19 results about "Linear differential equation" patented technology

The invention discloses a safety assessment method for an offshore wind power flexible direct current grid-connected system based on reachability analysis. The method comprises the following steps: constructing a high-dimensional nonlinear differential equation model and a nonlinear hybrid system model of the offshore wind power flexible direct current grid-connected system based on a Kron simplification method; constructing an uncertain variable model with a random change range by utilizing a sino polyhedron, and adding the uncertain variable model into the nonlinear hybrid system model as an uncertain input item; based on a reachability analysis theory, designing an improved reachability set calculation algorithm based on an adaptive time step optimization method, and dynamically balancing the calculation precision and the calculation efficiency of the reachability set by adjusting the time step; and an improved reachable set calculation algorithm is applied to calculate reachable set results of the offshore wind power flexible direct current grid-connected system under the influence of different operation conditions and uncertain factors. According to the method, the operation state of the offshore wind power flexible direct current grid-connected system can be subjected to safety evaluation according to the reachable set result, and important guidance is provided for guaranteeing safe and stable operation of the system.

The present invention relates to a method for adaptive observation of a system comprising, at time t: - a set of input quantities including the control setpoint ut and modeled as a vector: Ut, - a set of output quantities modeled as a vector: Yt, and - a set of quantities representing the state of the system and modeled as a vector: xt; the method being implemented in a computing unit and comprising: - a first step E1 of programming a set of linear differential equations between the input quantities, the system state quantities, and the output quantities, - a step E2 of determining the slowly evolving parameters, and - a step E3 of adaptive observation comprising the numerical calculation of the system state quantities xt at time t by solving the set of linear differential equations. Figure for the abstract: Figure 6.

This invention provides a method and related apparatus for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics. The method includes: representing the dynamic processes of discontinuous components in the main and control loops of the hybrid DC transmission system using a step function; approximating the step function as a continuous function using a linear combination of hyperbolic tangent functions to obtain a continuous expression; obtaining modular nonlinear differential equations for the rectifier, inverter, and AC / DC networks, and replacing the discontinuous dynamic parts involved in the equations with the continuous expression; and interconnecting the modules according to their input-output relationships to obtain a complete nonlinear mathematical model of the hybrid DC transmission system. This invention establishes a nonlinear mathematical model of a hybrid DC transmission system that accurately reflects discontinuous dynamic characteristics by employing the continuous approximation method using step functions and hyperbolic tangent functions, thereby improving the accuracy and practicality of system modeling.

The invention provides a small disturbance stability estimation method for a grid-following type and grid-constructing type hybrid grid-connected converter, and relates to the technical field of power grids, and the method comprises the steps: aiming at each preset time period, based on the corresponding control and structure parameters of the grid-following type grid-connected converter and the grid-constructing type grid-connected converter in a small disturbance scene, calculating the stability of the grid-following type and grid-constructing type hybrid grid-connected converter; determining a system stable equilibrium point, a system unstable equilibrium point and equilibrium point stability conditions corresponding to the preset time period; determining a period stability analysis result corresponding to the preset time period based on a balance point linear differential equation, the system stable balance point, the system unstable balance point and the balance point stability condition; and determining a target stability analysis result based on the period stability analysis results corresponding to all the preset time periods. The method is applied to the condition of series-parallel connection of the following grid-connected converter and the construction grid-connected converter, is not influenced by a relatively high model order of the grid-connected converter, and can obtain an accurate stability analysis result.

The present invention relates to a method for determining insulation resistance (R1, R2) and discharge capacitance (C1, C2) for ground (PE) of an ungrounded DC power supply system, wherein a linear difference equation is implemented as a function of a measurement voltage (UG(k)) and a grid voltage (UN(k)) with a measurement voltage (UM(k)), and a grid parameter (θi) formed from a shunt (RM), insulation resistance (R1, R2) to be determined, and discharge capacitance (C1, C2) to be determined. Using N linear differential equations, a measurement value equation system is implemented with a sample sequence ((UG(k), UN(k), UM(k))) and a grid parameter (θi) for measurement times from k = 1, 2 to N with a sampling period T. Another method step comprises a step (S6) of calculating the estimated grid parameter (θi) as an approximate solution to the measurement value equation system, wherein the sum of squared errors between the grid parameter (I) and the estimated grid parameter (θi) is minimized, a step (S7) of minimizing the sum of squared errors through QR decomposition of the measurement-value matrix (Ψ), wherein the QR decomposition is recursively calculated, and a step (S8) of calculating each insulation resistance (R1, R2) and each discharge capacitance (C1, C2) from the estimated grid parameter (I) and repeating the method step with the estimated grid parameter (I), each calculated to include samples available at the current measurement time.

The invention relates to a method for the adaptive observation of a system at a time t, the system comprising:-a set of inputs comprising the control setpoint ut and modeled in the form of vectors: Ut; -a set of output quantities, the set of output quantities being modeled in the form of vectors: Yt; and-a set of quantities representing the state of the system, the set of quantities modeled in the form of vectors: xt; the method is implemented in a computing unit and comprises: a first step E1 of programming a set of linear differential equations relating to the input, the system state and the output; a step E2 of determining a slow-varying parameter; and-an adaptive observation step E3 comprising numerical calculation of the quantity xt of the system state at the moment t by solving the set of linear differential equations.

The application provides a clutch damping control method for a wave energy device, considers the survival problem of the wave energy device in actual sea conditions, establishes a time domain motion equation and a state space equation, simplifies the time domain motion equation by using the state space equation, rewrites the time domain motion equation into a linear differential equation, represents whether the inner oscillator and the wave energy device are connected by loading and unloading control commands in the linear differential equation, and obtains the motion state of the wave energy device by solving the motion differential equation with the control. A Hamilton function about the control command is defined, a constraint problem of displacement minimization is converted into an unconstrained optimization problem, the Hamilton function is expanded according to the state space equation of the wave energy device, the Hamilton function is solved, the optimal control sequence of the displacement of the optimized wave energy device in the extreme environment is obtained when the Hamilton function is minimum, the motion of the wave energy device is adjusted by using the optimal control sequence, and the effect of maximizing the survival ability of the optimized wave energy device is realized.

The invention belongs to the technical field of chaotic circuits, and discloses a sine nonlinear characteristic-based third-order circuit system, which comprises a sine nonlinear function circuit and a third-order linear differential equation circuit, the input end of the sine nonlinear function circuit is connected with the x output end of the third-order linear differential equation circuit, and the output end of the sine nonlinear function circuit is connected with the x output end of the third-order linear differential equation circuit. The output end is connected with one input end of the x integrator of the third-order linear differential equation circuit; the sine nonlinear function circuit is composed of a first operational amplifier A1, resistors R1 to R16 and diodes D1 to D6, and the output and the input of the sine nonlinear function circuit are in a sine nonlinear function relationship; the third-order linear differential equation circuit forms three anti-phase addition integrators by three anti-phase operational amplifiers, three capacitors and seven resistors, and the sine nonlinear function circuit provides nonlinear signals to generate three Chua's chaotic signal outputs of the sine nonlinear third-order Chua's circuit; according to the invention, various chaotic line systems and chaotic secret communication systems can be formed.

The invention discloses a method for constructing a tension calculation model of inert gas in human tissues. The method comprises the following steps of: establishing a pressure change rate function of a certain tissue of a human body and performing form transformation to obtain a corresponding first-order inhomogeneous linear differential equation; constructing a standard form and a general solution form of a first-order inhomogeneous linear differential equation; the first-order inhomogeneous linear differential equation and the general solution form thereof are correspondingly assigned and substituted into the general solution form to obtain a general human body certain tissue pressure function; respectively constructing a pressure function g1 (x) of a certain tissue of the human body in a respiratory gas index pressurization scene, a pressure function g2 (x) of a certain tissue of the human body in a linear decompression scene and a pressure function g3 (x) of a certain tissue of the human body in a linear pressurization scene by using a universal pressure function of a certain tissue of the human body; and respectively constructing inert gas tension calculation models G1 (x), G2 (x) and G3 (x) of a certain tissue of the human body under the scenes of index pressurization, linear decompression and linear pressurization by using the g1 (x), g2 (x) and g3 (x) and the inert gas percentage content d.

The invention belongs to the technical field of chaotic circuits, and discloses a sine nonlinear signal processing-oriented multi-order circuit system, which comprises a sine nonlinear function circuit, a fourth-order linear differential equation circuit and a fifth-order linear differential equation circuit, and is characterized in that the sine nonlinear function circuit consists of an operational amplifier A1, resistors R1 to R16 and diodes D1 to D6; the output and the input are in a sine nonlinear function relationship; the fourth-order and fifth-order linear differential equation circuit consists of an inverting operational amplifier, a capacitor and a resistor, and is used for generating a plurality of Chua's chaotic signal outputs of the sine nonlinear fourth-order and fifth-order Chua's circuit; the circuit can form various chaotic circuit systems and chaotic secret communication systems.

The application discloses a kind of centrifugal pump dynamic performance optimization method under given flow mutation, first deduce the maximum slope when motor torque rises and falls;Second, the turning point of torque instruction mutation is deduced;Finally, the corresponding torque instruction is sent out: when flow mutation time to turning point, this section of time gives forward vector, so that torque rises according to maximum slope, after reaching turning point, give retreat vector, so that torque falls at maximum slope, until torque returns to initial value, speed tracks on mutation after given speed, flow reaches given flow, system reaches stable state.The application controls torque linearly in dynamic time, and the control rate is the hardware limit value.A linear differential equation is constructed with the torque integral of dynamic imbalance and the given speed increment being equal as a constraint to solve the torque turning point, which makes up for the speed overshoot of traditional speed PI loop, and realizes the optimal torque control curve and optimal flow response curve under dynamic linear control.

The present application is a method for constructing an inert gas tension calculation model in human tissue: a pressure change rate function of a certain tissue in a human body is established and is transformed to obtain a first-order non-homogeneous linear differential equation; a standard form and a general solution form of the first-order non-homogeneous linear differential equation are constructed; the first-order non-homogeneous linear differential equation and the general solution form are correspondingly assigned and substituted into the general solution form to obtain a general pressure function of a certain tissue in a human body; the general pressure function of a certain tissue in a human body is used to construct a pressure function g1(x) of a certain tissue in a human body under an exponential pressurization scenario of respiratory gas, a pressure function g2(x) of a certain tissue in a human body under a linear depressurization scenario, and a pressure function g3(x) of a certain tissue in a human body under a linear pressurization scenario; and the g1(x), g2(x) and g3(x) are used together with an inert gas percentage content d to construct inert gas tension calculation models G1(x), G2(x) and G3(x) of a certain tissue in a human body under the exponential pressurization, linear depressurization and linear pressurization scenarios.

The invention relates to a high-dimensional complex nonlinear differential equation periodic response efficient universal easy-to-use solving method, which is characterized in that an automatic differential technology and a harmonic balance method are fused, and the method comprises the following steps: step 1, solution setting: representing the periodic response of a system by using discrete Fourier series; step 2, harmonic balance: substituting periodic response in a Fourier series form of the system back to a system kinetic equation, and converting a differential equation into an algebraic equation through a harmonic balance program; 3, calculating a Jacobian matrix, namely, quickly obtaining an accurate Jacobian matrix of the algebraic equation after harmonic balance by utilizing an automatic differential technology; and 4, solving an algebraic equation, namely calculating by using a Newton-Raphson method to obtain a system periodic response. The method solves the problems that a high-dimensional complex nonlinear differential equation response solving method is low in efficiency, not universal and not easy to use, can be widely applied to calculation of high-dimensional complex nonlinear system dynamic response, and has the advantages of being efficient, universal, capable of being used immediately after being opened and modularized.

The application provides a clutch damping control method for a wave energy device, considers the survival problem of the wave energy device in actual sea conditions, establishes a time domain motion equation and a state space equation, simplifies the time domain motion equation by using the state space equation, rewrites the time domain motion equation into a linear differential equation, represents whether the inner oscillator and the wave energy device are connected by loading and unloading control commands in the linear differential equation, and obtains the motion state of the wave energy device by solving the motion differential equation with the control. A Hamilton function about the control command is defined, a constraint problem of displacement minimization is converted into an unconstrained optimization problem, the Hamilton function is expanded according to the state space equation of the wave energy device, the Hamilton function is solved, the optimal control sequence of the displacement of the optimized wave energy device in the extreme environment is obtained when the Hamilton function is minimum, the motion of the wave energy device is adjusted by using the optimal control sequence, and the effect of maximizing the survival ability of the optimized wave energy device is realized.

A method for determining an insulation resistance and a discharge capacitance to earth of an unearthed DC power supply system, wherein a linear differential equation is implemented with a measured voltage as a function of the measurement voltage and the grid voltage and with grid parameters formed from the shunts (RM), from the insulation resistances to be determined and from the discharge capacitances to be determined. N linear differential equations are used to implement a measured value equation system with the sample sequences and the grid parameters for k=1, 2 to N measurement times with the sampling period T.

The present invention relates to a method for determining at least one control setpoint ut of a system comprising, at time t: - a set of input quantities including the control setpoint ut and modeled as a vector: Ut, - a set of output quantities modeled as a vector: Yt, and - a set of quantities representing the state of the system and modeled as a vector: xt; the method being implemented in a computing unit and comprising: - a first step E1 of programming a set of linear differential equations between the input quantities, the system state quantities, and the output quantities, and - a step E4 of determining the optimal control setpoint using the quadratic programming method. Figure 6 for the abstract.

The application discloses a DC power transmission subsequent commutation failure prediction method and optimization method based on a turn-off angle dynamic equation, and the prediction method comprises the following steps: obtaining the turn-off angle of the LCC-HVDC inverter side based on the turn-off angle output characteristics of the LCC-HVDC inverter side; analyzing the process of the first commutation failure and the subsequent commutation failure of the LCC-HVDC system based on the inverter side DC current control, the low-voltage current limiting control, the fixed turn-off angle control and the current deviation control; obtaining the transient nonlinear differential equation about the turn-off angle by analyzing the dynamic characteristics of the DC current and the trigger advance angle during the first commutation failure recovery in combination with the control characteristics of the low-voltage current limiting control and the fixed turn-off angle control; and drawing the phase diagram curve of the turn-off angle under different AC voltages and AC voltage change rates based on the transient nonlinear differential equation about the turn-off angle, and obtaining the criterion for predicting the occurrence of the subsequent commutation failure by analyzing the phase diagram curve. The application improves the stability and operation reliability of the system.

The invention relates to a method for determining at least one control setpoint ut of a system at a time t, the system comprising:-a set of input variables comprising the control setpoint ut and modeled in the form of a vector: Ut,-a set of output variables modeled in the form of a vector: Yt, and-a set of quantities representing the state of the system, the set of quantities modeled in the form of vectors: xt; the method is implemented in a computing unit and comprises:-a first step E1 of programming a set of linear differential equations relating to the input variables, the system state variables and the output variables, and-a step E4 of determining an optimal control setpoint by means of a quadratic programming method.

This invention discloses a constrained following active disturbance rejection control (CFADRC) method for autonomous motorcycles. This method mainly includes two features: First, it constructs an extended state observer (ESO) using a linear variable parameter model (LPV) of the autonomous motorcycle to observe the uncertainties and internal and external disturbances of the system, and compensates for them in the system state equations, thereby reducing the impact of uncertainties and internal and external disturbances on the system. Second, it utilizes the principle of constrained following control (CFC) to design the control problem of lateral tilt balance as a state constraint with a tilt angle of 0. This objective constraint is equivalently represented using a second-order linear differential equation, and the constrained following active disturbance rejection control law is designed based on the disturbance terms observed by the extended state observer. The constrained following active disturbance rejection control of this invention for autonomous motorcycles has a standardized design process, a simple control structure, low dependence on the accuracy of the system's dynamic model, and relatively easy parameter tuning subject only to unilateral constraints. It exhibits strong robustness and provides a simple and effective solution for designing balance control strategies for autonomous motorcycles.