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39 results about "Second order differential equations" patented technology

Active feedback-controlled bass coloration abatement

InactiveUS7190796B1Reduces low-frequency colorationImprove sound qualityEar treatmentGain controlDamping ratioEngineering
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.
Owner:DESIGN IMAGING & CONTROL

Real time parameter identification method of air-conditioning belonged building second order equivalent thermal parameter model

ActiveCN105159085ABuild accuratelyMake up for lack of researchAdaptive controlSmart gridSimulation
The invention discloses a real time parameter identification method of an air-conditioning belonged building second order equivalent thermal parameter model, and a real time built air-conditioning belonged building second order equivalent thermal parameter model, which are used to build and real time control an air-conditioning load equivalent polymerization model; a second order differential equation group of the air-conditioning load belonged building is built and the input & output quantity and the parameter needs to be identified are determined; the real time data acquisition of the input & output quantity is conducted through a high-grade metering terminal of an intelligent power grid; data transmission to a load aggregator is conducted; and the real time parameter identification is conducted through the cooperation particle swarm algorithm by the load aggregator. According to the invention, research insufficient in domestic air-conditioning load real time modeling is made up; an accurate air-conditioning load model is constructed; and technical support for demand response is provided.
Owner:SOUTHEAST UNIV

Auto-catalytic oscillators for locomotion of underwater vehicles

A system is provided to control maneuvering flapping foils of an underwater vehicle. An oscillator generates periodic signals in which effects of external disturbances are minimized or amplified as required; the periodic signal can be either sinusoidal or can depart significantly from a sinusoid; the amplitude and frequency are varied by changing the oscillator parameters and the phase between the signals are varied by changing the parameters. The oscillator restores the parameters after a disturbance. Since the oscillator functions without external sensors, the oscillator serves as an inner-loop controller with a centralized control. An open loop control architecture for the controller, results in a motion where the vehicle maneuvers execute as force and moment commands. The non-linear, auto-catalytic oscillator can be realized using a variety of second-order differential equations. An oscillator model is added to a conventional motor control, where the outputs of the oscillator control the foils in real-time.
Owner:UNITED STATES OF AMERICA +1

Active disturbance rejection control method used for fast reactor power and coolant outlet temperature

The invention belongs to the nuclear power plant control technology field and especially relates to an active disturbance rejection control method used for fast reactor power and a coolant outlet temperature. The method comprises the following steps of establishing point reactor dynamic equation according to a neutron characteristic in a reactor, establishing the average temperature equation of afast reactor fuel and a coolant outlet temperature equation according to the law of conservation of macroscopic energy, and establishing the reaction equation of a control rod and a reactor overall reactivity equation; acquiring a fast reactor power and coolant outlet temperature second-order differential equation; designing an active disturbance rejection controller based on linear extended stateobserver; determining an extended state observer bandwidth range, and determining a PD bandwidth range by using deviation and executing mechanism motion speed allowing range; giving a coolant outlettemperature during the balance of a system and the fast reactor power during the balance of the system, carrying out LADRC parameter setting, acquiring a controller bandwidth and an observer bandwidth, determining a reactor power control system and a coolant outlet temperature control system, and completing active disturbance rejection control.
Owner:NORTH CHINA ELECTRIC POWER UNIV (BAODING)

Multi-turning-tool parallel turning stability judgment method based on differential quadrature method

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.
Owner:无锡黎曼机器人科技有限公司

Imaging apparatus and image processing method

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.
Owner:CANON KK

Mathematical modeling method for steady-state random power fluctuation of alternating current connecting line

The invention provides a mathematical modeling method for steady-state random power fluctuation of an alternating current connecting line. Power grids are interconnected through the alternating current connecting line, and under the steady-state condition, long-cycle and irregular random power fluctuation on the connecting line is caused by load random fluctuation in the power grids at two ends. Based on a two-area alternating current connecting line power fluctuation model, according to the steady state operation and weak connecting line characteristics of large area power grids, a relation between the random power fluctuation and the power angle difference of equivalent generators is established, and a steady state random power fluctuation mathematical model of a two-area connecting line is obtained by solving a second-order differential equation of the power angle difference of the equivalent generators. The mathematical modeling method is applicable to theoretical and simulation analysis of a power system, the dynamic characteristic and connecting line random power fluctuation mechanism of two large-area interconnection power systems are mastered, the maximum amplitude of the steady-state random power fluctuation is computed, the system can conveniently operate, an analyst can timely take effective measures, and the safety and steady operation level of the power system is improved.
Owner:CHINA ELECTRIC POWER RES INST +1

RSC control-considered analytic method of double-fed wind generator three-phase short-circuit current

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.
Owner:KUNMING UNIV OF SCI & TECH

A safety design method for water tank used in airtightness test of aeroengine casing

A safety design method for water tank used in airtightness test of aeroengine casing is disclosed. Based on the relevant technical parameters of the water tank and the machine case with specific requirements, By using the equations of motion and gas state, combining with dimensionless time and pressure and initial conditions, the second order differential equations of dimensionless pressure and flight angle of plug fracture are established, the differential equations can be used to calculate different internal pressures, the initial and angular velocities of the plug fragment as it exits at the debris size, and then the mechanics equation is established by using the fluid mechanics principle, a method for calculating the impact velocity of plug considering the resistance coefficient of medium is established, the theorem of kinetic energy and the law of conservation of energy are used to model and estimate the wall thickness of water tank, the impact force of plug fragment and the impact strength of fragment. In order to meet the needs of engineering calculation, a conservative formula for calculating the initial velocity of plug separation is established. Finally, the safety designscheme of water tank for aero-engine casing airtightness test which meets the technical requirements can be obtained.
Owner:NANCHANG HANGKONG UNIVERSITY

Modeling method for aircraft longitudinal phase plane directly based on three-dimensional model

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.
Owner:XIAN FEISIDA AUTOMATION ENG

A decentralized electric heating load modeling system based on a parameter library and a modeling method thereof

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.
Owner:NORTHEAST DIANLI UNIVERSITY +1

An Analytical Method for Three-phase Short-Circuit Current of Doubly-fed Fans Considering RSC Control

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.
Owner:KUNMING UNIV OF SCI & TECH

Silicon-based annular resonant cavity structure for solving second order differential equation

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.
Owner:SHANGHAI JIAO TONG UNIV

An active disturbance rejection control method for a Cuk converter

The invention provides an active disturbance rejection control method of a Cuk converter, belonging to the technical field of electronic control. The invention solves the problems that the input voltage disturbance, the parasitic parameter disturbance and the load disturbance of the Cuk converter in the prior art have serious influence on the output voltage. The method comprises the following steps: a, establishing a mathematical model of a Cuk converter according to a Cuk circuit; B, designing a second-order differential equation to determine a tracking differentiator, and extracting an original signal and a derivative signal of an input reference voltage in a mathematical model of the Cuk converter through the tracking differentiator; C, establishing an extended state observer accordingto the second-order nonlinear system to estimate the total disturbance of the system; D, determining the nonlinear state error feedback control law by nonlinear combination of the error signal, its derivative signal and its integral signal, and the control quantity of the system is composed of the nonlinear combination and the total disturbance. This control method can make the output voltage giveyou better robustness, adaptability and stability.
Owner:HAINING SWITCH FACTORY CO LTD +2

Aspheric surface analysis method for simulating human eye crystalline lens based on three-liquid lens structure

The invention discloses an aspheric surface analysis method for simulating a human eye crystalline lens based on a three-liquid lens structure. A three-layer liquid structure of a first conductive liquid + an insulated liquid + a second conductive liquid is employed to simulate a structure of a human eye crystalline lens. a voltage is applied on the first conductive liquid and the second conductive liquid to change the contact angles of the conductive liquids and the insulated liquid, therefore the interface curvature is changed and zooming is achieved. The structure is subjected to the Laplace formula, and a second-order differential equation of an aspheric surface type and a density difference is obtained. The Runge-Kutta algorithm is employed to calculate the second-order differential equation of an aspheric surface type and a density difference, and an aspheric surface type arithmetic solution is obtained. The obtained arithmetic solution is subjected to fitting through the even-order aspheric surface formula, and a fit aspheric surface formula is obtained. According to the fit aspheric surface formula, the structure is subjected to imaging analysis. An adjustable visual model can be provided for achieving simulation of a zooming characteristic of a human eye crystalline lens.
Owner:NANJING UNIV OF POSTS & TELECOMM

Disturbance compensation control method for CSTR system

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.
Owner:扬中市广善科创服务有限公司

Numerical analysis method of anti-aliasing filtering circuit in time domain

The invention discloses a numerical analysis method of an anti-aliasing filtering circuit in a time domain. The method comprises the steps of A, creating a current transfer equation set of nodes according to the kirchhoff current law and based on the anti-aliasing filtering circuit; B, performing formal transformation for the transfer equation set, wherein the function relation between an input signal and an output signal can be shown as a second order differential equation; C, solving the equation by the numerical differentiation method to obtain a numerical model of the anti-aliasing filtering circuit. According to the method, a novel method for studying the numerical model of the anti-aliasing filtering circuit in the time domain is proposed, which can perform filtering, and pulse width and amplitude analysis and control for an output pulse signal of a front end pulse detector within the time domain; therefore, the digital model is of practical guide significance for the design and test of filtering and amplitude and width analyzing circuits of an actual pulse signal; the working efficiency of the actual circuit design can be increased, and the target selectivity of an electronic device is improved.
Owner:CHENGDU UNIVERSITY OF TECHNOLOGY

A Calculation Method for Shell Stress of Solid Rocket Motor

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.
Owner:HEFEI UNIV OF TECH

Distributed electric heating load modeling system based on measured parameter identification and modeling method thereof

The invention relates to a distributed electric heating load modeling system based on measured parameter identification and a modeling method thereof. The modeling method is characterized in that, theelectric heating system operation state time sequence data in the past period of time is acquired by constructing an electric heating load modeling system, and the initial parameters of the second-order model are simplified through the cloud computing system and the fitting electric heating load on the basis of actually measured time sequence data and historical data; the initial parameters are further corrected according to historical temperature database parameters; an electric heating load simplified second-order model is obtained. The electric heating load modeling basic principle for identifying the second-order differential equation through actual measurement parameters is determined. Meanwhile, a modeling method and a system architecture which can be implemented by a computer are provided. The invention can provide an accurate model for electric heating load. In this way, an actual simulation result is obtained, and the accuracy of the electric heating load model is improved.
Owner:NORTHEAST DIANLI UNIVERSITY +1

Four-element Phase Plane Analysis Equivalent Modeling Method for Three-Dimensional Motion of Aircraft at High Angle of Attack

InactiveCN106508034BReduce or even avoid analysisAvoid aerodynamicsSpecial data processing applicationsNonlinear phenomenaInstability
The invention relates to an equivalent model modeling method for four-element phase plane analysis of a large angle of attack three-dimensional motion of an aircraft, which belongs to the field of flight mechanics and control technology and is used to solve the technical problem of poor stability of the analysis model established by the existing modeling method . The established analytical model avoids incorrect approximations such as ignoring the aerodynamic effect in the aerodynamic moment equation. The equivalent second-order differential equations are obtained through the aircraft motion equation and the experimentally obtained aerodynamic force and aerodynamic moment models; through the equations, It can directly apply the phase plane analysis method for theoretical analysis or use the Ode45 module in MATLAB for direct numerical analysis; this model can be used to analyze the situation where the pitch angle is 90 degrees, and more nonlinear phenomena and system instability and unsafety can be found Factors can reduce or even avoid problems such as instability and unsafe flight caused by the analysis model.
Owner:NORTHWESTERN POLYTECHNICAL UNIV

Modal modeling method of kinematic system with spatial six degrees of freedom

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.
Owner:HARBIN INST OF TECH

Stability Judgment Method for Multi-tool Parallel Turning Based on Differential Quadrature Method

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.
Owner:无锡黎曼机器人科技有限公司

Solid rocket engine shell seal head stress calculation method

The invention discloses a solid rocket engine shell seal head stress calculation method which mainly comprises the following steps: S1, intercepting a unit body from a shell, and establishing an equilibrium equation according to a symmetry condition and assuming that a film force is not close to a critical value; s2, introducing two new variables, and converting the balance equation into two second-order differential equations; s3, converting the two second-order differential equations into a fourth-order homogeneous linear differential equation; and S4, solving the differential equation by utilizing the connection condition of two adjacent shell elements, and further calculating the stress distribution of each part of the seal head. The method is used for calculating an orthotropic rotating surface shell bearing axisymmetric loads under small internal pressure, on a complex surface with variable angles, variable thicknesses and variable stiffness, the size and distribution of the linear stress of the seal head are solved through an accurate control equation of the seal head and a fragmentation analysis method, the result is matched with a finite element result, and a theoretical basis can be provided for the strength analysis of the seal head of the solid rocket engine shell.
Owner:HEFEI UNIV OF TECH

Training method and system of deep neural network based on critical damping momentum

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.
Owner:SHENZHEN GRADUATE SCHOOL TSINGHUA UNIV

Adjustable second-order differential equation derivation device

The invention provides an adjustable second-order differential equation derivation device and belongs to the technical field of blackboards. The device comprises a demonstration board, vertical rods, supporting legs, rolling wheels, a reinforcing cross rod, a gel pen storage box, an ink dust receiving assembly, an auxiliary stable pedal assembly, and a dust sweeping assembly. By means of the ink dust receiving assembly, ink dust generated during writing and wiping can be received; by means of the auxiliary stable pedal assembly, the stability of the whole device can be improved by treading a pedal and utilizing rigid connection between the pedal and the whole device, the demonstration board does not shake during writing, and the comfort degree and definition of writing are improved; by means of the dust sweeping assembly, ink dust borne by a fixing frame can be swept; the gel pen storage box is divided into two areas by a partition plate, so that gel pens which can be used and gel pens which cannot be used can be separately stored, and the gel pens are convenient to take and use.
Owner:CHONGQING UNIVERSITY OF SCIENCE AND TECHNOLOGY
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