3 results about "Second order differential equations" patented technology

The application discloses a kind of based on vibration sinking amount underwater block stone cushion vibration compaction parameter control method and system, method includes: S100, based on spring-damping-mass theory, the vibration system of block stone cushion vibration compaction is established;S200, the vibration system of block stone cushion vibration compaction is stressed analysis, obtains the overall dynamics equation of vibration device and reference vibration block stone;S300, the overall dynamics equation in step S200 is combined with the displacement of vibration system, obtains the third-order differential equation about elastic deformation;S400, the overall dynamics equation in step S200 is combined with the reaction of soil, obtains the second-order differential equation about elastic deformation;S500, the iteration algorithm based on Runge-Kutta method is prepared, differential equation is solved, and its numerical solution is obtained;S600, the output parameter in vibration process is obtained, and the input value of vibration system is adjusted according to the output parameter. Overall consideration block stone cushion in vibration compaction process elasticity, damping and plastic deformation.

The invention discloses a model order reduction method based on a first-order singular perturbation theory and a grid-connected system stability analysis method, and belongs to the field of transient stable operation and control of a novel power system, and the method comprises the steps: determining a differential equation set and an algebraic equation set of a new energy grid-connected system; calculating a time constant of a system state quantity, and dividing the new energy grid-connected system into a fast subsystem and a slow subsystem based on the time constant; according to the first-order singular perturbation theory, after derivation is conducted on the differential equation set of the fast subsystem, a second-order differential item in the second-order differential equation set of the fast subsystem is made to be 0, then the second-order differential item is substituted into the differential equation set and the algebraic equation set of the fast subsystem, and a first-order perturbation equivalent model algebraic equation is obtained; therefore, the first-order perturbation dynamic state-considered order reduction model of the new energy grid-connected system is obtained by combining the differential equation set and the algebraic equation set of the slow subsystem, the dominant dynamic state in the new energy grid-connected system can be effectively identified, and model order reduction is realized, so that the stability analysis efficiency is improved, and the accuracy is ensured.

The application belongs to the technical field of motor system control, and discloses a motor selection method based on expected tracking tasks and controller structures, which comprises the following steps: first, a second-order differential equation describing the generalized position and generalized speed characteristics of a motor is established; second, the load and expected trajectory involved in the expected tracking task are determined, and constants are selected to represent the upper and lower bounds of the load and expected trajectory; third, an error variable is defined, and an adaptive tracking controller is designed based on the second-order differential equation; fourth, a Lyapunov function is selected to analyze the upper and lower bounds of the error variable; fifth, based on the controller structure, controller parameters, initial value of the error variable, upper and lower bounds of the error variable, and expected task, the upper and lower bounds of the required control torque of the motor and the upper bound of the power are determined, and motor selection is completed according to the boundary conditions. The application realizes the analysis of the peak torque and maximum power of the motor and the tracking of the expected motor position.