Systems described by second-order differential equations are called second-order systems. Many high-order systems are often studied as second-order systems under certain conditions. The quality of dynamic characteristics of control system is evaluated by the performance index of dynamic characteristics.
The performance index of control system dynamic characteristics is usually defined according to some characteristic quantities of system unit step response. The dynamic process of most control systems has oscillation characteristics. Therefore, we choose the underdamped oscillation process as a typical representative to define the performance indexes of dynamic characteristics, and use these indexes to describe the dynamic process quality of the control system.
A form when the control system of a second-order system is classified according to a mathematical model. It is a system that can be expressed as a second-order linear ordinary differential equation by mathematical model. The form of the solution of the second-order system can be judged and divided by the denominator polynomial P(s) corresponding to the transfer function W(s). The general form of P(s) is quadratic trinomial algebra of transformation operator S.
Between 0.4 and 0.8 is appropriate. When zeta > 0.8, the effect of oscillation is not obvious, and the output speed is relatively slow. While zeta < 0.4, the output has obvious oscillation, large overshoot and slow attenuation, which is also undesirable in the control system.
The definition and characteristics of second-order system;
1. definition of second-order system: second-order system is a common dynamic system, which consists of two state variables (position and velocity) and two inputs (force and torque), and its dynamic equation can be used to describe its behavior.
2. The second-order system has two state variables, its output can be controlled by two inputs, and its dynamic equation can be used to describe its behavior, which has the characteristics of self-excited oscillation and oscillator.