Preparation of equations of automatic control system (ACS)

Formulas used in solving

The transfer function of the control for an open system:

(3.1)

Disturbing transfer function for an open-loop system:

(3.2)

The transfer function of the control for a closed system:

(3.3)

The transfer function of the disturbing effects for a closed system:

(3.4)

The transfer function of the control for the error:

(3.5)

Disturbance transfer function for error:

(3.6)

A (p) - Polynomial open automatic system

B (p) - Polynomial control action of an open automatic system

C (p) - Polynomial disturbing effect of an open automatic system

(3.7)

D ( p ) is the characteristic polynomial of a closed automatic system.

The equations for an open automatic system, for a closed automatic system and for an error:

(3.8)

(3.9)

(3.10)

The characteristic polynomials of the open A (p) and closed D ( p ) systems, as well as the roots of the corresponding characteristic equations, play an important role in the study of the dynamic properties of speakers.

Transfer functions they are called the main or main operators of the automatic system, since they completely determine the dynamic and accuracy characteristics of the system.

Transfer functions They are not the main operators, as they depend on the point of application of the disturbing action.

In practical studies of the automatic system, you need to know the links between the main operators:

(3.11)

(3.12)

(3.13)

Thus, it is enough to know one of the main operators and the transfer function of feedback to define all the other main operators.

Examples of problem solving