Course paper on the course "Management Theory" Completed: art gr. Accepted(a): tashkent-2022 bbedenie

1.1. Determination of transfer functions of open and closed systems and disturbing effects. Determination of the transfer function by error and calculation of the system accuracy

Transfer function of an open ACS based on the input signal:

;

Transfer function of a closed ACS based on the input signal:

Transfer function of a closed self-propelled gun by mistake:



Since the transfer function has a zero pole, the system is astatic with first-order astaticism.
One of the most important requirements that the automatic control system must meet is to ensure the necessary accuracy of reproducing the setting (controlling) signal in steady-state mode.
The steady-state calculation scheme is as follows:
Sourcedata


,

where — position error; — speed error; — acceleration error.

Closed-loop error transfer function

The transfer function is represented as a series:

converging at small "n" ; which corresponds to a steady-state regime or sufficiently high values of time t. The coefficients of this series are called error coefficients and are determined using the expressions:

For our example ,; (since the order of astaticism is 1) is a position error.

– speed error rate.

– acceleration error rate.
So With₀= 0; With₁= 0.139; With₂= 0.0625.
Using the found error coefficients С₀C0, С_C1, С_{and C2}, we determine the errors of a closed corrected system under various input actions
a) x (t)= 1 (t); ; ;
b) x(t)= t; ; ;
c) x(t)= т^t2; ; ;
Based on the analysisы of the accuracy ofwater systems, it canbe concluded that this system is astatic with respect to the input effect, which hasщa constant emu value.
Transfer function of an open systems overщаюa disturbedemu signal.
;
Transfer function of a closed systems overщаюa disturbedemu signal.