63 results about "Linear differential equation" patented technology

A method of stably controlling the temperature of a sample placed on a sample stage to a desired temperature by estimating a sample temperature accurately, the sample stage including a refrigerant flow path to cool the sample stage, a heater to heat the sample stage, and a temperature sensor to measure the temperature of the sample stage. This method comprises the steps of: measuring in advance the variation-with-time of supply electric power to the heater, temperature of the sample, and temperature of the temperature sensor, without plasma processing; approximating the relation among the measured values using a simultaneous linear differential equation; estimating a sample temperature from the variation-with-time of sensor temperature y1, heater electric power u1, and plasma heat input by means of the Luenberger's states observer based on the simultaneous linear differential equation used for the approximation; and performing a feedback control of sample temperature using the estimated sample temperature.

The invention discloses a power system transient stability simulating method based on implicit numerical integration. Compared with an existing power system transient stability numerical simulation implicit trapezoidal integration method, the power system transient stability simulating method employs a power-angle integration formula with a smaller local truncation error, namely, enables a non-linear differential equation set for describing a power system transient process to be expressed as a linear portion and a non-linear portion. An accurate analysis expression of a state transition matrix is obtained by reasonably selecting a system matrix of the linear portion as a singular matrix, and a group of implicit integration formulas is obtained by leading linear integrable functions to be approximate to the non-linear portion of the differential equation set. The local truncation error of the power-angle implicit integration formulas of the generator refers to O (h5) which is larger than a local truncation error O (h3) of implicit trapezoidal integration, the calculated quantity of integration each time is equivalent to that of the implicit trapezoidal integration. By means of the high-precision implicit integration formulas, iteration times of each integration step under the same iteration precision condition are decreased, so that the simulated calculated quantity is remarkably decreased.

A method and system thereof for simulating behaviour of a thermodynamic system over time, including a momentum refreshment process and a conservative dynamics process, where the momentum refreshment process includes partially refreshing a momentum to define refreshed momentum by considering solutions for a starting momentum determined by a numerical implementation for integrating a generating linear differential equation.

Diagnosing a pump apparatus having a downhole pump disposed in a deviated wellbore characterizes axial and transverse displacement of a rod string with two coupled non-linear differential equations of fourth order, which include axial and transverse equations of motion. To solve the equations, derivatives are replaced with finite difference analogs. Initial axial displacement of the rod string is calculated by assuming there is no transverse displacement and solving the axial equation. Initial axial force is calculated using the initial axial displacement and assuming there is no transverse displacement. Initial transverse displacement is calculated using the initial axial force and the initial axial displacement. Axial force and friction force are calculated using the initial displacements, and the axial displacement at the downhole pump is calculated by solving the axial equation with the axial force and the friction force. Load at the downhole pump is calculated so a downhole card can be generated.

The invention discloses a method for finding an abnormal electric energy meter based on a gray GM (1, 1) model. The method comprises the following steps that first, normally-measuring power utilization data of a user electric energy meter are obtained from a user power utilization system database; second, obtained data samples are arrayed according to the time sequence, original data are accumulated to form new regular data, a linear first-order differential equation is established for the new data, the model is subjected to identifying and parameter estimation, a prediction equation is obtained, and finally a short-term predicted value is obtained by regressive restoring; and third, an obtained load predicted value and a value collected by the user electric energy meter are compared, whether the user electric energy meter is normal is judged, and if an anomaly exists, a user is suspected of stealing electricity. The method for finding the abnormal electric energy meter based on the gray GM (1, 1) model has the advantages that a large number of samples are of no need, the high regularity of the samples is of no need, computing workload is low, operation cost is low, a mounted electric energy meter does not need to be transformed, manpower investment of an electric power company is lowered, and judging is accurate.

A method and system thereof for simulating behavior of a thermodynamic system over time, including a momentum refreshment process and a conservative dynamics process, where the momentum refreshment process includes partially refreshing a momentum to define refreshed momentum by considering solutions for a starting momentum determined by a numerical implementation for integrating a generating linear differential equation.

The invention provides a transient response analytic calculation method for a high-voltage direct current power transmission system. The method comprises the following steps that: A, a smoothing reactor, a direct current filter and a direct current power transmission circuit of the high-voltage direct current power transmission system are combined with a voltage current relationship to obtain a differential algebraic equation set of the high-voltage direct current power transmission system under different operation work conditions according to a circuit principle; according to the logic relationship of a control system, a differential equation of the control system is built, and a state equation (shown as the accompanying drawing) of the high-voltage direct current power transmission system is finally formed, wherein the differential algebraic equation set is a constant-coefficient nonhomogeneous linear differential equation set, x is the state quantity under the i-th operation work condition, Ai is a state matrix, Bi is an input matrix, the input u(t) is a rectifier-side and inverter-side three-phase voltage instantaneous expression, and Ci is a component after the addition of the control system; B, through the steady state response calculation on the high-voltage direct current power transmission system, the relationship x(t) of the state quantity of the high-voltage direct current power transmission system varying with time and initial values of each operation quantity of the control system are obtained; C, under the alternate current voltage change, the direct current transient response calculation is carried out; and D, the calculation is completed.

The invention provides a direct-current power distribution and utilization system state feedback control method based on Taylor expansion, which is characterized by comprising the following steps of: 1, establishing an equivalent order reduction circuit of a direct-current power distribution and utilization system, and calculating an equivalent filter capacitance Ceq, an equivalent filter inductance Leq and a constant-power load equivalent current IL; 2, establishing a linear differential equation set of the equivalent order reduction circuit of the direct-current power distribution and utilization system considering state feedback control, and calculating state feedback gains k1 and k2; and 3, realizing stable control over the direct-current bus voltage of the direct-current power distribution and utilization system by considering state feedback control.

A method of stably controlling the temperature of a sample placed on a sample stage to a desired temperature by estimating a sample temperature accurately, the sample stage including a refrigerant flow path to cool the sample stage, a heater to heat the sample stage, and a temperature sensor to measure the temperature of the sample stage. This method comprises the steps of: measuring in advance the variation-with-time of supply electric power to the heater, temperature of the sample, and temperature of the temperature sensor, without plasma processing; approximating the relation among the measured values using a simultaneous linear differential equation; estimating a sample temperature from the variation-with-time of sensor temperature y1, heater electric power u1, and plasma heat input by means of the Luenberger's states observer based on the simultaneous linear differential equation used for the approximation; and performing a feedback control of sample temperature using the estimated sample temperature.

The invention discloses a two-dimension phase fast unwrapping method using an L<0> norm cost function; the method comprises the following steps: numerical realization of solving a differential equation algorithm, firstly converting a differential relation into a difference relation corresponding to discrete data, then carrying out difference equation iteration solving, wherein each step treatmentis carried out on the basis of the previous step treatment result in the iteration process, and the difference [delta] [phi] between the two processing steps becomes the solving important content. Thetwo-dimension phase fast unwrapping method using the L<0> norm cost function can solve the problems that an existing phase unwrapping method is low in efficiency when processing big data blocks. Themethod aims at the conventional minimum norm unwrapping method, analyzes the cost function characteristics, and provides the two-dimension phase fast unwrapping method complying with the L<0> norm cost function; combined with a data partitioning scheme, the method can solve the full low frequency aberration convergence problems in the linear differential equation, and improving the unwrapping efficiency.

Provided is a controller of a robot manipulator, a performance analysis method thereof and a parameter determination method thereof. The controller computes an error value of an output value of a control target for a target value through a computational equation and provides a control input value of the control target, and includes an outer loop controller which constitutes closed loop control of the control target, and an inner loop controller which performs feedback linearization to remove nonlinearity of the control target, wherein the computational equation is a linear differential equation designed considering exogenous disturbance acting in the controller and a computational error.

The invention relates to a radio energy transmission tuning control technology, in particular to a radio energy transmission system tuning feedback control method considering dynamic performance. Themethod includes the steps of obtaining the phase nonlinear differential equation model of the transmitting end and the receiving end of a system through analysis by utilizing a coupling mode theory and a circuit theory; utilizing a small signal linearization method to linearize a phase nonlinear differential equation model nearby a system resonance point, and analyzing the closed-loop dynamic performance of the system; taking the linear model as a controlled object and the phase value of the output voltage of an inverter circuit of the system as a reference phase, and forming a system tuning closed-loop feedback control loop by using the phase value of the transmitting end and the phase difference value of the transmitting end and the receiving end as the given values of the system transmitting end and the receiving end control loops when the system works in a resonance state. The control method can quickly and accurately control a magnetic coupling wireless energy transmission systemto work under the working states of high transmission efficiency and power, and has good robustness for detuning disturbance.

Embodiments of methods are provided that can be used to estimate network relationships between genes of an organism using time course expression data and a set of linear differential equations. Aikaike's Information Criterion and mask tools can be used to reduce the number of elements in a matrix by determining which elements are zero or not significantly changed under the conditions of the study. Maximum likelihood estimation and new statistical methods are used to evaluate the significance of a proposed network relationship.

The invention discloses a pulse laser ranging system transistor type receiving circuit error correcting method. The pulse laser ranging system transistor type receiving circuit error correcting methodcomprises the following steps that (10) a circuit modeling is received, wherein a circuit equation set is listed according to a circuit structure and a transistor classic model; (20) a circuit equation set is solved, wherein a numerical value approximation solution of the circuit equation set is solved by means of discretization and numerical analysis; (30) the circuit equation set is simplified,wherein the circuit equation set is reserved according to the numerical value approximation solution of the circuit equation set; (40) a linear differential equation set is solved, the linear differential equation set is solved to obtain an approximate relation between the walking error and the input current; (50) an error relation is determined, wherein a double-threshold moment is substituted into the approximate relation to obtain the relation between the walking error and the double-threshold moment; and (60) time error is corrected, wherein the specific numerical value of the double-threshold moment is substituted into the relation to obtain an error value, and the error value is subtracted from the time interval to obtain an accurate time interval. The error correcting method is small in error and high in system measuring precision.

According to the invention, a simulation is carried out based on the fundamental motion equation (1) for simulating the system by means of: transformation of the fundamental motion equation into linear differential equations of the first order; further transformation of the linear differential equations into time-discrete state variables; determination of the time response of the system by actualization of the resulting algebraic differential equations in the sampling raster of an associated control processor. Higher simulation accuracy is obtained at an essentially smaller calculating capacity.

The invention discloses a method and device for determining bottom hole pressure of a gas well and a storage medium in the technical field of gas reservoir exploitation. The method comprises the stepsof determining a seepage area of the bottom of a gas well and a plurality of unit grids included in the seepage area and a seepage linear differential equation and a linear constraint condition of the seepage area; determining a discrete numerical model of each unit grid in the plurality of unit grids so as to determine the bottom hole pressure of the gas well based on the discrete numerical model of each unit grid and the seepage linear differential equation and linear constraint condition of the seepage area. The seepage area is dispersed into a plurality of unit grids, and the discrete numerical model of each unit grid is determined under the condition that the wellbore reservoir effect and the epidermis effect are considered. The bottom hole pressure of the gas well is determined based on the discrete numerical model of each unit grid and the seepage linear differential equation and the linear constraint condition of the seepage area, so that accuracy of the bottom hole pressure is improved.

The embodiment of the present invention relates to the field of automotive electronic test technology, and discloses an adjustable two-stage supercharged engine model building method and a simulationplatform. In the invention, the method comprises the following steps of: obtaining multivariate nonlinear differential equations of an adjustable two-stage turbo supercharged engine; and decoupling and simplifying the multivariate nonlinear differential equations to obtain a real-time simulation model of the adjustable two-stage turbo supercharged engine. An embodiment of the invention also discloses an adjustable two-stage supercharged engine simulation platform. The embodiments of the present invention achieves semi-physical real-time simulation of the adjustable two-stage turbo superchargedengine and provides a basis for the development of control strategies for the engine and the two-stage turbo supercharged system.

The present invention discloses a Laguerre output method for a rigid body space motion state. According to the method, three velocity components of a machine shaft system and a three-ary number form linear differential equations by defining the three-ary number; a Laguerre orthogonal polynomial is adopted to proximately and closely depict a rolling angle p, a pitching angle q, and a yawing angular velocity r; a state transition matrix of the system can be solved according to a manner of an arbitrary order keeper so as to acquire an expression of a rigid body motion discrete state equation, such that the singularity problem of the attitude equation is avoided so as to acquire the main motion state of the rigid body. According to the present invention, the three-ary number is introduced, such that the state transition matrix is the block upper triangular manner, and can be solved by reducing the order so as to substantially simplify the calculation complexity, and be easily used by the engineering.

The invention discloses a multi-rate parallel circuit simulation method and system. The method implemented by a computer comprises the steps that a circuit is divided into multiple partitions, wherein each partition is represented by a set of linear differential equations; the simulation time step of each of the multiple partitions is determined; the multiple partitions form a plurality of sets, wherein each set comprises one or more partitions with the simulation time steps within the preset definition range; the equation of the multiple sets is solved through the corresponding simulation time steps in a parallel mode.

The invention discloses a Hartley output method of rigid body space motion states, which enables three velocity components and a ternary figure of a body axis to form linear simultaneous differential equations by defining the ternary figure, and adopts a Hartley function to conduct approximate approaching description of roll rate P, pitching rate Q and yaw rate R. Users can solve a state-transition matrix of a system in accordance with arbitrary order keeper modes, and then obtain expression of rigid motion discrete state equations, thereby avoiding gesture equation strange problems and obtaining main motion states of a rigid body. The Hartley output method enables the state-transition matrix to be a blocking upper triangular form by introducing the ternary figure, can reduce order to solve the state-transition matrix, greatly simplifies computational complexity and is convenient to use in construction.

The invention discloses a polynomial type output method for a spatial motion state of a rigid body. In the method, by defining a ternary number, three speed components of a machine body axis system and the ternary number constitute a linear simultaneous differential equation, polynomials are used for performing approximate description on roll rate p, pitch rate q and yaw rate r, a state-transition matrix of a system can be solved according to a random-order keeper manner so as to further obtain an expression of a motion discrete state equation of the rigid body, and thus, the problem of a singular gesture equation is avoided and the main motion state of the rigid body is obtained. In the invention, by introducing the ternary number to make the state-transition matrix be of a blocked upper triangular form, the state-transition matrix can be solved in a reduced order manner, the computation complexity is greatly simplified, and engineering purposes are facilitated.

The invention provides an analysis method for analyzing the dynamic and reactive power control interactive impact in a wind power convergence region. The analysis method comprises the steps of forming a node admittance matrix and a network equation according to a spatial grid structure in a to-be-analyzed wind power convergence region; establishing a dynamic equation and an output equation of a dynamic reactive power compensation device according to the control mode of the dynamic reactive power compensation device in the to-be-analyzed wind power convergence region; according to the network equation, the dynamic equation and the output equation, forming a linear differential equation and a linear state matrix of the to-be-analyzed wind power convergence region; according to the linear state matrix, acquiring the characteristic roots of the dynamic reactive power compensation device in different control modes; and based on the participation vector analysis of the characteristic roots, generating an analysis result for analyzing the dynamic and reactive power control interactive impact in the to-be-analyzed wind power convergence region.

A multi-purpose chaoti photon device based on chaotic theory, the biologic effect of photon and traditional Chinese medicine for medical purpose and optimizing seeds is composed of biologic spectrum generator, modulator, driver, output unit and power supply. Its advantages are high health-care and medical effect and and high effect on improving quality of seed in resisting disease and pests.

The invention belongs to the field of power system power distribution network control, and particularly relates to an electric water heater load group dynamic system and a control model thereof. A linear state equation constructed in the invention is suitable for modeling of various electric water heaters, the load group of the electric water heater is controlled in real time by using a sliding mode control strategy, and the design of a control rate is related to the number of the electric water heater groups, the use condition of hot water and the like, and has relatively strong robustness for eliminating wind power, a corresponding mathematical model is established according to the physical characteristics of the electric water heater groups by using a linear differential equation, a temperature value is set by adopting a discrete sliding mode, and the load of the electric water heater groups is controlled so as to achieve the goal of eliminating the wind power.

The invention discloses a method for designing a simplified model of a comprehensive energy system based on a balance transformation theory. The method comprises the following steps of: establishing dynamic models and electric network equations of a boiler, a steam turbine, a generator, a natural gas pipeline, an energy storage battery and a fan; combining all the dynamic models and the electric network equations to obtain an integral complex model of the comprehensive energy system described by a high-order nonlinear differential-algebraic equation set; obtaining a high-order linear differential equation of the comprehensive energy system described by general differential equation systems through model linearization and interface expansion; and performing dimensionality reduction and simplification on the high-order linear model by using a balance transformation theory to obtain a simplified model of the comprehensive energy system. The method for designing a simplified model providedby the invention can reduce the complexity of the model on the premise of not influencing the main dynamic characteristics of the comprehensive energy system, and provides a model basis for the establishment of a simulation platform and a control algorithm of the comprehensive energy system.

A method is described for ascertaining a computational model for a position encoder system, in particular for a position encoder for controlling a gas mass flow rate for an internal combustion engine, having the following steps: providing a differential equation system with at least one nonlinear term; dividing the differential equation system to obtain a linear part which is describable by a linear differential equation and a nonlinear part which is describable by a nonlinear differential equation; discretizing the linear part of the differential equation system with the aid of a first discretization method to obtain a computational model for the discretized linear part; discretizing the nonlinear part of the differential equation system with the aid of a second discretization method to obtain a computational model for the discretized nonlinear part; combining the computational models of the discretized linear part and the discretized nonlinear part of the differential equation system to obtain the computational model for the position encoder system.

The invention discloses a differential equation-based rapid detection method for harmonious waves in a power system and particularly provides a method for rapidly detecting the phases and the amplitudes of signals different in frequency in the power system. The method comprises the following steps of (1) collecting sampling points at a sampling rate higher than two times a highest frequency multiplication, wherein the number of sampling points is one less than at least four times the harmonic quantity; (2) constructing a homogeneous linear differential equation of a harmonic and fitting an equation coefficient with two times the highest frequency multiplication as an order; (3) calculating the complex root of the differential equation by adopting the above equation coefficient, and calculating the frequency, the amplitude and the phase of the harmonic according to the complex root. Based on the above manner, the required amount of data is small and a result can be calculated only based on data much less than that of a cycle length of a fundamental frequency compared with the prior art. Compared with the fast Fourier transform method, the problem of frequency leakage is avoided. Meanwhile, the method can be used for calculating the frequency of each actual waveform in harmonic signals in the self-adaptive manner, and is strong in anti-jamming capability and anti-noise capacity.

The invention discloses a Chebyshev output method for the space motion state of a rigid body. The method comprises the steps of: defining a ternary number so that three speed components of the set of axes of the body and the ternary number form a system of linear differential equations; and performing approximation description on rolling, pitching and yawing angular speeds p, q and r by using Shifted Chebyshev orthogonal polynomials, wherein the state transfer matrix of the system can be solved in the manner of any order holder, thus obtaining the expression of the discrete state equation of the motion of the rigid body; and the problem of singularity of the attitude equation is avoided; therefore, the main motion state of the rigid body is obtained. The Chebyshev output method is characterized in that the ternary number is introduced so that the state transfer matrix is in the form of portioned upper triangles and thereby can be solved through deflation; therefore, the complexity of calculation is greatly simplified; and the Chebyshev output method is convenient for engineering use.

The invention discloses an electromagnetic transient rapid simulation method based on a static var compensator. The method comprises the following steps: step 1, acquiring basic parameters of an SVC device; wherein parameters needing to be acquired comprise an inductor L of a TCR branch, a capacitor Cs of a fixed capacitor FC, a resistor Rf of a filter, an inductor Lf, a capacitor Cf, external input voltages uA, uB and uC and a thyristor trigger angle alfa. By introducing sine auxiliary variables, a state equation of SVC is converted into a homogeneous linear differential equation set from a non-homogeneous linear differential equation set. The solution of the equation set is rapidly obtained through a matrix index integration method, and meanwhile, the state equations are unified in formunder all working conditions. Compared with a system model required to be solved in traditional electromagnetic transient calculation, the method has the advantages that the system model required to be solved is changed only when the on-off states of the thyristors are changed, so that calculation is more efficient, and working efficiency is greatly improved.