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.

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 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.

Methods and systems are disclosed related to multi-rate parallel circuit simulation. In one embodiment, a computer implemented method of partitioning the circuit into a plurality of partitions, wherein each partition is represented by a set of linear differential equations, determining a simulation time step for each partition of the plurality of partitions, grouping the plurality of partitions into multiple groups, wherein each group includes one or more partitions having simulation time steps within a predefined range of each other, and solving the multiple groups with their corresponding simulation time steps in parallel.