10 results about "Second order differential equations" patented technology

The invention discloses an underwater block stone cushion vibration density parameter control method and system based on vibration settlement, and the method comprises the steps: S100, building a block stone cushion vibration density vibration system based on a spring-damping-concentrated mass theory; s200, carrying out stress analysis on a vibration system of the block stone cushion layer vibration density to obtain an overall kinetic equation of a vibration device and the block stone to be vibrated; s300, combining the overall kinetic equation in the step S200 with the displacement of the vibration system to obtain a third-order differential equation about elastic deformation; s400, combining the overall kinetic equation in the step S200 with a soil body reaction force to obtain a second-order differential equation about elastic deformation; s500, an iterative algorithm based on the Runge-Kutta method is compiled, the differential equation is solved, and a numerical solution of the differential equation is obtained; and S600, obtaining an output parameter in the vibration process, and adjusting an input value of the vibration system according to the output parameter. And the elasticity, damping and plastic deformation of the block stone cushion layer in the vibration compaction process are comprehensively considered.

The invention discloses a tool path fairing method based on a B-spline curve, and the method comprises the steps: representing an original tool path through the B-spline curve, carrying out the Fourier low-pass filtering of an original curvature vector, and removing the high-frequency noise to smooth the curvature; then re-parameterizing the B spline curve by using an arc length parameter, constructing a second-order differential equation with a boundary condition, and ensuring that the end point position and the tangential direction of the curve meet the requirements of an original path; secondly, discretizing an equation based on a Rayleigh-Ritz method, constructing a stiffness matrix and a right-end term, and generating a linear equation set; and the solving of the linear equation set is converted into a least square optimization problem with deviation tolerance constraint, and the deviation of a fairing curve and an original curve is limited. And finally, solving an optimization problem, and outputting a fairing tool path curve which meets the endpoint position and tangential constraint and controls the vertex deviation to be within an allowable range.

The invention relates to a method for solving a refracted starlight path in atmosphere, and belongs to the field of celestial navigation. The method comprises the following steps: firstly, carrying out Taylor expansion on a Snell theorem by utilizing an infinitesimal thought to obtain a function of a curvature of a starlight path relative to a refractive index; then constructing a second-order differential equation of a refracted starlight path by using a Gladstone-Dale theorem and a curvature equation under a Cartesian coordinate system; and finally, carrying out numerical integration on the differential equation, and solving to obtain an expression of a refracted starlight path in the atmospheric profile. According to the method, the existing atmospheric density observation data is directly utilized, the method does not depend on an atmospheric density mathematical model, and the propagation path of the refracted starlight in the complex atmospheric environment is calculated by utilizing a numerical integration method, so that the problem of overlarge deviation from the actual working condition caused by ideal hypothesis and a simple atmospheric mathematical model is avoided. The method is especially suitable for refraction light path resolving of media with irregular refractive indexes, continuous and guidable distribution, and can improve the precision of quantity measurement and the precision of navigation and positioning in an indirect sensitive horizon navigation and positioning method.

A control method for a lower limb rehabilitation exoskeleton robot includes: establishing a single-leg lower limb exoskeleton dynamic model using motor output torque as the system control input signal, and transforming it into a second-order differential equation of the lower limb exoskeleton robot using the Euler-Lagrange method to complete system modeling; designing a non-singular terminal sliding surface based on the lower limb rehabilitation exoskeleton robot model; designing a super-torsional sliding mode control algorithm based on the constructed non-singular terminal sliding surface for the established lower limb rehabilitation exoskeleton robot dynamic model; furthermore, initializing the lower limb exoskeleton robot is required, and the exoskeleton's motion mode is determined through a signal input device; simultaneously, the signals collected by the joint motor encoders are input to the super-torsional terminal sliding mode controller, which calculates the motor output torque that has a good tracking effect on the desired gait trajectory based on the information returned by the sensors and according to the current exoskeleton joint angle and the set joint angle.

A method (300) for simulating vibrations in an electric motor including a rotatable shaft which extends horizontally and is secured, via at least two intermediary elements of finite stiffness on each side of a rotor, to a stator. The method comprises: providing (310) a 1-degree-of-freedom, 1-DOF, model to represent the electric motor in terms of a horizontal component of a transverse displacement of the shaft; simulating (320) vibrations in the shaft by solving a second-order differential equation for said displacement, which differential equation includes an oscillating drive term; and performing a technical manipulation (330) relating to the electric motor on the basis of the vibration simulation.

The application discloses a kind of based on vibration sinking amount underwater block stone cushion vibration compaction parameter control method and system, method includes: S100, based on spring-damping-mass theory, the vibration system of block stone cushion vibration compaction is established;S200, the vibration system of block stone cushion vibration compaction is stressed analysis, obtains the overall dynamics equation of vibration device and reference vibration block stone;S300, the overall dynamics equation in step S200 is combined with the displacement of vibration system, obtains the third-order differential equation about elastic deformation;S400, the overall dynamics equation in step S200 is combined with the reaction of soil, obtains the second-order differential equation about elastic deformation;S500, the iteration algorithm based on Runge-Kutta method is prepared, differential equation is solved, and its numerical solution is obtained;S600, the output parameter in vibration process is obtained, and the input value of vibration system is adjusted according to the output parameter. Overall consideration block stone cushion in vibration compaction process elasticity, damping and plastic deformation.

The invention discloses a nine-phase eight-vector SVPWM (Space Vector Pulse Width Modulation) control method based on dynamic sliding mode control in a nine-phase rectification system, and belongs to the field of multiphase motor rectification. The invention provides a solution for the problems of harmonic suppression, robustness and the like of the existing multi-phase rectification technology. According to the method, a mathematical model is obtained through analysis based on the topology of a nine-phase rectification circuit; in the modulation technology, on the basis of a multi-phase space decoupling transformation equation, a nine-phase eight-vector SVPWM control strategy is adopted, and the switching time of an MOSFET is calculated; in closed-loop control, a reactive component adopts sliding mode control, and a sliding mode surface is constructed to solve a control law of the reactive component; a second-order differential equation is constructed on an active component, a new sliding mode surface is constructed on the basis of a traditional sliding mode variable structure, and a discontinuous item is transferred to a first-order derivative of a control quantity to obtain a dynamic sliding mode control law which is essentially continuous in time. According to the invention, a nine-phase eight-vector and dynamic sliding mode combined control strategy is adopted, and the problems of overlarge low-order harmonics in a multi-phase rectification system and jittering in sliding mode control are solved.

The invention discloses a model order reduction method based on a first-order singular perturbation theory and a grid-connected system stability analysis method, and belongs to the field of transient stable operation and control of a novel power system, and the method comprises the steps: determining a differential equation set and an algebraic equation set of a new energy grid-connected system; calculating a time constant of a system state quantity, and dividing the new energy grid-connected system into a fast subsystem and a slow subsystem based on the time constant; according to the first-order singular perturbation theory, after derivation is conducted on the differential equation set of the fast subsystem, a second-order differential item in the second-order differential equation set of the fast subsystem is made to be 0, then the second-order differential item is substituted into the differential equation set and the algebraic equation set of the fast subsystem, and a first-order perturbation equivalent model algebraic equation is obtained; therefore, the first-order perturbation dynamic state-considered order reduction model of the new energy grid-connected system is obtained by combining the differential equation set and the algebraic equation set of the slow subsystem, the dominant dynamic state in the new energy grid-connected system can be effectively identified, and model order reduction is realized, so that the stability analysis efficiency is improved, and the accuracy is ensured.

The invention discloses a battery pack active equalization system based on a differential equation model, and aims to solve the problem of inconsistency of single batteries in a battery pack, improve the performance of the batteries and prolong the service life of the batteries. The system comprises a battery pack, an energy conversion and distribution module, a multipath gating module, a data acquisition module and a control circuit module. The control circuit module realizes intelligent balance management based on acquired data and an innovative differential equation model. According to the equalization method, an equivalent circuit model including equivalent inductance, equivalent dynamic internal resistance, equivalent capacitance and equivalent static internal resistance is constructed for a charging loop of a battery unit. By establishing and solving a second-order differential equation describing current changes, key electrical parameters of a loop can be accurately obtained, and multi-dimensional analysis is carried out by using the parameters. And through data driving and modeling control, high-precision, high-efficiency and high-intelligence active equalization of the battery pack is realized, and the service life of the battery is remarkably prolonged.

The application belongs to the technical field of motor system control, and discloses a motor selection method based on expected tracking tasks and controller structures, which comprises the following steps: first, a second-order differential equation describing the generalized position and generalized speed characteristics of a motor is established; second, the load and expected trajectory involved in the expected tracking task are determined, and constants are selected to represent the upper and lower bounds of the load and expected trajectory; third, an error variable is defined, and an adaptive tracking controller is designed based on the second-order differential equation; fourth, a Lyapunov function is selected to analyze the upper and lower bounds of the error variable; fifth, based on the controller structure, controller parameters, initial value of the error variable, upper and lower bounds of the error variable, and expected task, the upper and lower bounds of the required control torque of the motor and the upper bound of the power are determined, and motor selection is completed according to the boundary conditions. The application realizes the analysis of the peak torque and maximum power of the motor and the tracking of the expected motor position.