10 results about "Linear differential equation" patented technology

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 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 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.