39 results about "Second order differential equations" patented technology

A system for actively damping the low-frequency coloration of sound in a listening room is provided comprising an acoustic wave sensor, an acoustic wave actuator, and an electronic feedback controller. The listening room defines at least one mode of low-frequency coloration. The acoustic wave actuator is substantially collocated with the acoustic wave sensor within the listening room. The electronic feedback controller is operative to generate a signal at its output by applying a feedback controller transfer function. The feedback controller transfer function comprises a second order differential equation including a first variable representing a predetermined damping ratio and a second variable representing a tuned natural frequency and creates a 90 degree phase lead substantially at the resonant frequencies of at least one mode of low-frequency coloration. The feedback controller output signal represents a rate of change of volume velocity to be produced by the acoustic wave actuator. Further provided are methods for actively damping the low-frequency coloration of sound within a listening room and systems for actively treating noise within a fluid-carrying duct, including those which employ active low- and high-pass acoustic filters.

The invention relates to a decentralized electric heating load modeling system based on a parameter library and a modeling method thereof. By constructing the electric heating load modeling system, The time series data of the electric heating system in the past period of time are obtained. Based on the measured time series data and the historical data, the initial parameters of the simplified second-order model of electric heating load are fitted by cloud computing system, and then the initial parameters are modified according to the parameters of the historical temperature database to obtainthe simplified second-order model of electric heating load. The basic principle of electric heating load modeling for identifying second order differential equation with measured parameters is determined, and a computer-realizable modeling method and system architecture are proposed. The invention can provide an accurate electric heating load model, obtain a simulation result close to reality, andimprove the accuracy of the electric heating load model.

The invention relates to a RSC control -considered analytic method of double-fed wind generator three-phase short-circuit current, belonging to the technical field of wind power generation system fault analysis. The method comprises the following steps: listing a DFIG stator and rotor voltage equation, a stator and rotor flux-linkage equation and a rotor voltage equation of RSC control; determining an analytic expression of stator flux linkage after fault happens; getting a rotor current second order differential equation; further solving the rotor current second order differential equation, and obtaining a RSC control -considered DFIG rotor short-circuit current analytic expression; further obtaining a stator current equation, substituting the stator flux linkage analytic expression and the rotor current analytic expression into the stator current equation, namely obtaining the RSC control -considered DFIG stator short-circuit current analytic expression. The method provided by the invention can accurately calculate the analytic expression of the rotor side converter-considered double-fed induced wind generator three-phase short-circuit current, and has very important significancein model selection and protection action feature analysis of power system equipment containing the double-fed induced wind generator.

A silicon-based annular resonant cavity structure for solving a second order differential equation comprises a signal generation module, a resonant cavity signal solving module and a signal analyzing module, wherein the signal generation module is connected with an input of the resonant cavity signal solving module; the signal analyzing module is connected with an output of the resonant cavity signal solving module; and the resonant cavity signal solving module is formed by a straight waveguide and a self-coupling resonant cavity with an edge connected with the straight waveguide. The second order differential equation is solved by adjustments of coupling strength of interaction of optical models in the silicon-based annular resonant cavity; adjusting complexity is reduced; and solving process stability is improved.

Disclosed is an imaging apparatus for generating data of a phase image based on an interference pattern acquired by a shearing interferometer, including: a differential phase data calculating unit that calculates first differential phase data expressing a change of a phase in a first direction and second differential phase data expressing a change of a phase in a second direction, based on interference pattern data generated by an electromagnetic wave transmitted through a subject; a second-order differential phase data calculating unit that calculates first second-order differential phase data by differentiating the first differential phase data in the first direction, and calculates second second-order differential phase data by differentiating the second differential phase data in the second direction; and a phase data calculating unit that calculates the phase image by solving a second-order differential equation including the first and second second-order differential phase data as functions.

The invention discloses a disturbance compensation control method for a CSTR system and belongs to the technical field of automatic control. The method constructs an auxiliary system based on a disturbance observer theory by utilizing a dynamic input-output model in a CSTR system mathematical model, and then designs a novel disturbance observer. In the CSTR control system, output physical quantityis reactor temperature and cooling jacket temperature, an intermediate variable chemical reaction concentration in a CSTR system mathematical model expression is eliminated according to the CSTR system mathematical model expression, so as to obtain a second-order differential expression between the reactor temperature and a reaction input concentration. By using a second-order differential equation, the auxiliary system with the same structure is constructed, an output is z1, an input is h, and h is K times of error between x2 and z1. In the novel disturbance observer, an estimated value of disturbance of the CSTR system is q times of a difference between h and u1, wherein q is a system coefficient. The disturbance compensation control method for the CSTR system has the advantages of being easy to realize, stronger in load resistance, and capable of improving system performance and realizing better control effect.

The invention provides an active disturbance rejection control method of a Cuk converter, which belongs to the technical field of electronic control. It solves the problem that the output voltage is seriously affected by input voltage disturbance, parasitic parameter disturbance and load disturbance in the prior art. The method comprises: a, establishing a mathematical model of the Cuk converter according to the Cuk circuit; b, designing a second-order differential equation to determine the tracking differentiator, and extracting the original source of the input reference voltage in the mathematical model of the Cuk converter through the tracking differentiator signal and derivative signal; c. Establishing an extended state observer based on the second-order nonlinear system to estimate the total disturbance of the system; d. Using the error signal and its derivative signal and its integral signal for nonlinear combination to determine the nonlinear state error feedback control The control quantity of the system is constituted by the above-mentioned nonlinear combination and the total disturbance. This control method can make the output voltage have better robustness, adaptability and stability.

The invention discloses a method for calculating the stress of the head of a solid rocket motor shell, which mainly includes the following steps: S1. Cutting out a unit body from the shell, and establishing a balance equation based on the symmetry condition and assuming that the membrane force is not close to the critical value ; S2, introduce two new variables, transform the balance equation into two second-order differential equations; S3, transform the two second-order differential equations into a fourth-order homogeneous linear differential equation; S4, use two adjacent shells The differential equation is solved according to the handover conditions of the elements, and then the stress distribution around the head is calculated. This method is used to calculate the orthotropic rotating surface shell bearing axisymmetric load under small internal pressure. On the complex shape surface with variable angle, variable thickness and variable stiffness, the precise control equation of the head is used, The magnitude and distribution of the linear stress of the head are solved by the slice analysis method, and the results are in good agreement with the finite element results, which can provide a theoretical basis for the strength analysis of the head of the solid rocket motor casing.

The invention provides a modal modeling method of a kinematic system with spatial six degrees of freedom, which comprises the following steps: scattering a parallel kinematic system with complex spatial six degrees of freedom into a plurality of substructures; computing the modalities of the previous orders of the substructures by adopting a substructure transfer matrix method to acquire low-order modality characteristics of the substructures; constructing a modal matrix; converting physical coordinates into modal coordinates by modal coordinate conversion; establishing a modal kinematic second order differential equation for each substructure; removing the redundant degree of freedom; carrying out modal synthesis on each substructure, thereby establishing an integral modal kinematic equation of the parallel kinematic system with spatial six degrees of freedom to acquire a modal model of the parallel kinematic system with spatial butted six degrees of freedom; and finally, converting the modal model into physical coordinates through coordinate conversion to acquire a physical spatial dynamic equation. The modal modeling method of the kinematic system, which is provided by the invention, has overlarge working space, overlong kinematic routes of supporting legs and high bandwidth and accuracy requirements of the system, and overcomes the limitation of multi-rigid body modeling of a spatial butted overlarge kinematic system.

The invention discloses a meandering motion analysis method of a flexible bogie of a rail vehicle. The method includes establishing an analysis model of the serpentine motion of the wheelset with lateral movement and no yaw; establishing an analysis model of the serpentine motion of the wheelset with lateral movement and shaking; establishing a flexible bogie model with primary suspension; and analyzing the serpentine motion of the flexible bogie. In order to solve the problem that the method for calculating the meandering motion wavelength of the flexible bogie in the prior art cannot be directly applied to the calculation process of the meandering wavelength of the actual wheelset and the frame, the present invention derives three first-order motions of the free wheelset longitudinal, lateral and shaking motions. The differential equation is substituted into the second-order differential equation of the flexible bogie considering the primary suspension as the excitation of the meandering motion, and the meandering frequency and wavelength of the frame under different wheelset traverses are calculated based on the characteristics of the meandering motion. Computational models are more accurate.

The invention provides a multi-turning-tool parallel turning stability judgment method based on a differential quadrature method. The multi-turning-tool parallel turning stability judgment method comprises the steps that dynamics modeling is carried out on a multi-turning-tool parallel turning system, and a multi-delay second order differential equation is built; a normalized state space equation is built and obtained; the second kind of Chebyshev points is adopted as discrete points in adjacent unit intervals (0, 1) and (-1, 0); speed items are expressed by displacement items at the discrete points based on a Lagrange's interpolation function by using the differential quadrature method; the intervals where the discrete points of delay items are located are judged, and the delay items are expressed by the second kind of Chebyshev points of the intervals where the discrete points of the delay items are located; state transfer matrixes between the adjacent unit intervals are constructed, and the stability of an original system is judged based on the Floquet theory. Compared with traditional single-turning-tool turning, the dynamic characteristic of the multi-turning-tool parallel turning system is analyzed by adopting the differential quadrature method, optimized cutting parameters are obtained, and machining efficiency is greatly improved.

The invention discloses a training method and system of a deep neural network based on critical damping momentum. The method comprises the following steps: S1, starting a new round of iteration; S2, inputting a batch of new images, and calculating traces of a Hessel matrix of a loss function of the neural network, the Hessel matrix being a matrix formed by second derivatives of the loss function to each parameter of the neural network; S3, substituting the trace of the Hessel matrix into a critical damping solution of a second-order differential equation, and calculating to obtain a momentum coefficient of a neural network weight parameter; S4, updating parameters of the neural network in cooperation with a learning rate attenuation strategy; S5, judging whether all image batches are calculated or not, and if so, executing the step S6; if not, returning to the step S2; and S6, judging whether the iteration turns reach the maximum or not, if so, ending the training, and if not, returning to the step S1. According to the method, a stochastic gradient descent method containing momentum is improved, and an ideal training effect is achieved.

The invention provides a modeling method for an aircraft longitudinal phase plane directly based on a three-dimensional model. The built model performs equivalent transformation directly based on an aircraft three-dimensional motion model, and avoids incorrect direct approximate cuased by the aerodynamical moment effect, the lateral-directional influence and the like ignored in an aerodynamic force equation; an equivalent second-order differential equation set is obtained through a three-dimensional aircraft motion equation and aerodynamic force and aerodynamical moment models obtained through experiments; the equation set expresses a system stability model, can directly adopt a phase plane analytical method to perform theoretical analysis, or adopts an Ode45 module and the like in MATLAB (matrix laboratory) to dreictly perform numerical analysis; more non-linear phenomena and unstable factors and unsafe factors of the system can be found out; and problems of unstable and unsafe flight and the like are reduced or even avoided.