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

1.4. Description of the unadjusted system in the space state and calculation of the system dynamics

Fig. 7. Block diagram of an uncorrected self-propelled gun.

Let's create a detailed block diagram:

Figure 8. Detailed block diagram.

A system of differential equations describing the dynamics of a linear ACS:

Equations for coupling output signals with state variables:

Let us consider the matrix of the system (coefficients of the system) – A, the matrix of inputs (control) - B, and the matrix of output (observation) - C:

;


; ;

Let's write the matrix transfer function of a closed system under zero initial conditions:

, where is the identity matrix


;
The transition matrix is described by the expression: ;
By performing the inverse Laplace transform from  matrix, we obtain the fundamental matrix of the system.
The state variables are defined by the expression:
, where is the vector of initial conditions.

Let's model a detailed system in MATLAB:

Figure 9. Uncorrected self-propelled guns modeled in Matlab.

10. Graphs of state variables of the system modeled in MATLAB.

2. Calculation of a nonlinear automatic control system


Task:

1. 
   It detects the presence of self-oscillations in the system, detects their stability, and calculates the parameters (if there are no self – oscillations in the system, it will achieve them by changing the parameters of the linear part or non-linear element).
   
2. 
   The dynamic modes of the system are investigated by the phase plane method for a given static characteristic of a nonlinear element (HE).
   
3. 
   Builds a transition process in a non-linear system.
   

Fig. 11. Initial block diagram of the ACS.