] Advanced reaching law: Employs a hybrid reaching law combining exponential and sine functions. The exponential term provides rapid reaching momentum when far from the equilibrium point, ensuring high dynamic response speed of the system. The sine term generates micro-chattering near the equilibrium point, forming a smooth sliding band effect that effectively absorbs high-frequency unmodeled dynamics, significantly suppressing the chattering phenomenon inherent in traditional sliding mode control, and improving control smoothness and stability.

[0013] 2. Extended State Observer (ESO) – The System's Intelligent Sensing Unit Unified disturbance observation: The uncertainty of the system model, external load disturbance, and the most complex multi-axis motion coupling effect are all defined as the total disturbance of the system.

[0014] Real-time estimation and compensation: The ESO acts as the eye of the control system, capable of estimating the total disturbances that cannot be directly measured in real time and feeding them forward to the controller for proactive compensation. This allows the controller to always operate in a simplified, linearized, and deterministic environment.

[0015] Key advantages: This design eliminates the need for complex 6-axis coupled mechanical Jacobian matrix calculations, freeing the controller from dependence on an accurate model and greatly simplifying the algorithm structure.

[0016] 3. Independent Synchronizer Coordinator – The System's Command Center Virtual coupling mechanism: It does not rely on the physical coupling model, but uses an upper-level coordinator to monitor and compare the tracking errors of each axis to its respective command trajectory in real time.

[0017] Dynamic speed adjustment: Based on the tracking error, the tracking speed (i.e., speed) of each axis to its command trajectory is finely adjusted in real time and dynamically, so that all axes remain synchronized during the movement, as if they are connected by a virtual elastic system.

[0018] Core objective: To ensure the synchronization accuracy and fidelity of the overall motion trajectory, especially suitable for scenarios with extremely high requirements for trajectory realism, such as ocean wave simulation and robot collaborative operations.

[0019] This invention proposes a control method for simulating ocean wave trajectories based on adaptive sliding mode control, comprising the following steps: The control strategy is decomposed into a synchronous control part and a single-axis control part. The synchronous control part calculates the synchronous error of each axis sliding on its respective single-axis trajectory and coordinates the speed of each axis sliding on its respective trajectory through a synchronous control matrix. The single-axis control part achieves dynamic response through adaptive iterative parameter adjustment, and at the same time, it estimates the uncertain disturbance terms through an extended state observer. The uniaxial system is transformed into state equation form, and a dynamic model of the uniaxial system is established; a linear sliding surface is selected. Design sliding mode control rate and adaptive control law Design an adaptive sliding mode controller to achieve the first... Response time constant of shaft system Adaptive estimation; Construct extended state equations and design extended state observers. Use these observers to predict all states and disturbance terms of the system over the entire time period; then, use the observed values ​​of the disturbance terms... Introducing the control law as disturbance compensation yields a new sliding mode control law. A synchronous control method is obtained by scaling the motion trajectory of the six axes in the time dimension to compensate for real-time motion.

[0020] Furthermore, the control strategy adopts a speed control mode, which will... The transfer function of the shaft system simplifies to: ;in, The sequence number for each axis; For the first The velocity Laplace transform function is defined by the axis, where s is the complex frequency variable in the Laplace transform. For the first The Laplace transform function for the velocity feedback from the shaft displacement sensor; For the first The response time constant of the shaft system.

[0021] Furthermore, the simplified first The dynamic differential equation of the shaft system is: ;in, For the first The speed of the shaft, For the first Axis acceleration; sliding mode control rate As the first Axis control input, It controls the proportional gain of the input; set up For the first Displacement of the axis, For the first The speed of the shaft, For the first The acceleration of the axis transforms the above equation into the first... The state equation of the shaft is: ; in, This refers to the uncertainties of the system. No. The state equations of the shaft system are: ; in, For the first The actual displacement of the shaft is used as the output of the single-axis system. For the first Axial displacement The rate of change.

[0022] Furthermore, select a linear sliding surface. : ; in, It is the first Actual displacement of the shaft and expected displacement value of trajectory The error, It is the proportionality coefficient for error convergence. For error The first derivative; Sliding mode control rate for: ; in, for The predicted value, The expected acceleration value of the trajectory. For the self-designed sliding switch control rate, For the first The rate of change of the actual displacement of the shaft.

[0023] Adaptive control law for: ; in, The expected acceleration value of the trajectory. For the switching control rate of the sliding diaphragm control; pass Iterative calculations are performed to complete the calculations. The parameters are adjusted to achieve the goal of adaptive parameter estimation.

[0024] Furthermore, take As the third state variable in the system extension, the extended state equation is: ; in, The third state variable for system extension rate of change, For system uncertainties The rate of change; Design an extended state observer: ; in, The gain coefficient of the observer. Let be the estimate of the real-time displacement by the observer on the i-th axis. The observer for the i-th axis estimates the real-time displacement. rate of change, Let be the real-time velocity estimate of the observer on the i-th axis. Let be the estimate of the real-time acceleration by the observer on the i-th axis. The third state variable for system extension The estimated value, The third state variable for system extension The estimated rate of change, For system uncertainties rate of change, No. The estimated value of the shaft displacement. For the first The actual displacement of the shaft.

[0025] Furthermore, the observed values ​​of the interference term = As a disturbance compensation, a new sliding mode control law is obtained. : .

[0026] Furthermore, the real-time motion is compensated by scaling the six-axis motion trajectory in the time dimension: Design a synchronization controller : ; in, To simulate the target's trajectory; Based on the system feedback, the real-time synchronization error of the 6 axes is obtained. : ; It is the system state observed through an extended observer.

[0027] Furthermore, The synchronization control matrix via the synchronization controller is in the following form: ; in, This is the proportional gain of the synchronous controller.

[0028] Compared with the prior art, the present invention has the following beneficial effects: (1) Excellent engineering feasibility: By using ESO to handle coupling, the cumbersome decoupling calculation of MIMO system is avoided. The control structure is clear and the algorithm has a small amount of computation, which greatly reduces the difficulty and cost of implementation on a multi-axis servo drive platform.

[0029] (2) Extremely high synchronization control accuracy: The independent synchronization coordinator can effectively suppress the propagation of single-axis dynamic error in the system, ensure that the multi-axis moves as a whole, and significantly improve the realism of complex trajectory reproduction.

[0030] (3) Superior dynamic and steady-state performance: Adaptive sliding mode control ensures the system’s fast response capability; while the advanced hybrid approach law solves the chattering problem while maintaining speed, achieving the best balance between dynamic response and stability.

[0031] (4) Strong robustness and anti-interference capability: The adaptive mechanism copes with changes in internal system parameters. The ESO compensation mechanism copes with external disturbances and inter-axis coupling. The dual protection makes the system highly insensitive to various uncertainties and disturbances from the inside and outside, and its operation is stable and reliable. Attached Figure Description

[0032] Figure 1 Schematic diagram of the motion principle of a tandem articulated 3P3R wave simulation platform; Figure 2 This is a block diagram of a synchronous control system. Figure 3 This is a block diagram of a single-axis control system. Figure 4 Comparison diagrams of the improved sliding film switching function, where (a) is a displacement comparison diagram, (b) is a displacement error comparison diagram, and (c) is a velocity comparison diagram; Figure 5 The figures show a comparison of the effects of conventional sliding mode control and adaptive sliding mode control, where (a) is a comparison of displacement and (b) is a comparison of displacement error. Figure 6 The figures show a comparison of the effects of adaptive sliding mode control and adaptive sliding mode control with added uncertainty compensation, where (a) is a displacement comparison figure and (b) is a displacement error comparison figure. Figure 7 The figures show a comparison of the effects of the synchronous controllers. In the figures, (a) is the overall displacement curve without a synchronous controller, (b) is the local displacement curve without a synchronous controller, (c) is the displacement curve with a synchronous controller, and (d) is the local displacement curve with a synchronous controller. Detailed Implementation

[0033] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0034] Because ocean waves move significantly in the vertical direction and sensors are relatively small in size and weight, a series articulated motion platform is suitable for ocean wave simulation platforms, such as... Figure 1The image shows a series-jointed 3P3R mobile platform. The control strategy of this invention controls a 6-DOF series-jointed wave simulation platform. The first three joints are linear sliding modules, divided into XYZ axes, which are sequentially linked to simulate translational motion. The last three joints are rotational motion modules, divided into ABC axes, which are sequentially linked to simulate the tilting motion of wave surface points and the self-rotation motion of buoys.

[0035] The motion parameters of the wave simulation platform referenced in this patent are as follows: X-axis: It adopts an AC servo motor, reducer, gear rack drive, and magnetic scale (displacement feedback). The servo motor has a rated speed of 3000 rpm, the reducer has a transmission ratio of 1 / 9, the gear rack lead is 0.32 m / rpm, the magnetic scale accuracy is 0.01 mm, and the maximum load is 200 kg. Z-axis: It adopts an AC servo motor, ball screw drive, and magnetic scale (displacement feedback). The servo motor has a rated speed of 3000 rpm, a gear and rack lead of 0.05 m / rpm, a magnetic scale accuracy of 0.01 mm, and a maximum load of 60 kg. Y-axis: It adopts an AC servo motor, ball screw drive, and magnetic scale (displacement feedback). The servo motor has a rated speed of 3000 rpm, a gear and rack lead of 0.25 m / revolution, a magnetic scale accuracy of 0.01 mm, and a maximum load of 15 kg. A-axis: Uses a brushless servo motor, reducer, and encoder (angular displacement feedback). The servo motor has a rated speed of 20,000 rpm, the reducer has a transmission ratio of 1 / 27, the encoder accuracy is <0.01°, and the maximum load is 10 kg. B-axis: Uses a brushless servo motor, reducer, and encoder (angular displacement feedback). The servo motor has a rated speed of 20,000 rpm, the reducer has a transmission ratio of 1 / 27, the encoder accuracy is <0.01°, and the maximum load is 8 kg. C-axis: It adopts a brushless servo motor, reducer, and encoder (angular displacement feedback). The servo motor has a rated speed of 20,000 rpm, the reducer has a transmission ratio of 1 / 27, the encoder accuracy is <0.01°, and the maximum load is 5kg. This control strategy successfully integrates adaptive sliding mode control, extended state observer, and independent synchronous control to construct a high-performance, robust, and easy-to-implement multi-axis motion control solution. It represents a shift from model-based to disturbance observation-based advanced control concepts and is particularly suitable for 6-DOF ocean wave trajectory simulation platforms requiring high-precision synchronous control.

[0036] 1 Overall Control Strategy The overall control strategy can be divided into two parts: (1) Synchronous control, which is mainly accomplished by a 6-axis synchronous controller. The synchronous controller calculates the synchronization error of each axis sliding on its own single-axis trajectory based on the displacement, velocity and acceleration data fed back from the 6 axes, and coordinates the speed rhythm of each axis sliding on its own trajectory through the synchronous control matrix to achieve the effect of synchronous control. This can prioritize ensuring the spatial shape of the simulated waves. (2) Single-axis control, which adopts an adaptive sliding film control strategy (insensitive to the system model) and selects adaptive iterative adaptive parameter adjustment to achieve a better dynamic response effect (so that each axis has a better following characteristic on its own trajectory); at the same time, by using an extended state observer to observe and estimate the uncertain disturbance term, it can effectively resist the influence of real-time disturbances and ensure the characteristics of the simulated waves in terms of time period. By adopting this overall control, not only can the realism of the simulated waves in terms of waveform be guaranteed, but also the realism of the simulated wave period be guaranteed, which can provide an accurate experimental environment for the performance testing, calibration and calibration of the sensor. Figure 2 This is a block diagram of a synchronous control system. Figure 3 This is a block diagram of a single-axis control system.

[0037] 2 Single-axis control section 2.1 Establishing a dynamic model of a single-axis system (1) Dynamic model A single-axis system consists of a servo motor, servo driver, transmission, and load. There are also coupling effects between multi-axis movements, making it a very complex system with many uncertainties and time-varying parameters.

[0038] Based on the characteristics of the single-axis drive system and the compensation of the servo driver for the single-axis system, this control strategy adopts a speed control mode, which can... The transfer function of the shaft system simplifies to: (1); in, The sequence number for each axis, ; For the first The Laplace transform function for the axis speed setting is equivalent to the system input; For the first The Laplace transform function of the velocity feedback from the shaft displacement sensor is equivalent to the system output. For the first The response time constant of the axis system is affected by uncertainties such as simulated motion load, servo driver internal parameter tuning, and multi-axis motion coupling. It is unknown, but Moreover, for fixed single-axis systems, The fluctuation range is within a certain range, that is, it meets the following conditions: ; for The upper limit, for The lower limit. In this control strategy, the lower limit is... As an unknown quantity, it is predicted and adjusted through adaptive control law, so that... The predicted value and the actual value approach each other within a finite time.

[0039] Using the dynamic model of the shaft system based on relation (1), a simplified first... Dynamic differential equations of the shaft system: (2); in, For the first The speed of the shaft, For the first The acceleration of the shaft; For the first Axis control input, It controls the proportional gain of the input.

[0040] set up For the first The displacement of the axis (also through the first) Feedback value from the shaft displacement sensor. For the first The speed of the shaft, For the first The acceleration of the axis. Equation (2) can be transformed into the first... The state equation of the shaft is: (3); ; This is the uncertainty term of the system, which is the sum of the effects of the coupled motion of the six axes, external disturbances, etc., satisfying the following conditions: This means that external disturbances must have an upper bound; otherwise, the system will inevitably become uncontrollable. In this control strategy, [the following is defined as follows:] This is expanded to include new state variables of the system, which are then predicted using a system observer. The observed values ​​and the true values ​​approach each other within a finite time.

[0041] According to relation (3), we can obtain the first... State equations of the shaft system: (4); in, For the first The actual displacement of the shaft is the measured value of the displacement sensor, which serves as the output of the single-axis system. For the first Axial displacement The rate of change.

[0042] 2.2 Adaptive Sliding Mode Controller Design Slippery Controller Design Select linear sliding surface : (5); in, It is a sliding surface function; It is the first Actual displacement of the shaft and expected displacement value of trajectory The error, It is the proportionality coefficient for error convergence ( The larger the value, the faster the error convergence, but the jitter will increase. Adjustments can be made to... A relatively ideal trajectory tracking effect can be obtained. For error The rate of change (first derivative). In calculating During the derivative process, combined with the state equation (4), we can obtain: (6); in For error The second derivative; For the first The rate of change of the actual displacement of the shaft can be obtained by discretizing the measured value in real time and taking the derivative. This represents the expected acceleration value for the trajectory.

[0043] The Lyapunov function is chosen as follows: (7); in, The error between the estimated and actual response time. , for The predicted value. Taking the derivative of relation (7), we can obtain: (8); Combining relations (3), (5), and (6), formula (8) can be transformed into the following form: (9); Sliding mode control rate design The switching control rate of the sliding control is designed as follows: (10); in, It is a symbolic function; For the self-designed switching control function components, The specific format is as follows: ; satisfy: (11); It controls the proportional gain of the input; For the first Maximum speed of the shaft The gain coefficient of the exponential switching control section ( >0, The larger the exponent, the faster it approaches the mean. It is generally determined through laboratory adjustments, and the initial value can be 1). The gain coefficient of the symbol switching control section ( >0, The larger the value, the greater the stability margin of the synovial control, but the more jitter and overshoot will increase. It is generally determined through laboratory adjustments, and the initial value can be set to... ), The width of the synovial band is a sinusoidal relationship. Increasing the value appropriately can effectively reduce the jitter of the sign switching function. This value is generally determined by laboratory adjustments, and the initial value can be 1).

[0044] This sluice switch function adds a sinusoidal switching term to the exponential approach rate, which not only increases the correction speed for small errors but also makes the system's sluice switch smoother and more natural, effectively reducing system chattering. (Based on data...) Figure 4 A comparison plot of the improved synovial switching function can be seen: In In smaller cases, the jitter in speed control is significantly reduced.

[0045] Exponential reaching law parameters: ; Improved reaching law parameters: ; According to relation (9), the cleverly designed sliding mode control rate is: (12); Adaptive control law design Design an adaptive control law: (13); pass Iterative calculations can complete the calculation of... The parameters are adjusted to achieve the goal of adaptive parameter estimation.

[0046] Controllability verification Substituting relations (10), (12), and (13) into relation (9), we can obtain (14); Based on relation (11), relation (14) can be transformed into the following form: (15); because ,but ,at the same time , Then relation (15) can be transformed into (16); Only needs to satisfy: (17); That is, we can get: (18); By using inequalities (17) and (18), we can obtain: as long as and , No. The closed-loop system of the axis is asymptotically stable. That is to say, based on the aforementioned sliding mode control law and adaptive control law, the first step can be achieved through displacement feedback and velocity control. Tracking of the axis.

[0047] At the same time, since the system is controllable, then It approaches 0 within a finite amount of time, that is... ,in Representing a finite time. Based on relation (13), we can obtain: ; therefore, For uncertain variables The iterative prediction converges uniformly within a finite time, as can be expressed as follows: (19); Through data Figure 5 The effect comparison chart of adaptive sliding mode control verifies that: (1) the adaptive sliding mode controller is controllable and the error tends to be dynamically stable; (2) the adaptive sliding mode control continuously adjusts in the initial stage. As the displacement error approaches the true value, it continuously decreases (from the original ±3 mm error to ±1 mm error), thus improving control accuracy.

[0048] Standard synovial control parameters: .

[0049] Adaptive sliding membrane control parameters: .

[0050] 2.3 Prediction and Observation Design for System Interference To achieve better control, it is necessary to adjust the interference items. Make predictions and participate in the overall control rate to compensate for the impact of disturbances.

[0051] (1) Observer Design Pick As the third state variable in the system extension, the extended state equation can be obtained through state equation (4): (20); Based on the extended system state equation (20), an extended state observer is designed: (twenty one); in, The gain coefficient of the observer is calculated using the frequency method, which enables the observation of the system state. Let be the observation value of the real-time displacement of the observer on the i-th axis. For the observer of the i-th axis, the real-time displacement observation value rate of change, Let be the real-time velocity observation value of the observer on the i-th axis. Let be the observation value of the real-time acceleration from the observer on the i-th axis. The third state variable for system extension The observed values ​​(due to) , That is, the uncertain term The observed values, The observed values ​​are used express), The third state variable for system extension The observed rate of change, For system uncertainties rate of change, No. Observed values ​​of shaft displacement, For the first The actual displacement of the axis. The observations are obtained by discretization and iteration (mature theory) of the state equation (20) based on the extended observer. Only the principle of the observer is provided here. The calculation process of the observations is existing technology and will not be elaborated.

[0052] According to relation (21), the characteristic root equation can be calculated as follows: (twenty two); To ensure that the observation error of the extended state observer is convergent, the roots of the characteristic equation (22) are first configured using the bandwidth method: (twenty three); in, It is the bandwidth frequency of the observer. Larger: Better real-time prediction performance, but it amplifies the impact of noise; Smaller: Predictive real-time performance will be reduced, but noise will be effectively filtered. Here, the effective period of the simulated wave motion can be used as a reference. To configure based on the effective period of simulated wave motion To configure This is to adapt to simulated wave motion under different sea conditions. Under normal circumstances... >3. The optimal parameters can be obtained through experience or on-site testing.

[0053] Based on relations (22) and (23), the following combinations can be calculated: ; In actual control, Using adaptive parameters To approximate substitution, it can improve Accuracy is beneficial for improving control performance, that is: (twenty four); By setting an appropriate observer bandwidth By using the state observer (21) and the forward Euler discretization method, all states of the system over the entire time period can be observed: Meanwhile, the predicted values ​​of the observer designed using the bandwidth method satisfy: (25); The parameters provide state parameters for the 6-axis synchronous controller and participate in the synchronous control calculations. It provides compensation for sliding mode control, enhancing the system's anti-interference capability.

[0054] (2) Sliding mode control rate optimization design Here, the sliding mode control law is redesigned, and the observed values ​​of the disturbance term are... As interference compensation, a new sliding mode control law is obtained. : (26); (3) Control performance verification Substituting relations (13) and (26) back into relation (9), we get: (27); Using equations (19) and (25), we can see that the fluctuation amplitude of the compensated interference term is smaller than that of the uncompensated interference term, that is: ; therefore: ; Therefore, after disturbance compensation, the control law reduces energy faster, the system error converges faster, and the control effect is better.

[0055] Through data Figure 6 The effect comparison chart of adaptive sliding mode control can be verified: (1) through The optimized adaptive sliding mode controller is controllable, and the error tends to be dynamically stable; (2) the control is continuously adjusted at the beginning stage. (approaching the true value) and The speed of displacement error convergence is improved by compensation adjustment, and the dynamic response performance is improved; (3) the anti-interference performance is improved: under the condition of an instantaneous displacement of 0.1 meters in 12 seconds, the controller with compensation optimization has a significantly better recovery process for uncertain interference (the recovery speed is faster at the beginning and the overshoot is reduced by about 50%) than the controller without compensation optimization.

[0056] Adaptive sliding membrane control parameters: ;

[0057] Adaptive + Uncertainty Compensation Control Parameters: ;

[0058] 2.4 Synchronous Controller Design Synchronous control is achieved by scaling the motion trajectory of the six axes in the time dimension to compensate for real-time motion. The specific implementation is as follows.

[0059] The synchronous controller is designed as follows: (28); in, To simulate the target's trajectory: (29); in, Let be the displacement value of the simulated target trajectory along the i-th axis. ; Let be the simulated target trajectory velocity value along the i-th axis. ; Let be the acceleration value of the simulated target trajectory along the i-th axis. .

[0060] The system state is observed through an extended observer: (30); in, Let be the estimate of the real-time displacement by the observer on the i-th axis. ; Let be the real-time velocity estimate of the observer on the i-th axis. ; Let be the estimate of the real-time acceleration by the observer on the i-th axis. .

[0061] Based on the system feedback status, the real-time synchronization error of the 6 axes is as follows: (31); The desired displacement trajectory output by the synchronous controller: (32); in, Let be the desired displacement value of the i-th axis after adjustment by the synchronous controller. ; Let i be the desired speed value of the i-th axis after adjustment by the synchronous controller. ; Let be the desired acceleration value of the i-th axis after adjustment by the synchronous controller. .

[0062] To achieve synchronous control using the synchronous controller's control matrix, the controller must calculate the optimal synchronous displacement points for all six axes based on their individual axis errors (displacement, velocity, and acceleration feedback). (Here, a weighted average method is used, treating all six axis errors equally. Following matrix calculation rules, the weighted average synchronous control matrix can be calculated: the diagonal is 5 / 6, and the rest are -1 / 6.) Based on these optimal synchronous displacement points, the displacement correction values ​​for each axis are calculated to coordinate the speed of sliding along their respective trajectories, achieving synchronous control. The design is as follows: (33); in, The proportional gain of the synchronous controller can effectively improve the speed of local synchronization adjustment. The specific details can be adjusted and determined based on the actual system through simulation experiments (initially, you can take...). =1 (adjust according to the load size to obtain the best synchronization effect): When the speed is too small, the effect of adjusting the speed synchronously is not obvious; increase the speed. It can increase the adjustment speed, but it will increase the overshoot (jitter will increase), therefore It should not be too large; the desired effect can be obtained through simulation experiments.

[0063] like Figure 7 As shown, (a) is the overall displacement curve without a synchronous controller, (b) is the local displacement curve without a synchronous controller, (c) is the displacement curve with a synchronous controller, and (d) is the local displacement curve with a synchronous controller. The data... Figure 7 The local displacement curves in the comparison diagram of the synchronous controller's effect show that, under the same initial error conditions, the synchronization speed of the 6-axis trajectory is improved by using a 6-axis synchronous controller, which prioritizes the waveform and also ensures the periodicity.

[0064] No synchronous controller parameters: ;

[0065] Synchronous controller parameters: .

[0066] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A control method for simulating ocean wave trajectories based on adaptive sliding mode control, characterized in that, Includes the following steps: The control strategy is decomposed into a synchronous control part and a single-axis control part. The synchronous control part calculates the synchronous error of each axis sliding on its respective single-axis trajectory and coordinates the speed of each axis sliding on its respective trajectory through a synchronous control matrix. The single-axis control part achieves dynamic response through adaptive iterative parameter adjustment, and at the same time, it estimates the uncertain disturbance terms through an extended state observer. The uniaxial system is transformed into state equation form, and a dynamic model of the uniaxial system is established; a linear sliding surface is selected. Design sliding mode control rate and adaptive control law Design an adaptive sliding mode controller to achieve the first... Response time constant of shaft system Adaptive estimation; Construct extended state equations and design extended state observers. Use these observers to predict all states and disturbance terms of the system over the entire time period; then, use the observed values ​​of the disturbance terms... Introducing the control law as disturbance compensation yields a new sliding mode control law. A synchronous control method is obtained by scaling the motion trajectory of the six axes in the time dimension to compensate for real-time motion.

2. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 1, characterized in that, The control strategy adopts a speed control mode, which will... The transfer function of the shaft system simplifies to: ;in, The sequence number for each axis; For the first The velocity Laplace transform function is defined by the axis, where s is the complex frequency variable in the Laplace transform. For the first The Laplace transform function for the velocity feedback from the shaft displacement sensor; For the first The response time constant of the shaft system.

3. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 2, characterized in that, Simplified first The dynamic differential equation of the shaft system is: ;in, For the first The speed of the shaft, For the first Axis acceleration; sliding mode control rate As the first Axis control input, It controls the proportional gain of the input; set up For the first Displacement of the axis, For the first The speed of the shaft, For the first The acceleration of the axis transforms the above equation into the first... The state equation of the shaft is: ； in, This refers to the uncertainties of the system. No. The state equations of the shaft system are: ； in, For the first The actual displacement of the shaft is used as the output of the single-axis system. For the first Axial displacement The rate of change.

4. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 2, characterized in that, Select linear sliding surface : ； in, It is the first Actual displacement of the shaft and expected displacement value of trajectory The error, It is the proportionality coefficient for error convergence. For error The first derivative; Sliding mode control rate for: ； in, for The predicted value, The expected acceleration value of the trajectory. For the self-designed sliding switch control rate, For the first The rate of change of the actual displacement of the shaft; Adaptive control law for: ； in, The expected acceleration value of the trajectory. For the switching control rate of the sliding diaphragm control; pass Iterative calculations are performed to complete the calculations. The parameters are adjusted to achieve the goal of adaptive parameter estimation.

5. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 4, characterized in that, Pick As the third state variable in the system extension, the extended state equation is: ； in, The third state variable for system extension rate of change, For system uncertainties The rate of change; Design an extended state observer: ； in, The gain coefficient of the observer. Let be the estimate of the real-time displacement by the observer on the i-th axis. The observer for the i-th axis estimates the real-time displacement. rate of change, Let be the real-time velocity estimate of the observer on the i-th axis. Let be the estimate of the real-time acceleration by the observer on the i-th axis. The third state variable for system extension The estimated value, The third state variable for system extension The estimated rate of change, For system uncertainties rate of change, No. The estimated value of the shaft displacement. For the first The actual displacement of the shaft.

6. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 5, characterized in that, The observed values ​​of the interference term = As a disturbance compensation, a new sliding mode control law is obtained. : 。 7. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 6, characterized in that, Real-time motion is compensated by scaling the motion trajectory of the six axes in the time dimension: Design a synchronization controller : ； in, To simulate the target's trajectory; Based on the system feedback, the real-time synchronization error of the 6 axes is obtained. : ; It is the system state observed through an extended observer.

8. The control method for simulating ocean wave trajectories based on adaptive sliding mode control according to claim 7, characterized in that, The synchronization control matrix via the synchronization controller is in the following form: ； in, This is the proportional gain of the synchronous controller.

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