29 results about "Generalized coordinates" patented technology

The invention relates to the technical field of new energy power generation and control, and discloses a new energy station operation decision support system based on multi-objective optimization, which comprises a multi-source state space reconstruction module, a Riemannian manifold geometry engine module, a self-adaptive inertia Hamiltonian evolution module and a symplectic geometric integral and instruction mapping module. The system collects station data to construct a dimensionless state space, constructs a Riemannian metric tensor according to physical constraints to reconstruct a Riemannian manifold space, and calculates a geometric connection strength factor; the factor is used to adaptively modulate a virtual inertia matrix, and a dissipative Hamiltonian kinetic model is constructed; and finally, solving the steady-state generalized coordinates through a pungent-preserving numerical integration algorithm, and decoding the steady-state generalized coordinates into an equipment control instruction. According to the method, physical constraints are converted into geometric measurements, and a self-adaptive inertia mechanism is introduced, so that the problem of optimization convergence under multivariable strong constraints is solved, and the safety and accuracy of a control instruction are ensured.

The invention provides a robot full-flexible rigid-flexible coupling parametric modeling method and system, and belongs to the technical field of robot modeling. According to the method, firstly, based on MDH flexible expansion parameters, a floating coordinate method, a finite element method and a Rayleigh beam model are combined, and a full-flexible kinematics model containing flexible deformation of a base, joints and connecting rods is established; secondly, the speed and acceleration of key nodes of the model and any point of the flexible connecting rod are calculated in a recursive mode; constructing a local kinetic equation of each concentrated mass component and each distributed mass component based on a virtual power principle, and converting the local kinetic equations into a generalized coordinate space through a generalized Jacobian matrix; and finally, assembling to form a unified robot rigid-flexible coupling kinetic equation. According to the method, high efficiency and automation of the modeling process are realized, the accuracy of the model for describing the dynamic characteristics of the robot is improved, and an accurate basic model is provided for high-precision dynamic analysis and control of the robot.

The invention discloses a tethered satellite system dynamics modeling method considering perturbation factors. The tethered satellite system dynamics modeling method comprises the steps that a geocentric coordinate system, an orbital coordinate system of a Kepler orbit where a tethered satellite system is located and a body coordinate system of a unit satellite are established; according to the movement of the centroid of the tethered satellite system on the orbit, the generalized coordinates are the distance from the centroid of the system to the earth center and the true anomaly of the orbit, the Lagrange function of the centroid of the system is obtained; according to the movement of the unit star relative to the centroid, the generalized coordinates are the distance between the unit star and the centroid, the relative first rotation angle and the relative second rotation angle, the relative Lagrange function of the unit star is obtained; comprehensively considering perturbation factors to obtain non-spherical earth, third gravitational force and solar pressure perturbation potential energy; establishing a system kinetic equation considering comprehensive perturbation factors; and obtaining a complete Lagrange equation of the tethered satellite system. The error problem caused by the fact that the master satellite directly serves as the mass point of the system and the influence of comprehensive perturbation on system motion is not considered is solved, and the number of the slave satellites is not limited.

The invention relates to the technical field of computer-aided analysis, in particular to a floating foundation structure dynamic response real-time analysis system and method.The system comprises a residual vector calculation module for generating a residual force vector based on a full-order external excitation force vector, an increment base generation module for calculating a modal amplitude and constructing an increment base vector, and an increment base generation module for generating an increment base vector; the reduced-order matrix updating module constructs an enhanced reduced-order model by using the updated projection matrix, and the transient response solving module solves and obtains a corrected generalized coordinate value based on the enhanced reduced-order model and maps the corrected generalized coordinate value into a dynamic displacement field. According to the method, a residual vector is generated by calculating a difference value between full-order external excitation and internal force, residual force is mapped into static deformation distribution by using a stiffness matrix inverse operator, an incremental base is constructed through orthogonalization processing, adaptive updating of a projection space of a reduced-order model is realized, the system dimension is reduced, and the precision is guaranteed. And the calculation efficiency and the real-time performance of dynamic response analysis of the floating structure are improved.

The invention relates to the technical field of industrial automatic motion control, in particular to a gantry synchronous control method based on inertia equivalence and disturbance estimation. According to the technical scheme, the method comprises the following steps that dynamic modeling is conducted on a double-drive gantry system based on a Lagrange equation, the system is described as a generalized coordinate system with cross beam midpoint displacement, workbench offset and a cross beam rotation angle, a nonlinear dynamic equation is derived, the equivalent mass of each drive shaft is calculated in real time according to the model, and the equivalent mass of each drive shaft is calculated. According to the calculated real-time equivalent mass and an expected acceleration instruction given by the system, dynamic feed-forward compensation force is generated and used for pre-compensating inertia force, changed due to load movement, of the system. According to the method, the problem that the synchronization precision is reduced due to inertia time variation caused by load change and unknown disturbance is solved, and the response speed, the steady-state precision and the anti-interference capability are jointly improved.

The invention discloses an all-digital quantitative converter valve multispectral monitoring data fusion method, which comprises the following steps: establishing a converter valve element-level generalized coordinate model which comprises a three-dimensional data set of element static characteristics, space field distribution characteristics and time-varying reference characteristics; acquiring infrared and ultraviolet spectrum data of the converter valve, and mapping heterogeneous image data to a unified physical space of the generalized coordinate model by calculating a scale factor and a spatial resolution factor; extracting a multi-dimensional state feature vector, and calculating a mahalanobis distance by using a reference vector constructed by historical data and a covariance matrix; and the element deviation degree is evaluated according to the mahalanobis distance numerical value, and if the element deviation degree exceeds a preset dynamic threshold value, the fault type is judged by calculating the normalized contribution degree of the thermal field and electric field components to the mahalanobis distance. According to the method, conversion from a qualitative image to a quantitative value is realized, and an early compound fault with a single physical quantity not exceeding the standard but extremely low joint probability can be identified.

This invention relates to the field of multibody system dynamics, specifically a dynamic modeling method for simulating the flight motion of a morphing aircraft with an arbitrary number of rotating components. The method first abstracts the morphing aircraft as a tree-like multibody system containing virtual rigid bodies and virtual hinges. Rigid bodies and hinges are uniformly numbered using a depth-first traversal search, with the relative rotation angles between rigid bodies used as generalized coordinates. Then, a path matrix is ​​used to describe the system topology, and the center-of-mass velocity, center-of-mass acceleration, angular velocity, and angular acceleration of each rigid body are derived using the generalized coordinates. Next, based on the above kinematic parameters, the deflection velocity, deflection angular velocity, generalized active force, and generalized inertial force are calculated and substituted into the Kane equations to establish the multibody system dynamic equations. Finally, the dynamic equations are solved, and the motion state is updated according to a set time step, repeating the process until the simulation of the set duration is completed. This invention has strong versatility and good scalability, and is applicable to the flight motion simulation of morphing aircraft with an arbitrary number of rotating components.

This invention discloses a tiltrotor dynamics simulation method based on multibody dynamics, belonging to the field of aircraft dynamics modeling and simulation technology. It constructs a modular system including an input module, an output module, a fuselage module, a propeller module, a coupling mechanism module, and a dynamics solution module. The fuselage module has six generalized coordinates. In the propeller module, each propeller is independently modeled as a rigid body. The coupling mechanism module models the active actuator hinge between the rotor and the fuselage through rigid connections. The Kane method is used to perform dynamic modeling of the system, forming the system's equations of motion by constructing partial velocity expressions and inertial force forms for each component. The equations of motion are then numerically integrated and solved using a solver in the Simulink environment. The advantages of this invention are: accurate description of gyrocoupling effects, support for rapid changes in multirotor configurations, provision of comprehensive component-level mechanical data output, and improved simulation fidelity and engineering application value.

The application discloses a kind of dynamics analysis and attitude control methods of electric power multi-rope structure, belong to the dynamics and control field of spacecraft orbit and attitude.The application implementation method is: based on the operation law of vector array, six generalized coordinate dynamics equations of electric power multi-rope structure are derived by Lagrange equation;Through the dynamics analysis to electric power multi-rope structure, the dynamics model of electric power multi-rope structure is constructed, the coupling dynamics characteristics between tether and host star are characterized by the dynamics model of electric power multi-rope structure;Through the extended time-delay self-synchronization control strategy, the attitude of virtual pole is controlled based on the dynamics equation of virtual pole attitude angle and the dynamics equation of virtual pole attitude angle;The attitude of host star is controlled based on the dynamics equation of host star attitude angle, the dynamics equation of host star attitude angle, the dynamics equation of host star attitude angle γ, realize the purpose of simultaneously stabilizing virtual pole and host star attitude movement, reduce the complexity of control system.

The invention provides a quaternion discrete rod dynamics modeling method for overhead line toughness evaluation, and belongs to the technical field of power systems, the method comprises the following steps: using a three-dimensional catenary equation to simulate and calculate a static equilibrium curve of a wire under the action of self weight, and completing initial shape finding of the wire; dispersing the lead into rod sections with mass, rotational inertia and quaternion attitude parameters, and constructing a discrete rod model containing geometric and physical attributes; calculating translation and rotation kinetic energy of the conductor section, introducing gravitational potential energy and elastic potential energy, representing energy dissipation through a damping function, and forming a Lagrange function element; introducing external load simulation, and solving attributes of the overhead line in various aspects under the action of an external environment; the node position and the rod section attitude quaternion are used as generalized coordinates, a kinetic equation containing constraints is established in combination with the Lagrange-Arrange principle, and solution is carried out through numerical integration. According to the invention, the translation, bending and torsion coupling characteristics of the lead are accurately depicted, and high precision and high efficiency are both considered.

The invention discloses a theoretical model for spiral self-feeding shape correction of a pipe, which comprises the following steps of: establishing a theoretical formula of total kinetic energy T of the pipe on the basis of a thin-wall hypothesis under the conditions that a rotating shaft of the pipe is assumed to coincide with a bent plane and axial rolling of the pipe is ignored; establishing a simplified theoretical formula of potential energy V of the pipe on the basis of a reciprocating bending unified curvature theorem and a bidirectional effect under the condition of neglecting plastic dissipation of the pipe; modeling is conducted on the movement track of the pipe on the basis of the Lagrange equation so as to obtain a movement track equation set, and the movement track equation set comprises a coupling relational expression among the circumferential bending angle of the pipe, the spiral azimuth angle of the pipe and the axial self-feeding displacement s; wherein the Lagrange equation is as follows: Qq is the generalized force applied to the pipe, L is the Lagrange quantity, and q is the generalized coordinate system and is a first derivative of q.

This invention relates to a time-domain calculation method for the dynamic response of suspended tunnels under multi-load coupling, belonging to the field of dynamic response analysis of suspended tunnels. Addressing the problems of poor versatility and difficulty in handling multi-load coupling and structural variations caused by inconsistent governing equations in traditional methods, this invention proposes establishing a unified equation of motion for the tunnel body. This equation is decomposed into a system of generalized coordinate ordinary differential equations using the modal superposition method. An implicit Newmark-β method is employed for solving the equations, and a sub-loop iteration mechanism is embedded to achieve dynamic coupling between loads and tunnel motion. By independently modeling anchor cable constraint reactions and using a modular environmental load interface, the method is compatible with complex terrain and various load coupling effects. This invention improves the versatility and computational efficiency of dynamic response analysis of suspended tunnels, solves the accuracy and stability challenges under multi-load interaction, and provides a reliable basis for engineering design.

The invention provides a novel dynamic modeling method for a fatigue loading device considering the action of a wind power blade, and aims to solve the problem of insufficient modeling precision caused by neglecting the coupling action of a large flexible wind power blade and the loading device in the prior art. The novel fatigue loading device is based on a two-degree-of-freedom 5R parallel robot, adopts a Lagrangian method to construct a kinetic model, and specifically comprises the following steps: analyzing the stress condition of the novel fatigue loading device, and selecting generalized coordinates; and calculating kinetic energy, potential energy and dissipated energy of the system, deducing generalized force corresponding to the generalized coordinates, substituting each energy parameter and the generalized force into a Lagrange equation, and simplifying to obtain a kinetic model. The model incorporates blade quality, rigidity and damping parameters, can accurately reflect dynamic behaviors of the novel fatigue loading device under actual fatigue test conditions, can be used for evaluating loading system performance, provides a basis for device structure optimization and control strategy design, and is suitable for the field of large-scale flexible wind power blade fatigue test.

This invention discloses a method for predicting the pose error of a machine tool slide and the force on the slider, specifically for a double-guide-rail, four-slider linear motion system. First, a unified geometric and mechanical model of the system is established. The guide rail is abstracted as a continuous, smooth curve in space, and the interface between the guide rail and the slider is assumed to be continuous, uniform, and linearly elastic, with constant stiffness coefficients per unit length in both directions. The slide and guide rail are considered rigid bodies. Then, based on the model, the system is decoupled between the horizontal and vertical planes, using the position and attitude errors of the slide as generalized coordinates. Based on deformation compatibility conditions and the principle of minimum potential energy, a balance equation is established between the slide pose error caused by the guide rail contour error and the force on the slider. Solving this equation yields the slide pose error, which is then substituted into the slider force expression to obtain the force and torque distribution of each slider. This method enables the prediction of the multi-degree-of-freedom pose error of the slide and the force state of each slider throughout its entire stroke.

The invention discloses a GLS-based vibroseis-near-surface unified modeling method, relates to the technical field of geophysical exploration and vibroseis, constructs a near-surface pore elastic model, and improves the interaction simulation precision among a heavy hammer, a substrate and pore fluid. According to the method, a generalized coordinate system based on a heavy hammer, ground and fluid displacement and velocity is used, an energy structure function constrained by a sweep frequency signal is established under the GLS theory, an Euler-Lagrange equation is substituted, and a kinetic equation considering near-surface pore structure characteristics is derived; and then solving the equation by adopting a Newmark-Beta method to finish the simulation experiment of the input and output signals of the vibroseis. According to the model, near-surface pore structure characteristics and a vibration energy attenuation mechanism thereof are fully considered, the modeling capability of an existing vibroseis system on porous medium response is remarkably improved, and a parameter matrix definitely represents the mass, rigidity and damping coupling relation of a heavy hammer, a base plate, a ground framework and pore fluid.

The invention relates to a method for efficiently calculating the temperature of a spacecraft structure in a thermal environment, and belongs to the technical field of spacecrafts. Establishing an antenna model based on finite element software, extracting a thermal parameter matrix, and establishing a traditional heat conduction equation; secondly, simulating a multi-orbit periodic temperature field through spaceflight thermal analysis software, and storing a transient temperature sample; secondly, processing a temperature sample by adopting intrinsic orthogonal decomposition (POD), and constructing a POD base mode to realize ten-thousand-dimensional model order reduction; thirdly, establishing a dimensionality reduction heat conduction equation, modeling a radiation heat flow item of the dimensionality reduction heat conduction equation by a feedforward neural network, and implicitly fitting quadruple nonlinearity through a ReLU activation function by the network by taking a temperature generalized coordinate as an input; finally, neural network expression is combined with a POD method, and a complete low-order nonlinear radiation heat conduction equation is established; the method has both physical mechanism completeness and calculation efficiency, wherein the model dimension is reduced by two orders of magnitude, and the real-time processing requirement of a satellite-borne platform is met; the neural network retains the radiation nonlinear nature, and the prediction precision is high.

A method for determining the hinge reaction torque in the event of a holding-moment hinge deployment impact includes: establishing the system dynamic equations; setting the current values ​​(HoldMarker_H5, HoldMarker_H6) of the holding hinge flags for hinges H5 and H6, and the updated values ​​(HoldMarker_H5_update, HoldMarker_H6_update) of the holding hinge flags for hinges H5 and H6; updating the system generalized coordinate matrix q, the generalized coordinate first-order derivative matrix with respect to time, and obtaining the system generalized coordinate q at the next moment. i The constraint reaction force of each hinge is compared with the structural strength of the hinge. This invention solves the problem of high safety design and testing costs of the entire satellite hinge caused by the large impact torque during satellite antenna deployment.

The application provides a character recognition method and system based on a Hamiltonian shape conservation network, a medium and equipment, belonging to the technical field of character recognition based on deep learning. The system comprises an input module, a feature extraction module, an initial feature generation module, an energy conversion network ETN, a Hamiltonian dynamics evolution network HDNN and a Transformer decoder. The input module acquires an optical character recognition (OCR) image and performs preprocessing; the feature extraction module performs feature extraction on the preprocessed OCR image to obtain a spatial feature map F; the initial feature generation module performs serialization processing and semantic conversion on the spatial feature map F based on Mamba technology to obtain initial generalized coordinates and initial generalized momentum of a Hamiltonian system; the Hamiltonian dynamics evolution network HDNN performs Hamiltonian dynamics evolution according to and according to the Hamiltonian energy conservation, and outputs an evolution result; and the Transformer decoder obtains a character recognition result through decoding, thereby improving the character recognition accuracy in a complex writing scenario.

The invention belongs to the technical field of seismic wave field forward modeling, and particularly relates to a high-precision seismic wave field forward modeling method. Inputting a longitudinal wave velocity model, a transverse wave velocity model, a density model, a longitudinal wave anisotropy parameter model, a transverse wave anisotropy parameter model, a polarization angle model, an azimuth angle model, a longitudinal wave quality factor model, a transverse wave quality factor model and a corresponding body-fitted grid which comprise undulating surface characteristics; based on an input parameter model, constructing a viscoelastic TTI medium wave equation under a three-dimensional Cartesian coordinate system, establishing a mapping relation between the Cartesian coordinate system and a body-fitted grid coordinate system through generalized coordinate transformation, and converting the viscoelastic TTI medium wave equation into the body-fitted grid coordinate system to obtain a viscoelastic TTI medium wave equation; and a viscoelastic TTI medium wave equation under the three-dimensional body-fitted grid coordinate system is obtained. And discrete solution is carried out through a high-precision Runge-Kutta method and a high-order co-location grid finite difference method, so that high-precision seismic wave field forward modeling simulation under the three-dimensional undulating surface viscoelastic TTI medium is realized.

The invention provides a multi-flexible-body coupling dynamics modeling method and device for a rotary non-inertial system gear system, and the method comprises the steps: dividing the gear system into a shaft system substructure and a box body substructure, and respectively building the kinematic equations of the shaft system substructure and the box body substructure; a generalized coordinate kinetic equation of the box body is obtained, the generalized coordinate kinetic equation comprises fixed-axis rotation coordinates and flexible node coordinates, and the non-inertial system effect of random body rotation is included; a shaft system generalized coordinate kinetic equation is obtained, discretization is carried out, and a composite motion effect is included; performing order reduction on the box body and the shaft system through a state space fixed interface modal synthesis method, retaining interface nodes and mapping internal nodes to a low-order modal space; bearing coupling is achieved through multi-point constraint, and shafting bearing force is equivalently distributed to flexible joints of a box body; establishing a gear meshing coupling model, and loading a gear backlash, a meshing error and time variable stiffness; and all subsystem equations are coupled to form an integral reduced-order model, and a dimension-increasing fine integration algorithm is adopted for solving. The invention provides an efficient and accurate tool for the design of a gear transmission system.

This invention discloses a theoretical model for spiral self-feeding straightening of pipes, including, under the assumption that the rotation axis of the pipe coincides with the bending plane and axial roll of the pipe is ignored, establishing the total kinetic energy of the pipe based on the thin-wall assumption. T The theoretical formula is derived; neglecting the plastic dissipation of the pipe, a simplified potential energy model for the pipe is established based on the unified curvature theorem of reciprocating bending and the bidirectional effect. V The theoretical formula is used to model the motion trajectory of the pipe based on the Lagrange equation, thereby obtaining a set of motion trajectory equations. These equations include the circumferential bending angle of the pipe, the helical azimuth angle of the pipe, and the axial self-feed displacement. s The coupling relationship between them; where the Lagrange equation is, Q q For the generalized forces acting on the pipe, L For Lagrange units, q For a generalized coordinate system, , for q The first derivative.

This invention belongs to the technical field of vehicle trajectory control. It discloses a model predictive control method and device for vehicle trajectory tracking based on Lie group Hamiltonian dynamics and the NND (Neural Regular Differential Equation). The steps are as follows: S1, describing the vehicle's attitude and motion using a Lie group; S2, establishing vehicle dynamics equations on the Lie group; S3, constructing the NND based on the obtained vehicle dynamics equations, integrating the derivatives of the generalized coordinates and generalized velocities to obtain predicted values ​​of the generalized coordinates and velocities, comparing the predicted and actual values ​​to calculate the mean square error, and then using it for backpropagation to update and optimize the parameters of the NND; S4, using a vehicle dynamics model trained based on the NND to describe the vehicle's state changes over time, and then using model predictive control for vehicle trajectory tracking control. This invention improves applicability.

The application provides a new fatigue loading device dynamics modeling method considering the action of a wind power blade, and aims to solve the problem of insufficient modeling accuracy caused by ignoring the coupling action of a large flexible wind power blade and a loading device in the prior art. The new fatigue loading device is based on a 2-DOF 5R parallel robot, and a dynamics model is constructed by using the Lagrange method, and the specific steps include: analyzing the stress condition of the new fatigue loading device, selecting generalized coordinates; calculating the kinetic energy, potential energy and dissipation energy of the system, deducing the generalized force corresponding to the generalized coordinates, substituting the energy parameters and the generalized force into the Lagrange equation, and simplifying to obtain the dynamics model. The model includes the mass, stiffness and damping parameters of the blade, can accurately reflect the dynamic behavior of the new fatigue loading device under actual fatigue test working conditions, can be used for evaluating the performance of the loading system, can provide a basis for device structure optimization and control strategy design, and is suitable for the field of large flexible wind power blade fatigue testing.

The application discloses a knowledge graph entity field conflict detection method based on semantic processing and relates to the technical field of natural language processing, and comprises the following steps: S1, generating a static semantic feature vector by encoding entity attribute features through semantics; S2, calculating the vector from a semantic particle to a category clustering center as field gravity; S3, iteratively solving the change rate of the generalized coordinates and the generalized momentum of the semantic particle through a Hamilton equation; S4, calculating the tangent space Jacobian matrix of the dynamic state sequence and the local Lyapunov index of the semantic particle; S5, performing reverse time integration on the Hamilton equation; S6, generating a semantic dissipation coefficient by using a Langevin equation parameter; and S7, correcting the entity attribute features. The application overcomes the limitations of traditional methods, such as the ignorance of the dynamic evolution mechanism, the difficulty in detecting implicit conflicts and the non-optimization of the correction strategy, and provides an efficient solution for the dynamic consistency maintenance of a knowledge graph.

This invention discloses a unified modeling method for controlled seismic sources and near-surface surfaces based on GLS, relating to the fields of geophysical exploration and controlled seismic sources. It constructs a near-surface porosity-elastic model, improving the simulation accuracy of the interaction between the weight, the base plate, and the pore fluid. The method uses a generalized coordinate system primarily composed of the displacement and velocity of the weight, the ground, and the fluid. Under GLS theory, it establishes an energy structure function constrained by a swept-frequency signal. Substituting this into the Euler-Lagrange equations, it derives dynamic equations considering the characteristics of the near-surface pore structure. Then, the Newmark-Beta method is used to solve the equations to complete simulation experiments of the input and output signals of the controlled seismic source. The model of this invention fully considers the characteristics of the near-surface pore structure and its vibration energy attenuation mechanism, significantly improving the modeling capability of existing controlled seismic source systems for the response of porous media. Its parameter matrix clearly characterizes the mass, stiffness, and damping coupling relationships of the weight, the base plate, the ground skeleton, and the pore fluid.

The invention discloses a dynamic modeling method and system for a double-internal-gearing planetary gear transmission system, and relates to the technical field of planetary gears, and the method comprises the steps: defining components and a transmission form of the transmission system, only considering the vibration of each component in a torsion direction, taking the center of each component as a coordinate origin, constructing a coordinate system, and carrying out the dynamic modeling of the transmission system; defining a system generalized coordinate based on four degrees of freedom in the coordinate system; wherein the components comprise a sun gear, a planet gear, a planet carrier and an outer gear ring; deducing elastic deformation of a sun gear and planet gear meshing pair, elastic deformation of an outer gear ring and planet gear meshing pair and tangential and radial deformation of planet gears based on system generalized coordinates, and establishing a deformation formula; based on a deformation formula, constructing a dynamic differential equation set of the double-internal-gearing planetary gear transmission system; and calculating the dynamic excitation of the system through finite element analysis, inputting the excitation into the equation set, and solving the nonlinear response characteristics of the system. According to the method, nonlinear dynamic modeling of the double-internal-gearing planetary gear transmission system can be realized.

The application discloses a kind of space multibody system dynamics modeling method based on Lagrange multiplier method, first establish the coordinate conversion matrix of local to global coordinate system of each component in space;With centroid coordinates and Euler angle definition active component pose, determine generalized coordinate;Position constraint equation is established to kinematic pair, after first and second derivative, obtain the numerical expression of velocity, acceleration constraint equation;Through the cross product property of space angular velocity matrix and vector and the symmetry of vector cross product, the velocity constraint equation is converted, and the numerical expression of Jacobian matrix and time partial derivative term is obtained;Based on the modified Lagrange multiplier method, the cross product term of angular velocity and angular momentum of space component rotation is considered, the dynamics equation is established and solved;The correlation law of Euler angle and space angular velocity is established, the conversion of both is realized.Therefore, the method of the application is suitable for various space multibody systems, solves the problem of existing modeling method when dealing with complex constraints, fills the gap of prior art.

The application relates to a rigid-flexible coupling dynamic modeling method and device for height adjustment of a paddy field leveler. W O W Y W And a generalized coordinate system X1O1Y1; according to the vibration theory of an Euler Bernoulli beam, a transverse vibration mode function of the flexible beam under boundary conditions is obtained; according to the two-dimensional world coordinate system X W O W Y W , the generalized coordinate system X1O1Y1 and the transverse vibration mode function of the flexible beam, kinetic energy and potential energy of the flexible beam system are calculated; the force of the force equivalent spring exerted by the height cylinder for controlling the height movement of the leveler on the flexible beam is calculated to obtain the driving torque of the hydraulic cylinder of the flexible beam; the kinetic energy, the potential energy and the driving torque of the flexible beam system are substituted into the Lagrange equation, and the Lagrange equation is discretized by using the assumed mode method to obtain a transverse displacement function of an arbitrary point on the flexible beam changing with time when the height of the flat blade is adjusted. The method can accurately perform kinematic modeling on the flexible beam.

The application discloses a centering tracking control method and device based on FTESO and PNTSMC; the method comprises the following steps: a dynamic model of a centering platform is established, vertical displacement, pitch angle and roll angle of the centering platform are taken as generalized coordinates, and external disturbance and unmodeled dynamics are modeled as lumped disturbance; based on a finite time extended state observer, velocity states of the generalized coordinates and the lumped disturbance are estimated in real time; based on a pre-defined time nonsingular terminal sliding mode control strategy, a control law is designed; the control law controls driving force of a hydraulic cylinder based on disturbance estimation value provided by the finite time extended state observer, so that the centering platform can track an expected trajectory within a preset time. The application can realize fast, accurate and robust tracking of a pose of the centering platform, and allows a user to preset a convergence time, thereby significantly improving performance and reliability of an automatic centering process.