39 results about "Second order differential equations" patented technology

A system for actively damping the low-frequency coloration of sound in a listening room is provided comprising an acoustic wave sensor, an acoustic wave actuator, and an electronic feedback controller. The listening room defines at least one mode of low-frequency coloration. The acoustic wave actuator is substantially collocated with the acoustic wave sensor within the listening room. The electronic feedback controller is operative to generate a signal at its output by applying a feedback controller transfer function. The feedback controller transfer function comprises a second order differential equation including a first variable representing a predetermined damping ratio and a second variable representing a tuned natural frequency and creates a 90 degree phase lead substantially at the resonant frequencies of at least one mode of low-frequency coloration. The feedback controller output signal represents a rate of change of volume velocity to be produced by the acoustic wave actuator. Further provided are methods for actively damping the low-frequency coloration of sound within a listening room and systems for actively treating noise within a fluid-carrying duct, including those which employ active low- and high-pass acoustic filters.

The invention provides an active disturbance rejection control method of a Cuk converter, which belongs to the technical field of electronic control. It solves the problem that the output voltage is seriously affected by input voltage disturbance, parasitic parameter disturbance and load disturbance in the prior art. The method comprises: a, establishing a mathematical model of the Cuk converter according to the Cuk circuit; b, designing a second-order differential equation to determine the tracking differentiator, and extracting the original source of the input reference voltage in the mathematical model of the Cuk converter through the tracking differentiator signal and derivative signal; c. Establishing an extended state observer based on the second-order nonlinear system to estimate the total disturbance of the system; d. Using the error signal and its derivative signal and its integral signal for nonlinear combination to determine the nonlinear state error feedback control The control quantity of the system is constituted by the above-mentioned nonlinear combination and the total disturbance. This control method can make the output voltage have better robustness, adaptability and stability.

The invention discloses a meandering motion analysis method of a flexible bogie of a rail vehicle. The method includes establishing an analysis model of the serpentine motion of the wheelset with lateral movement and no yaw; establishing an analysis model of the serpentine motion of the wheelset with lateral movement and shaking; establishing a flexible bogie model with primary suspension; and analyzing the serpentine motion of the flexible bogie. In order to solve the problem that the method for calculating the meandering motion wavelength of the flexible bogie in the prior art cannot be directly applied to the calculation process of the meandering wavelength of the actual wheelset and the frame, the present invention derives three first-order motions of the free wheelset longitudinal, lateral and shaking motions. The differential equation is substituted into the second-order differential equation of the flexible bogie considering the primary suspension as the excitation of the meandering motion, and the meandering frequency and wavelength of the frame under different wheelset traverses are calculated based on the characteristics of the meandering motion. Computational models are more accurate.

The invention provides a modeling method for an aircraft longitudinal phase plane directly based on a three-dimensional model. The built model performs equivalent transformation directly based on an aircraft three-dimensional motion model, and avoids incorrect direct approximate cuased by the aerodynamical moment effect, the lateral-directional influence and the like ignored in an aerodynamic force equation; an equivalent second-order differential equation set is obtained through a three-dimensional aircraft motion equation and aerodynamic force and aerodynamical moment models obtained through experiments; the equation set expresses a system stability model, can directly adopt a phase plane analytical method to perform theoretical analysis, or adopts an Ode45 module and the like in MATLAB (matrix laboratory) to dreictly perform numerical analysis; more non-linear phenomena and unstable factors and unsafe factors of the system can be found out; and problems of unstable and unsafe flight and the like are reduced or even avoided.