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

2.1. Determination of the presence of self-oscillations in the system, measurement of their stability and calculation of parameters
Sourcedata: ; ; ;
Transfer function of the linear part: ;

Figure 12. Static characteristics of a nonlinear element.

Sequence diagram for determining the possibility of self-oscillations:

Coefficients of harmonic linearization HE of the hysteresis type:

; ;

Transfer function of a harmonically linearized HE:

;

Let us determine the parameters of self-oscillations by the Nyquist criterion.

Auto-fluctuations in the system will occur if  , then eats


;


;

Having solved this system, we get:  ; .

1 — , 2 — .
Figure 13. Determination of self-oscillation parameters

The self-oscillating mode can be investigated by the Goldfarb method. To do this, we construct and in the complex plane и . The point of their intersection gives us the amplitude of self-oscillations A and the frequency ω. From drawings ; . In our example, when we increase A, we leave the contour covered , so the self-oscillations are stable.

2.2. Investigation of dynamic modes of the system by the phase plane method for a given static characteristic of a nonlinear element

Consider a system in free motion, so:

; ; ;

After performing substitutions and grouping, we get:

;

Given the given nonlinearity, when describing the behavior of the system, we will consider two zones (-M,M), for which the differential equations will have the form:

zone 1: ;
zone 2: ;
Let's model a nonlinear system:

14. Nonlinear self-propelled guns modeled in MATLAB.

The phase trajectories and transition graph are shown in Fig. 15, 16.

Рис. 15. Phase trajectory.

Figure 16. Transition process.

conclusion

In the course of this course work, the knowledge gained was consolidated by calculating linear, nonlinear and discrete automatic control systems. The transfer function of an open and closed system was determined for a given structural scheme, the stability of the closed system using the frequency stability criterion, the LAX of the correcting element, and the transfer function based on the error of the original system. Self-propelled guns were synthesized and analyzed. The synthesis was performed using LFCH and LFCH.

A block diagram of the nonlinear system was drawn up (based on the task), the block diagram of the discrete system was constructed by the LAX and LFX of the corrected open-loop system.
Thus, the quality indicators of ACS regulation obtained by us during this course work by introducing serial and parallel correction devices into the system are close to the specified ones and qualitatively several times higher than the indicators of the original ACS.
Literature

1.