You get a bonus - 1 coin for daily activity. Now you have 1 coin

Example of transfer function modeling

Lecture



Consider an example of modeling with the gain K = 8 and the time constant of the aperiodic link T = 4. The transfer function of a closed system in this case takes the following form:

  Example of transfer function modeling

Roots of the characteristic equation

  Example of transfer function modeling

Processes in such a system will be oscillatory in nature with a frequency f and a period t of natural oscillations

  Example of transfer function modeling

The time constant from which the amplitude of oscillation decreases is   Example of transfer function modeling

Based on the obtained calculation results, we set the integration time equal to   Example of transfer function modeling and the maximum step is chosen less than the oscillation period of more than 40 times and equal to 0.1 s.

In the integration block, we set the initial deviation in X equal to 10. Accordingly, in the XY_Graf block we set the deviations in X , also equal to 10, and along the Y axis 1.4 times more and equal to 15.

Further on fig. 5.2 shows the result of modeling as a transient as a function of time, and Figure 3 shows the phase trajectory of this process. Figure 4 shows the phase portrait of the system, based on the results of modeling four transients with corresponding initial deviations.

According to the simulation results we can conclude:

a) the nature of the transient processes is indeed oscillatory,

b) the control system is stable,

c) the phase portrait consists of trajectories in the form of narrowing ellipses with a stable focus at the equilibrium point.

  Example of transfer function modeling

Fig. 5.2. The transition process in the system when the deviation X = 10.

  Example of transfer function modeling

Fig. 5.3. Phase trajectory at initial deviation X = 10

  Example of transfer function modeling Fig. 5.4. Phase Porting Automatic Control System


Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Mathematical foundations of the theory of automatic control

Terms: Mathematical foundations of the theory of automatic control