3 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 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.

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.