Static characteristics of control systems

Lecture #2

Definition	Description
Static characteristic	The dependence of the system’s output signal from the input. Static characteristics are defined at steady state operation of the system

Static characteristics describes the behavior of controlled objects (behavior of its output signal) while changing input signal. Looking at the static characteristics we can determine the level of object’s “possibilities” and “limits”.

Static characteristics of the controlled object are received in experimental way. While construction of static characteristics we measure value of the input signal and measured value of the corresponding output signal, and then these values are plotted. Value of the input signal corresponds to the x-axis and the values of the output signal corresponds to the y-axis.

Usually static characteristics of technical objects - are nonlinear and have several sections: dead zone, straight zone and saturation zone.

Example: static characteristic of DC engine. In experimental way the values of it’s input and output signal were determined and presented at the table 2.1.

Table 2.1.

Engine’s input and output signals

input signal (voltage, U (V))	u1(t)	u2(t)	u3(t)	ui(t)	…	un(t)
output signal (angular velocity, w(rad/s))	w1(t)	w2(t)	w3(t)	wi(t)	…	wn (t)

Figure 2.2. Static characteristics of engine

dead zone (or dead band)	This zone occurs because of friction forces on the motor shaft and the inertia forces. It is characterized by increase of input signal and zero value of output signal. Once the input signal will be sufficient to overcome all the forces, the motor will rotate and linear section of the static characteristic begins.
straight zone (or linear section)	This section is characterized by a smooth change of signals - namely, when input signal increases output signal increases too (one X-value corresponds to one Y- value). Straight section passes into saturation zone.
saturation zone	This zone is characterized by limiting the possibility of the object. With increasing of input signal the output can not grow because the engine is limited by the speed of rotation. In this case, the input signal increases and the output remains unchanged

We can manipulate with static characteristics of objects O₁ x₂=f(x₁) and O₂ x₃=f(x₂) which are the part of the system in order to get static characteristics of the whole system x₃=f(x₁).

Дата добавления: 2014-01-11