23.3 : 二阶系统 I

A servo system is an example of a second-order system. It consists of a proportional controller and load elements that align an output position with a given input position.

A second-order differential equation outlines the relationship between these elements. Applying the Laplace transform under zero initial conditions gives the transfer function, illustrating how inputs are converted to outputs.

A new interpretation of the system leads to the derivation of the closed-loop transfer function. Systems that possess two poles in this transfer function are defined as second-order systems.

The closed-loop transfer function can be rearranged and rewritten to reveal key parameters: the attenuation factor, the undamped natural frequency, and the damping ratio.

The damping ratio is defined as the ratio of actual damping to critical damping. With these parameters, the closed-loop transfer function can be rewritten in a standard form, representing the second-order system.

If the damping ratio is less than 1 but greater than 0, the system is considered underdamped.

If the damping ratio equals 1, the system is critically damped; if it's greater than 1, it is overdamped.