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10135.Исследование динамики процесса дымообразования при холодном копчении с целью получения начальных моделей для адаптивной системы управления процессом

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ɉɨɧɨɦɚɪɟɧɤɨ Ⱦ.Ⱥ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ…
ɂɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɩɪɢ
ɯɨɥɨɞɧɨɦ ɤɨɩɱɟɧɢɢ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɧɚɱɚɥɶɧɵɯ ɦɨɞɟɥɟɣ
ɞɥɹ ɚɞɚɩɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ
Ⱦ.Ⱥ. ɉɨɧɨɦɚɪɟɧɤɨ
ɉɨɥɢɬɟɯɧɢɱɟɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɌɍ, ɤɚɮɟɞɪɚ ɚɜɬɨɦɚɬɢɤɢ
ɢ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɬɟɯɧɢɤɢ
Ⱥɧɧɨɬɚɰɢɹ. ȼ ɫɬɚɬɶɟ ɩɪɢɜɟɞɟɧɵ ɦɟɬɨɞɢɤɢ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɜ
ɯɨɥɨɞɧɨɦ ɤɨɩɱɟɧɢɢ. Ɉɩɢɫɚɧɵ ɷɤɫɩɟɪɢɦɟɧɬɵ ɞɥɹ ɫɧɹɬɢɹ ɩɟɪɟɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɫɫɥɟɞɭɟɦɨɝɨ
ɩɪɨɰɟɫɫɚ, ɚ ɬɚɤɠɟ ɦɟɬɨɞɢɤɢ ɩɨɥɭɱɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɞɢɧɚɦɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ ɩɨ ɢɯ
ɩɟɪɟɯɨɞɧɵɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɧɨɝɨ ɩɚɤɟɬɚ Matlab.
Abstract. The paper contains the methodology of smoke generation dynamics research in the cold smoking. The
author has described the experiments for obtaining transient characteristics of the investigated process as well as
the methodologies for constructing the mathematical models of dynamic objects by means of their transient
characteristics using the programme package Matlab.
1. ȼɜɟɞɟɧɢɟ
ɉɪɨɰɟɫɫ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɩɪɢ ɯɨɥɨɞɧɨɦ ɤɨɩɱɟɧɢɢ ɹɜɥɹɟɬɫɹ ɧɟɫɬɚɰɢɨɧɚɪɧɵɦ ɹɜɥɟɧɢɟɦ,
ɩɚɪɚɦɟɬɪɵ ɤɨɬɨɪɨɝɨ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɦɟɪɟ ɡɚɜɢɫɹɬ ɨɬ ɫɨɫɬɨɹɧɢɹ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ, ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɢ
ɬ.ɩ. ɉɨɫɬɪɨɟɧɢɟ ɚɞɚɩɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɞɥɹ ɩɨɞɨɛɧɵɯ ɩɪɨɰɟɫɫɨɜ ɩɨɡɜɨɥɹɟɬ ɨɛɟɫɩɟɱɢɬɶ
ɫɨɨɬɜɟɬɫɬɜɢɟ ɫɨɫɬɨɹɧɢɹ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɜɵɛɪɚɧɧɨɦɭ ɤɪɢɬɟɪɢɸ ɨɩɬɢɦɚɥɶɧɨɫɬɢ ɢ ɩɨɜɵɫɢɬɶ
ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɚɜɬɨɦɚɬɢɡɢɪɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ ɜ ɰɟɥɨɦ.
Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɚɞɚɩɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɧɟɨɛɯɨɞɢɦɨ ɧɚɥɢɱɢɟ
ɷɬɚɥɨɧɧɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɚɜɬɨɦɚɬɢɡɢɪɭɟɦɨɣ ɫɢɫɬɟɦɵ, ɢɫɩɨɥɶɡɭɟɦɨɣ ɞɥɹ ɧɚɫɬɪɨɣɤɢ ɩɚɪɚɦɟɬɪɨɜ
ɪɟɝɭɥɹɬɨɪɨɜ. Ʉɪɨɦɟ ɬɨɝɨ, ɟɫɥɢ ɩɪɨɰɟɫɫ ɹɜɥɹɟɬɫɹ ɧɟɫɬɚɰɢɨɧɚɪɧɵɦ, ɬɨ ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜ
ɧɚɩɪɚɜɥɟɧɧɨɣ ɤɨɪɪɟɤɬɢɪɨɜɤɟ ɩɚɪɚɦɟɬɪɨɜ ɬɟɤɭɳɟɣ ɦɨɞɟɥɢ. Ɂɚɬɪɚɬɵ ɜɪɟɦɟɧɢ ɢ ɪɟɫɭɪɫɨɜ ɫɢɫɬɟɦɵ
ɭɩɪɚɜɥɟɧɢɹ ɧɚ ɤɨɪɪɟɤɬɢɪɨɜɤɭ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ ɦɨɠɧɨ ɫɨɤɪɚɬɢɬɶ, ɟɫɥɢ ɜ ɤɚɱɟɫɬɜɟ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ
ɞɥɹ ɧɚɫɬɪɨɣɤɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɚɱɚɥɶɧɭɸ ɦɨɞɟɥɶ, ɩɨɥɭɱɟɧɧɭɸ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ
ɢɫɫɥɟɞɨɜɚɧɢɹ ɚɜɬɨɦɚɬɢɡɢɪɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ.
Ⱥɜɬɨɪɨɦ ɪɚɡɪɚɛɨɬɚɧɚ ɦɟɬɨɞɢɤɚ ɩɨɥɭɱɟɧɢɹ ɧɚɱɚɥɶɧɵɯ ɦɨɞɟɥɟɣ ɩɨ ɩɟɪɟɯɨɞɧɵɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ
ɚɜɬɨɦɚɬɢɡɢɪɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɩɪɢ ɯɨɥɨɞɧɨɦ ɤɨɩɱɟɧɢɢ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɞɜɭɯ ɷɬɚɩɨɜ:
1) ɢɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɧɚɛɨɪɚ ɩɟɪɟɯɨɞɧɵɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɞɨɫɬɚɬɨɱɧɨɝɨ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɚɞɟɤɜɚɬɧɨɣ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɚ;
2) ɩɨɥɭɱɟɧɢɟ ɧɚɱɚɥɶɧɨɣ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɧɨɝɨ
ɩɚɤɟɬɚ Matlab, ɢɫɩɨɥɶɡɭɹ ɜ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɧɚɛɨɪ ɩɟɪɟɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɩɨɥɭɱɟɧɧɵɯ ɜ
ɪɟɡɭɥɶɬɚɬɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ.
2. ɂɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɧɚɛɨɪɚ ɩɟɪɟɯɨɞɧɵɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɤɨɧɬɭɪɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɤɨɩɬɢɥɶɧɨɣ ɤɚɦɟɪɵ
ɐɟɥɶɸ ɷɤɫɩɟɪɢɦɟɧɬɚ ɹɜɥɹɟɬɫɹ ɩɨɥɭɱɟɧɢɟ ɫɟɦɟɣɫɬɜɚ ɩɟɪɟɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɤɨɩɬɢɥɶɧɨɣ
ɤɚɦɟɪɵ (ɡɚɜɢɫɢɦɨɫɬɟɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɨɬ ɜɪɟɦɟɧɢ) ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ
ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɜɥɚɠɧɨɫɬɢ (ɞɚɥɟɟ – ɫɢɝɧɚɥɚɯ) ɧɚ ɟɟ ɜɯɨɞɟ ɞɥɹ ɩɨɫɥɟɞɭɸɳɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɯ ɩɪɢ
ɩɨɥɭɱɟɧɢɢ ɧɚɱɚɥɶɧɨɣ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ ɤɚɦɟɪɵ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ. ɇɚ ɤɨɧɰɟɧɬɪɚɰɢɸ
ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɜ ɤɚɦɟɪɟ ɨɤɚɡɵɜɚɸɬ ɜɥɢɹɧɢɟ ɫɥɟɞɭɸɳɢɟ ɩɨɬɨɤɢ ɤɨɩɬɢɥɶɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ:
ɩɨɬɨɤ ɩɪɢɜɧɨɫɢɦɵɯ ɫ ɞɵɦɨɦ ɜɟɳɟɫɬɜ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɞɢɧɚɦɢɤɭ ɩɨɜɵɲɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ
ɤɨɩɬɢɥɶɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ;
ɩɨɬɨɤ ɜɟɳɟɫɬɜ, ɨɫɟɞɚɸɳɢɯ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɪɵɛɵ, ɱɚɫɬɶ ɷɬɢɯ ɜɟɳɟɫɬɜ ɞɢɮɮɭɧɞɢɪɭɟɬ ɜɧɭɬɪɶ ɪɵɛɵ,
ɩɪɢɞɚɜɚɹ ɟɣ ɜɤɭɫ, ɰɜɟɬ ɢ ɚɪɨɦɚɬ ɤɨɩɱɟɧɨɫɬɢ;
ɩɨɬɨɤ ɜɟɳɟɫɬɜ, ɨɫɟɞɚɸɳɢɯ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɦɟɪɵ, ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɢ ɬ.ɞ., ɩɨɬɟɪɢ ɤɨɩɬɢɥɶɧɵɯ
ɤɨɦɩɨɧɟɧɬɨɜ;
ɩɨɬɨɤ ɜɟɳɟɫɬɜ, ɭɞɚɥɹɟɦɵɯ ɢɡ ɤɚɦɟɪɵ ɜɦɟɫɬɟ ɫ ɱɚɫɬɶɸ ɜɵɛɪɚɫɵɜɚɟɦɨɣ ɜ ɚɬɦɨɫɮɟɪɭ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ.
Ⱥɧɚɥɢɡ ɫɭɳɟɫɬɜɭɸɳɟɣ ɥɢɬɟɪɚɬɭɪɵ, ɨɩɢɫɵɜɚɸɳɟɣ ɞɢɧɚɦɢɤɭ ɞɚɧɧɨɝɨ ɩɪɨɰɟɫɫɚ, ɩɨɡɜɨɥɹɟɬ ɜɜɟɫɬɢ
ɫɥɟɞɭɸɳɢɟ ɞɨɩɭɳɟɧɢɹ:
494
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 7, ʋ3, 2004 ɝ.
ɫɬɪ.494-498
x Ʉɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜ, ɩɨɫɬɭɩɚɸɳɟɟ ɫ ɞɵɦɨɦ, ɛɭɞɟɬ ɭɜɟɥɢɱɢɜɚɬɶ ɤɨɧɰɟɧɬɪɚɰɢɸ ɜ ɤɚɦɟɪɟ. ɗɬɨ
ɟɞɢɧɫɬɜɟɧɧɵɣ ɢɫɬɨɱɧɢɤ ɩɨɜɵɲɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɨɩɬɢɥɶɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ. ɇɟɤɨɬɨɪɵɦ
ɤɨɥɢɱɟɫɬɜɨɦ ɜɟɳɟɫɬɜ, ɢɫɩɚɪɹɸɳɢɯɫɹ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɪɵɛɵ, ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ.
x ɇɚ ɫɧɢɠɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɨɫɧɨɜɧɨɟ ɜɥɢɹɧɢɟ ɨɤɚɡɵɜɚɟɬ ɨɛɧɨɜɥɟɧɢɟ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ,
ɨɩɪɟɞɟɥɹɟɦɨɟ ɩɨɥɨɠɟɧɢɟɦ ɡɚɫɥɨɧɨɤ ɞɵɦɚ ɢ ɫɜɟɠɟɝɨ ɜɨɡɞɭɯɚ. ɍɞɚɥɟɧɢɟ ɢɡ ɤɚɦɟɪɵ ɱɚɫɬɢ
ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɩɪɢɜɨɞɢɬ ɤ ɩɚɞɟɧɢɸ ɤɨɧɰɟɧɬɪɚɰɢɢ ɫɦɟɫɢ, ɭɫɢɥɟɧɧɨɦɭ ɩɨɞɚɱɟɣ ɜ ɤɚɦɟɪɭ
ɩɨɪɰɢɢ ɫɜɟɠɟɝɨ ɜɨɡɞɭɯɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɞɵɦɨɝɟɧɟɪɚɬɨɪɟ ɩɚɞɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɛɭɞɟɬ ɨɛɭɫɥɚɜɥɢɜɚɬɶɫɹ
ɬɚɤɠɟ ɩɪɨɝɨɪɚɧɢɟɦ ɨɩɢɥɨɤ ɜ ɤɚɫɫɟɬɟ ɢ ɩɪɨɰɟɫɫɨɦ ɢɯ ɡɚɦɟɧɵ ɧɚ ɧɨɜɵɟ.
ɋɧɢɠɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɡ-ɡɚ ɨɫɟɞɚɧɢɹ ɤɨɩɬɢɥɶɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ ɧɚ ɫɵɪɶɟ ɢ ɩɨɜɟɪɯɧɨɫɬɢ
ɤɚɦɟɪɵ ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɜɭɦɹ ɜɵɲɟɨɩɢɫɚɧɧɵɦɢ, ɤɪɨɦɟ ɬɨɝɨ ɢɯ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɜɨɡɦɨɠɧɨ ɢɡɦɟɧɹɬɶ
ɩɨ ɠɟɥɚɧɢɸ. ɉɨɷɬɨɦɭ ɫɩɟɰɢɚɥɶɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɵ ɩɨ ɨɰɟɧɤɟ ɜɥɢɹɧɢɹ ɷɬɢɯ ɮɚɤɬɨɪɨɜ ɩɪɨɜɨɞɢɬɶ ɧɟ ɧɭɠɧɨ,
ɧɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ ɨɫɚɠɞɟɧɢɟ ɤɨɩɬɢɥɶɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɫɵɪɶɹ ɫɨɫɬɚɜɥɹɟɬ ɫɭɳɧɨɫɬɶ
ɩɪɨɰɟɫɫɚ ɤɨɩɱɟɧɢɹ. Ⱦɥɹ ɢɧɬɟɧɫɢɮɢɤɚɰɢɢ ɩɪɨɰɟɫɫɚ ɤɨɩɱɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɩɨɞɞɟɪɠɢɜɚɬɶ, ɧɚɫɤɨɥɶɤɨ
ɜɨɡɦɨɠɧɨ, ɤɨɧɰɟɧɬɪɚɰɢɸ ɫɦɟɫɢ ɦɚɤɫɢɦɚɥɶɧɨɣ.
ɇɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɫɬɢ ɫɟɪɢɸ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɩɨɥɭɱɟɧɢɸ ɩɟɪɟɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɤɨɩɬɢɥɶɧɨɣ ɤɚɦɟɪɵ ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɧɚ ɧɟɟ ɫɬɭɩɟɧɱɚɬɨ ɢɡɦɟɧɹɸɳɟɝɨɫɹ ɩɨɬɨɤɚ ɤɨɩɬɢɥɶɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ
ɢ ɫɬɭɩɟɧɱɚɬɨɦ ɫɢɧɯɪɨɧɧɨɦ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɡɚɫɥɨɧɨɤ.
ɋɨɡɞɚɬɶ ɠɟɥɚɟɦɨɟ ɢɡɦɟɧɟɧɢɟ ɩɨɬɨɤɚ ɜɟɳɟɫɬɜ ɦɨɠɧɨ, ɪɟɝɭɥɢɪɭɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ
ɞɵɦɨɝɟɧɟɪɚɬɨɪɚ. ɂɡɦɟɧɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɚɜɬɨɪɨɦ ɞɵɦɨɝɟɧɟɪɚɬɨɪɚ ɫ ɩɨɞɜɨɞɨɦ ɬɟɩɥɚ
ɢɧɮɪɚɤɪɚɫɧɵɦ ɢɡɥɭɱɟɧɢɟɦ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡɦɟɧɟɧɢɟɦ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɢɡɥɭɱɟɧɢɹ. ȼɫɟɝɞɚ ɦɨɠɧɨ ɞɨɫɬɢɱɶ
ɬɚɤɨɣ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɟɧɢɹ ɦɨɳɧɨɫɬɢ, ɩɨɞɚɜɚɟɦɨɣ ɧɚ ɧɚɝɪɟɜɚɬɟɥɶɧɵɟ ɷɥɟɦɟɧɬɵ, ɩɪɢ ɤɨɬɨɪɨɣ ɷɬɨ ɢɡɦɟɧɟɧɢɟ
ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɧɹɬɨ ɫɬɭɩɟɧɱɚɬɵɦ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɜɪɟɦɟɧɟɦ ɩɪɨɬɟɤɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɢɡɦɟɧɟɧɢɹ
ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ. Ɉɞɧɚɤɨ ɢ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɢ ɩɪɢ ɪɟɚɥɢɡɚɰɢɢ ɫɢɫɬɟɦɵ
ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ ɤɨɩɱɟɧɢɹ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ, ɨɩɪɟɞɟɥɹɸɳɚɹ ɟɝɨ
ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ, ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɞɵɦɨɝɟɧɟɪɚɬɨɪɚ ɧɟ ɞɨɥɠɧɚ ɩɨɞɧɢɦɚɬɶɫɹ ɞɨ ɡɧɚɱɟɧɢɣ,
ɩɪɢ ɤɨɬɨɪɵɯ ɩɪɨɢɫɯɨɞɢɬ ɧɚɫɵɳɟɧɢɟ ɞɵɦɚ ɤɚɧɰɟɪɨɝɟɧɧɵɦɢ ɜɟɳɟɫɬɜɚɦɢ.
ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɨɫɭɳɟɫɬɜɥɹɥɨɫɶ ɫɨɝɥɚɫɧɨ ɥɢɬɟɪɚɬɭɪɟ (Ȼɚɥɚɤɢɪɟɜ ɢ ɞɪ., 1967;
ȼɢɫɤɨɜ, 2002). ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɩɢɫɚɧɧɨɣ ɜ ɜɵɲɟɩɪɢɜɟɞɟɧɧɵɯ ɪɚɛɨɬɚɯ ɦɟɬɨɞɢɤɨɣ ɞɥɹ ɢɡɭɱɟɧɢɹ ɫɜɨɣɫɬɜ
ɨɛɴɟɤɬɚ ɜ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɧɟɨɛɯɨɞɢɦɨ ɫɧɹɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɜɵɲɟɧɢɹ ɢ ɫɧɢɠɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ
ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɤɚɦɟɪɵ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɧɚ 25 %, 50 %, 75 % ɢ
100 % ɢ ɩɨɥɨɠɟɧɢɹ ɡɚɫɥɨɧɨɤ ɧɚ 22,5°, 45°, 67,5° ɢ 90°. ɉɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɢ ɜɥɚɠɧɨɫɬɶ ɫɦɟɫɢ ɞɨɥɠɧɵ
ɩɨɞɞɟɪɠɢɜɚɬɶɫɹ ɩɨɫɬɨɹɧɧɵɦɢ, ɬ.ɟ. ɫɢɫɬɟɦɵ ɫɬɚɛɢɥɢɡɚɰɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɜɥɚɠɧɨɫɬɢ ɜ ɤɚɦɟɪɟ ɞɨɥɠɧɵ
ɮɭɧɤɰɢɨɧɢɪɨɜɚɬɶ ɜ ɩɨɥɧɨɦ ɨɛɴɟɦɟ, ɢɧɚɱɟ ɜ ɪɟɡɭɥɶɬɚɬɚɯ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨɹɜɹɬɫɹ ɩɟɪɟɦɟɧɧɵɟ
ɫɨɫɬɚɜɥɹɸɳɢɟ, ɫɜɹɡɚɧɧɵɟ ɫ ɢɡɦɟɧɟɧɢɟɦ ɩɨɬɨɤɨɜ ɨɫɚɠɞɚɸɳɢɯɫɹ ɜɟɳɟɫɬɜ. ɏɨɬɹ ɫɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ
ɜɥɢɹɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɜɥɚɠɧɨɫɬɢ ɫɦɟɫɢ ɧɚ ɟɟ ɤɨɧɰɟɧɬɪɚɰɢɸ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɟɟ ɜɵɪɚɠɟɧɨ, ɱɟɦ ɜɥɢɹɧɢɟ
ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɜɥɚɠɧɨɫɬɶ.
Ʉɪɨɦɟ ɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɨɞɢɬɶ ɩɨɞɨɛɧɵɟ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɞɥɹ ɨɫɧɨɜɧɵɯ ɜɢɞɨɜ
ɞɪɟɜɟɫɢɧɵ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɞɵɦɚ, ɢ ɯɨɬɹ ɛɵ ɬɪɟɯ ɫɥɭɱɚɟɜ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɪɟɞɟɥɶɧɵɦ ɢ
ɫɪɟɞɧɟɦɭ ɡɧɚɱɟɧɢɹɦ ɩɚɪɚɦɟɬɪɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɫɵɪɶɟ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɞɵɦɚ (ɜɢɞ ɞɪɟɜɟɫɢɧɵ,
ɧɚɱɚɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ, ɫɪɟɞɧɢɣ ɪɚɡɦɟɪ ɱɚɫɬɢɰ ɨɩɢɥɨɤ). Ⱦɥɹ ɫɧɢɠɟɧɢɹ ɜɥɢɹɧɢɹ ɫɥɭɱɚɣɧɵɯ ɜɧɟɲɧɢɯ
ɮɚɤɬɨɪɨɜ ɢ ɩɨɜɵɲɟɧɢɹ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɪɟɡɭɥɶɬɚɬɨɜ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɢɯ ɫɥɭɱɚɹɯ, ɠɟɥɚɬɟɥɶɧɨ ɞɥɹ
ɤɚɠɞɨɝɨ ɧɚɛɨɪɚ ɢɫɯɨɞɧɵɯ ɮɚɤɬɨɪɨɜ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫɧɢɦɚɬɶ 5-7 ɡɚɜɢɫɢɦɨɫɬɟɣ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɨɛɴɟɦ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɚɛɨɬ ɜɟɥɢɤ. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɚɪɚɦɟɬɪɵ ɩɨɥɭɱɟɧɧɨɣ
ɧɚ ɨɫɧɨɜɚɧɢɢ ɧɚɛɨɪɚ ɫɧɹɬɵɯ ɩɟɪɟɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɧɚɱɚɥɶɧɨɣ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ ɜ ɞɚɥɶɧɟɣɲɟɦ
ɛɭɞɭɬ ɤɨɪɪɟɤɬɢɪɨɜɚɬɶɫɹ ɚɞɚɩɬɢɜɧɨɣ ɫɢɫɬɟɦɨɣ ɭɩɪɚɜɥɟɧɢɹ, ɤɨɥɢɱɟɫɬɜɨ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɦɨɠɧɨ ɫɨɤɪɚɬɢɬɶ.
ȼɦɟɫɬɨ ɪɵɛɵ ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ ɜɨɞɭ. ɇɟɨɛɯɨɞɢɦɨ ɩɨɥɭɱɢɬɶ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ
ɫɦɟɫɢ ɜ ɤɚɦɟɪɟ ɨɬ ɜɪɟɦɟɧɢ, ɢɥɢ, ɞɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɩɟɪɟɯɨɞɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɨɧɬɭɪɚ ɤɨɧɰɟɧɬɪɚɰɢɢ
ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɤɨɩɬɢɥɶɧɨɣ ɤɚɦɟɪɵ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɹɯ:
1. ɉɪɢ ɩɨɥɧɨɫɬɶɸ ɡɚɤɪɵɬɵɯ ɡɚɫɥɨɧɤɚɯ ɢ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɫɪɟɞɧɢɯ ɞɥɹ ɩɪɨɰɟɫɫɚ ɡɧɚɱɟɧɢɹɯ ɬɟɦɩɟɪɚɬɭɪɵ
ɢ ɜɥɚɠɧɨɫɬɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɡɚɞɚɬɶ ɦɢɧɢɦɚɥɶɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ,
ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɜ ɤɚɦɟɪɟ ɨɬ ɜɪɟɦɟɧɢ. ɉɨɫɥɟ
ɭɫɬɚɧɨɜɥɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɤɚɦɟɪɟ ɜɵɤɥɸɱɢɬɶ ɞɵɦɨɝɟɧɟɪɚɬɨɪ, ɩɨɥɧɨɫɬɶɸ ɨɬɤɪɵɬɶ ɡɚɫɥɨɧɤɢ ɞɵɦɚ
ɢ ɫɜɟɠɟɝɨ ɜɨɡɞɭɯɚ ɢ ɬɚɤɠɟ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ɷɤɫɩɟɪɢɦɟɧɬ ʋ 1).
2. ɉɪɢ ɩɨɥɧɨɫɬɶɸ ɡɚɤɪɵɬɵɯ ɡɚɫɥɨɧɤɚɯ ɢ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɫɪɟɞɧɢɯ ɞɥɹ ɩɪɨɰɟɫɫɚ ɡɧɚɱɟɧɢɹɯ ɬɟɦɩɟɪɚɬɭɪɵ
ɢ ɜɥɚɠɧɨɫɬɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɡɚɞɚɬɶ ɦɚɤɫɢɦɚɥɶɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ,
ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɜ ɤɚɦɟɪɟ ɨɬ ɜɪɟɦɟɧɢ. ɉɨɫɥɟ
ɭɫɬɚɧɨɜɥɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɤɚɦɟɪɟ ɜɵɤɥɸɱɢɬɶ ɞɵɦɨɝɟɧɟɪɚɬɨɪ, ɩɨɥɧɨɫɬɶɸ ɨɬɤɪɵɬɶ ɡɚɫɥɨɧɤɢ ɞɵɦɚ
ɢ ɫɜɟɠɟɝɨ ɜɨɡɞɭɯɚ ɢ ɬɚɤɠɟ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ɷɤɫɩɟɪɢɦɟɧɬ ʋ 2).
495
ɉɨɧɨɦɚɪɟɧɤɨ Ⱦ.Ⱥ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ…
3. ɉɪɢ ɨɬɤɪɵɬɵɯ ɧɚ 25 % ɡɚɫɥɨɧɤɚɯ ɢ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɫɪɟɞɧɢɯ ɞɥɹ ɩɪɨɰɟɫɫɚ ɡɧɚɱɟɧɢɹɯ ɬɟɦɩɟɪɚɬɭɪɵ ɢ
ɜɥɚɠɧɨɫɬɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɡɚɞɚɬɶ ɫɪɟɞɧɸɸ ɬɟɦɩɟɪɚɬɭɪɭ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ, ɡɚɮɢɤɫɢɪɨɜɚɬɶ
ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɜ ɤɚɦɟɪɟ ɨɬ ɜɪɟɦɟɧɢ. ɉɨɫɥɟ ɭɫɬɚɧɨɜɥɟɧɢɹ
ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɤɚɦɟɪɟ ɜɵɤɥɸɱɢɬɶ ɞɵɦɨɝɟɧɟɪɚɬɨɪ, ɨɬɤɪɵɬɶ ɡɚɫɥɨɧɤɢ ɞɵɦɚ ɢ ɫɜɟɠɟɝɨ ɜɨɡɞɭɯɚ ɧɚ
75 % ɢ ɬɚɤɠɟ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ɷɤɫɩɟɪɢɦɟɧɬ ʋ 3).
4. ɉɪɢ ɨɬɤɪɵɬɵɯ ɧɚ 75 % ɡɚɫɥɨɧɤɚɯ ɢ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɫɪɟɞɧɢɯ ɞɥɹ ɩɪɨɰɟɫɫɚ ɡɧɚɱɟɧɢɹɯ ɬɟɦɩɟɪɚɬɭɪɵ ɢ
ɜɥɚɠɧɨɫɬɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɡɚɞɚɬɶ ɫɪɟɞɧɸɸ ɬɟɦɩɟɪɚɬɭɪɭ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ, ɡɚɮɢɤɫɢɪɨɜɚɬɶ
ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɜ ɤɚɦɟɪɟ ɨɬ ɜɪɟɦɟɧɢ. ɉɨɫɥɟ ɭɫɬɚɧɨɜɥɟɧɢɹ
ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɤɚɦɟɪɟ ɜɵɤɥɸɱɢɬɶ ɞɵɦɨɝɟɧɟɪɚɬɨɪ, ɡɚɤɪɵɬɶ ɡɚɫɥɨɧɤɢ ɞɵɦɚ ɢ ɫɜɟɠɟɝɨ ɜɨɡɞɭɯɚ ɧɚ 50 %
ɢ ɬɚɤɠɟ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ɷɤɫɩɟɪɢɦɟɧɬ ʋ 4).
ɉɪɨɜɟɞɟɧɢɟ ɜɵɲɟɨɩɢɫɚɧɧɵɯ ɱɟɬɵɪɟɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɩɟɪɟɯɨɞɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɞɚɥɶɧɟɣɲɟɦ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɚ
ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ.
3. Ɉɩɢɫɚɧɢɟ ɦɟɬɨɞɢɤɢ ɩɨɥɭɱɟɧɢɹ ɧɚɱɚɥɶɧɵɯ ɷɬɚɥɨɧɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɞɢɧɚɦɢɱɟɫɤɢɯ
ɨɛɴɟɤɬɨɜ ɩɨ ɧɚɛɨɪɭ ɩɟɪɟɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɧɚɱɚɥɶɧɨɣ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ ɤɨɩɬɢɥɶɧɨɣ ɤɚɦɟɪɵ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɩɨ
ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɛɵɥ ɜɵɛɪɚɧ ɩɪɨɝɪɚɦɦɧɵɣ ɩɚɤɟɬ MATLAB 6.0 ɤɨɦɩɚɧɢɢ The
MathWorks, Inc. ɜɦɟɫɬɟ ɫ ɩɚɤɟɬɨɦ ɢɞɟɧɬɢɮɢɤɚɰɢɢ ɫɢɫɬɟɦ System Identification Toolbox. ɉɪɨɝɪɚɦɦɧɵɣ
ɩɚɤɟɬ MATLAB 6.0 (Ƚɨɜɨɪɭɯɢɧ, ɐɢɛɭɥɢɧ, 2000; ȿɝɨɪɟɧɤɨɜ ɢ ɞɪ., 1997) ɦɨɳɧɵɣ ɢ ɫɨɜɪɟɦɟɧɧɵɣ
ɢɧɫɬɪɭɦɟɧɬ ɞɥɹ ɩɪɨɜɟɞɟɧɢɹ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɹɜɥɹɸɳɢɣɫɹ ɧɚ ɫɟɝɨɞɧɹ ɩɪɚɤɬɢɱɟɫɤɢ ɫɬɚɧɞɚɪɬɨɦ ɞɥɹ
ɩɪɨɜɟɞɟɧɢɹ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɯ ɪɚɫɱɟɬɨɜ ɢ ɢɧɠɟɧɟɪɧɵɯ ɪɚɡɪɚɛɨɬɨɤ. ɗɬɨɦɭ ɫɩɨɫɨɛɫɬɜɭɟɬ ɛɨɝɚɬɚɹ
ɛɢɛɥɢɨɬɟɤɚ ɤɨɦɚɧɞ ɢ ɫɜɨɣ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɞɚɸɳɢɣ ɩɨɥɶɡɨɜɚɬɟɥɸ ɜɨɡɦɨɠɧɨɫɬɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ
ɜɵɱɢɫɥɟɧɢɣ. ȼ ɫɨɫɬɚɜ MATLAB ɜɯɨɞɹɬ ɢɧɬɟɪɩɪɟɬɚɬɨɪ ɤɨɦɚɧɞ, ɝɪɚɮɢɱɟɫɤɚɹ ɨɛɨɥɨɱɤɚ, ɪɟɞɚɤɬɨɪɨɬɥɚɞɱɢɤ, ɛɢɛɥɢɨɬɟɤɢ ɤɨɦɚɧɞ, ɫɢɦɜɨɥɶɧɨɟ ɹɞɪɨ ɩɚɤɟɬɚ MAPLE ɞɥɹ ɩɪɨɜɟɞɟɧɢɹ ɚɧɚɥɢɬɢɱɟɫɤɢɯ
ɜɵɱɢɫɥɟɧɢɣ, ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɛɢɛɥɢɨɬɟɤɢ MATLAB, ɝɟɧɟɪɚɬɨɪ ɨɬɱɟɬɨɜ ɢ ɛɨɝɚɬɵɣ ɢɧɫɬɪɭɦɟɧɬɚɪɢɣ
(Toolboxes). ɉɨ-ɩɪɟɠɧɟɦɭ ɩɨɞɞɟɪɠɢɜɚɹ ɞɢɚɥɨɝɨɜɵɣ ɪɟɠɢɦ ɞɥɹ ɩɪɨɫɬɵɯ ɜɵɱɢɫɥɟɧɢɣ, MATLAB
ɩɪɟɜɪɚɬɢɥɫɹ ɜ ɫɪɟɞɭ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɢ ɢɧɠɟɧɟɪɧɵɯ ɡɚɞɚɱ, ɜɤɥɸɱɚɹ ɪɚɡɪɚɛɨɬɤɭ
ɫɥɨɠɧɵɯ ɩɪɨɝɪɚɦɦ ɫ ɪɚɡɜɢɬɵɦ ɝɪɚɮɢɱɟɫɤɢɦ ɢɧɬɟɪɮɟɣɫɨɦ.
ɉɚɤɟɬ System Identification Toolbox (ɢɥɢ ɩɪɨɫɬɨ System Identification) (Ⱦɶɹɤɨɧɨɜ, Ʉɪɭɝɥɨɜ, 2002)
ɫɨɞɟɪɠɢɬ ɫɪɟɞɫɬɜɚ ɞɥɹ ɫɨɡɞɚɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɥɢɧɟɣɧɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ (ɫɢɫɬɟɦ) ɧɚ
ɨɫɧɨɜɟ ɦɚɫɫɢɜɚ ɩɨɥɭɱɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ. Ɉɧ ɢɦɟɟɬ ɭɞɨɛɧɵɣ ɝɪɚɮɢɱɟɫɤɢɣ ɢɧɬɟɪɮɟɣɫ,
ɩɨɦɨɝɚɸɳɢɣ ɨɪɝɚɧɢɡɨɜɚɬɶ ɞɚɧɧɵɟ ɢ ɫɨɡɞɚɜɚɬɶ ɦɨɞɟɥɢ. Ɇɟɬɨɞɵ ɢɞɟɧɬɢɮɢɤɚɰɢɢ, ɜɯɨɞɹɳɢɟ ɜ ɩɚɤɟɬ,
ɩɪɢɦɟɧɢɦɵ ɞɥɹ ɪɟɲɟɧɢɹ ɲɢɪɨɤɨɝɨ ɤɥɚɫɫɚ ɡɚɞɚɱ ɨɬ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɫɢɫɬɟɦ ɭɩɪɚɜɥɟɧɢɹ ɢ ɨɛɪɚɛɨɬɤɢ
ɫɢɝɧɚɥɨɜ ɞɨ ɚɧɚɥɢɡɚ ɜɪɟɦɟɧɧɵɯ ɪɹɞɨɜ. Ɉɫɧɨɜɧɵɟ ɫɜɨɣɫɬɜɚ ɩɚɤɟɬɚ ɫɥɟɞɭɸɳɢɟ:
• ɩɪɨɫɬɨɣ ɢ ɝɢɛɤɢɣ ɢɧɬɟɪɮɟɣɫ;
• ɩɪɟɞɜɚɪɢɬɟɥɶɧɚɹ ɨɛɪɚɛɨɬɤɚ ɞɚɧɧɵɯ, ɜɤɥɸɱɚɹ ɮɢɥɶɬɪɚɰɢɸ, ɭɞɚɥɟɧɢɟ ɬɪɟɧɞɨɜ ɢ ɫɦɟɳɟɧɢɣ;
• ɜɵɛɨɪ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɚɧɚɥɢɡɚ;
• ɷɮɮɟɤɬɢɜɧɵɟ ɦɟɬɨɞɵ ɚɜɬɨɪɟɝɪɟɫɫɢɢ;
• ɜɨɡɦɨɠɧɨɫɬɢ ɚɧɚɥɢɡɚ ɨɬɤɥɢɤɚ ɫɢɫɬɟɦ ɜɨ ɜɪɟɦɟɧɧɨɣ ɢ ɱɚɫɬɨɬɧɨɣ ɨɛɥɚɫɬɹɯ;
• ɨɬɨɛɪɚɠɟɧɢɟ ɧɭɥɟɣ ɢ ɩɨɥɸɫɨɜ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɫɢɫɬɟɦɵ;
• ɚɧɚɥɢɡ ɧɟɜɹɡɨɤ ɩɪɢ ɬɟɫɬɢɪɨɜɚɧɢɢ ɦɨɞɟɥɢ.
Ƚɪɚɮɢɱɟɫɤɢɣ ɢɧɬɟɪɮɟɣɫ ɩɚɤɟɬɚ ɭɩɪɨɳɚɟɬ ɤɚɤ ɩɪɟɞɜɚɪɢɬɟɥɶɧɭɸ ɨɛɪɚɛɨɬɤɭ ɞɚɧɧɵɯ, ɬɚɤ ɢ
ɞɢɚɥɨɝɨɜɵɣ ɩɪɨɰɟɫɫ ɢɞɟɧɬɢɮɢɤɚɰɢɢ ɦɨɞɟɥɢ. Ɉɩɟɪɚɰɢɢ ɡɚɝɪɭɡɤɢ ɢ ɫɨɯɪɚɧɟɧɢɹ ɞɚɧɧɵɯ, ɜɵɛɨɪɚ ɢɯ
ɞɢɚɩɚɡɨɧɚ, ɢɫɤɥɸɱɟɧɢɹ ɫɦɟɳɟɧɢɣ ɢ ɬɪɟɧɞɨɜ ɜɵɩɨɥɧɹɸɬɫɹ ɫ ɦɢɧɢɦɚɥɶɧɵɦɢ ɭɫɢɥɢɹɦɢ ɢ ɞɨɫɬɭɩɧɵ ɢɡ
ɝɥɚɜɧɨɝɨ ɦɟɧɸ.
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ ɢ ɦɨɞɟɥɟɣ ɫɢɫɬɟɦ ɢ ɨɛɴɟɤɬɨɜ ɨɪɝɚɧɢɡɨɜɚɧɨ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɜ
ɩɪɨɰɟɫɫɟ ɢɧɬɟɪɚɤɬɢɜɧɨɣ ɢɞɟɧɬɢɮɢɤɚɰɢɢ ɩɨɥɶɡɨɜɚɬɟɥɶ ɥɟɝɤɨ ɦɨɠɟɬ ɜɟɪɧɭɬɶɫɹ ɤ ɩɪɟɞɵɞɭɳɟɦɭ ɷɬɚɩɭ
ɪɚɛɨɬɵ. Ⱦɥɹ ɧɚɱɢɧɚɸɳɢɯ ɩɨɥɶɡɨɜɚɬɟɥɟɣ ɫɭɳɟɫɬɜɭɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɨɫɦɚɬɪɢɜɚɬɶ ɩɨɫɥɟɞɭɸɳɢɟ ɷɬɚɩɵ.
ɋɩɟɰɢɚɥɢɫɬɭ ɝɪɚɮɢɱɟɫɤɢɟ ɫɪɟɞɫɬɜɚ ɩɨɡɜɨɥɹɸɬ ɨɬɵɫɤɚɬɶ ɥɸɛɭɸ ɢɡ ɪɚɧɟɟ ɩɨɥɭɱɟɧɧɵɯ ɦɨɞɟɥɟɣ ɢ ɨɰɟɧɢɬɶ
ɟɟ ɤɚɱɟɫɬɜɨ ɜ ɫɪɚɜɧɟɧɢɢ ɫ ɞɪɭɝɢɦɢ ɦɨɞɟɥɹɦɢ.
ɉɚɤɟɬ ɩɨɞɞɟɪɠɢɜɚɟɬ ɜɫɟ ɬɪɚɞɢɰɢɨɧɧɵɟ ɜɢɞɵ ɦɨɞɟɥɟɣ, ɜɤɥɸɱɚɹ ɦɨɞɟɥɢ ɩɟɪɟɞɚɬɨɱɧɵɯ ɮɭɧɤɰɢɣ,
ɨɩɢɫɚɧɢɹ ɞɥɹ ɩɟɪɟɦɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹ (ɤɚɤ ɞɥɹ ɧɟɩɪɟɪɵɜɧɨɝɨ, ɬɚɤ ɢ ɞɥɹ ɞɢɫɤɪɟɬɧɨɝɨ ɜɪɟɦɟɧɢ) ɢ ɞɪɭɝɢɟ, ɫ
ɩɪɨɢɡɜɨɥɶɧɵɦ ɱɢɫɥɨɦ ɜɯɨɞɨɜ ɢ ɜɵɯɨɞɨɜ.
ɋ ɩɨɦɨɳɶɸ ɩɚɤɟɬɚ Matlab ɚɜɬɨɪɨɦ ɛɵɥɚ ɪɚɡɪɚɛɨɬɚɧɚ ɦɟɬɨɞɢɤɚ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɢɞɟɧɬɢɮɢɤɚɰɢɢ
ɨɛɴɟɤɬɨɜ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ, ɢɫɩɨɥɶɡɭɸɳɚɹ ɜ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɩɟɪɟɯɨɞɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɫɫɥɟɞɭɟɦɵɯ ɤɨɧɬɭɪɨɜ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɜɵɲɟɨɩɢɫɚɧɧɵɯ ɜ ɪɚɡɞ. 2
ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɢ ɫɨɯɪɚɧɟɧɧɵɟ ɜ ɜɢɞɟ ɮɚɣɥɨɜɨɝɨ ɚɪɯɢɜɚ.
496
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 7, ʋ3, 2004 ɝ.
ɫɬɪ.494-498
ɉɪɨɜɟɪɤɚ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɦɟɬɨɞɢɤɢ ɩɨɥɭɱɟɧɢɹ ɦɨɞɟɥɟɣ ɜ ɫɪɟɞɟ Matlab ɛɵɥɚ ɩɪɨɜɟɞɟɧɚ ɫ
ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɧɨɝɨ ɩɚɤɟɬɚ Autocont, ɪɚɡɪɚɛɨɬɚɧɧɨɝɨ ɧɚ ɤɚɮɟɞɪɟ Ⱥ ɢ ȼɌ ɆȽɌɍ (Ɇɚɫɥɨɜ, ɍɲɚɤɨɜ,
2000). Ⱦɚɧɧɵɟ ɜɫɟɯ ɱɟɬɵɪɟɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɛɵɥɢ ɨɛɴɟɞɢɧɟɧɵ ɜ ɟɞɢɧɵɣ ɦɚɫɫɢɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɜ ɜɢɞɟ
ɬɟɤɫɬɨɜɨɝɨ ɮɚɣɥɚ, ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɜ ɞɚɥɶɧɟɣɲɟɦ ɧɚ ɩɟɪɜɨɦ ɲɚɝɟ ɪɚɛɨɬɵ ɪɚɡɪɚɛɨɬɚɧɧɨɣ ɦɟɬɨɞɢɤɢ.
ȼɧɟɲɧɢɣ ɜɢɞ ɜɯɨɞɧɵɯ (ɦɨɳɧɨɫɬɢ ɧɚɝɪɟɜɚ) ɢ ɜɵɯɨɞɧɵɯ (ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɬɢ)
ɫɢɝɧɚɥɨɜ ɤɨɩɬɢɥɶɧɨɣ ɤɚɦɟɪɵ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɩɨ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɵɦɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ
ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 1.
Ɋɢɫ. 1. Ƚɪɚɮɢɤɢ ɜɵɯɨɞɧɵɯ ɢ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ:
u1 – ɫɢɝɧɚɥ ɧɚ ɜɯɨɞɟ ɢɫɫɥɟɞɭɟɦɨɝɨ ɨɛɴɟɤɬɚ, y1 – ɫɢɝɧɚɥ ɧɚ ɟɝɨ ɜɵɯɨɞɟ, Time – ɜɪɟɦɹ ɩɪɨɰɟɫɫɨɜ, ɫɟɤɭɧɞɵ
Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢɫɫɥɟɞɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ ɛɵɥɨ ɪɟɲɟɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ARX-ɦɨɞɟɥɶ (ɦɨɞɟɥɶ
ɚɜɬɨɪɟɝɪɟɫɫɢɢ ɫ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɜɯɨɞɨɦ (Ⱦɶɹɤɨɧɨɜ, Ʉɪɭɝɥɨɜ, 2002; Ʌɶɸɧɝ, 1991)), ɢɫɯɨɞɹ ɢɡ ɫɥɟɞɭɸɳɢɯ
ɫɨɨɛɪɚɠɟɧɢɣ:
ɜɫɟ ɨɛɴɟɤɬɵ ɭɩɪɚɜɥɟɧɢɹ ɩɪɢɧɹɬɵ ɧɚɦɢ ɢɦɟɸɳɢɦɢ ɨɞɢɧ ɜɯɨɞ ɢ ɨɞɢɧ ɜɵɯɨɞ;
ɲɭɦ ɧɚɛɥɸɞɟɧɢɣ ɧɨɫɢɬ ɧɟɤɨɪɪɟɥɢɪɨɜɚɧɧɵɣ ɯɚɪɚɤɬɟɪ, ɢɦɟɟɬ ɧɨɪɦɚɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɢ
ɧɚɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɩɨɤɚɡɚɧɢɹ ɞɚɬɱɢɤɨɜ (ɚɞɞɢɬɢɜɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ);
ɦɨɞɟɥɶ ɞɨɥɠɧɚ ɛɵɬɶ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ ɢɡ ɜɨɡɦɨɠɧɵɯ.
ɇɚɢɛɨɥɟɟ ɩɨɥɧɨ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɜɫɟɦ ɜɵɲɟɩɪɢɜɟɞɟɧɧɵɦ ɬɪɟɛɨɜɚɧɢɹɦ ARX-ɦɨɞɟɥɶ ɜɢɞɚ:
A(z) y(t) = B(z) u(t) + e(t)
ɢɥɢ ɜ ɪɚɡɜɟɪɧɭɬɨɦ ɜɢɞɟ:
y(t) + a1 y(t-1) +...+ ana y(t-n) = b1 u(t) + b2 u(t-1) +...+bnb u(t-m) + e(t).
(1)
(2)
ȼ ɜɵɪɚɠɟɧɢɹɯ (1) ɢ (2): A(z), B(z) – ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ai ɢ bi ɦɨɞɟɥɢ; na ɢ nb – ɫɬɟɩɟɧɢ ɦɚɬɪɢɰ
ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɦɨɞɟɥɢ; y(t), u(t) – ɡɧɚɱɟɧɢɹ ɜɵɯɨɞɧɨɝɨ ɢ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɨɜ ɜ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ t; e(t) –
ɞɢɫɤɪɟɬɧɵɣ ɛɟɥɵɣ ɲɭɦ.
ɂɫɩɨɥɶɡɭɹ ɩɪɨɝɪɚɦɦɧɭɸ ɫɢɫɬɟɦɭ Matlab 6.0 ɢ ɩɚɤɟɬ System Identification, ɛɵɥɢ ɫɨɫɬɚɜɥɟɧɵ
ɧɟɫɤɨɥɶɤɨ ARX-ɦɨɞɟɥɟɣ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɫɬɟɩɟɧɹɦɢ ɦɚɬɪɢɰ A(z), B(z) ɤɨɷɮɮɢɰɢɟɧɬɨɜ
ai ɢ bi ɦɨɞɟɥɢ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɥɟɞɭɸɳɢɯ ɮɭɧɤɰɢɣ ɩɚɤɟɬɨɜ:
1) prom=load('filename') – ɮɭɧɤɰɢɹ ɡɚɝɪɭɠɚɟɬ ɞɚɧɧɵɟ ɢɡ ɬɟɤɫɬɨɜɨɝɨ ɮɚɣɥɚ filename ɜ ɩɟɪɟɦɟɧɧɭɸ prom,
ɩɪɟɞɫɬɚɜɥɹɸɳɭɸ ɫɨɛɨɣ ɦɚɬɪɢɰɭ ɢɡ ɞɜɭɯ ɫɬɨɥɛɰɨɜ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɵɯɨɞɧɨɦɭ ɢ ɜɯɨɞɧɨɦɭ
ɫɢɝɧɚɥɚɦ, ɢ ɫɬɪɨɤ, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ;
2) promd=dtrend(prom,0) – ɮɭɧɤɰɢɹ ɭɞɚɥɟɧɢɹ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɢɡ ɪɟɡɭɥɶɬɚɬɨɜ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɢ
ɩɨɦɟɳɚɸɳɚɹ ɪɟɡɭɥɶɬɚɬ ɜ ɩɟɪɟɦɟɧɧɭɸ promd;
497
ɉɨɧɨɦɚɪɟɧɤɨ Ⱦ.Ⱥ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɤɢ ɩɪɨɰɟɫɫɚ ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ…
3) model=arx(promd, [na nb nk]) – ɮɭɧɤɰɢɹ ɫɨɡɞɚɧɢɹ ARX-ɦɨɞɟɥɢ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɷɤɫɩɟɪɢɦɟɧɬɨɜ. Ɂɞɟɫɶ:
promd – ɦɚɬɪɢɰɚ ɨɛɪɚɛɨɬɚɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ; [na nb nk] – ɡɚɞɚɜɚɟɦɵɟ ɩɚɪɚɦɟɬɪɵ
ARX-ɦɨɞɟɥɢ (ɫɬɟɩɟɧɢ ɦɚɬɪɢɰ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɦɨɞɟɥɢ ɢ ɜɟɥɢɱɢɧɚ ɡɚɞɟɪɠɤɢ); model – ɞɢɫɤɪɟɬɧɚɹ
ɦɨɞɟɥɶ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɜ ɬɟɬɚ-ɮɨɪɦɚɬɟ (ɜɧɭɬɪɟɧɧɟɦ ɮɨɪɦɚɬɟ ɩɚɤɟɬɚ System Identification).
ȼɦɟɫɬɨ ɮɭɧɤɰɢɢ arx ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɮɭɧɤɰɢɸ iv4 ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɲɭɦ ɧɚɛɥɸɞɟɧɢɣ ɹɜɥɹɟɬɫɹ
ɤɨɪɪɟɥɢɪɨɜɚɧɧɵɦ, ɚ ɬɚɤɠɟ ɮɭɧɤɰɢɸ segment ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɜɨɡɦɨɠɧɨ ɫɤɚɱɤɨɨɛɪɚɡɧɨɟ ɢɡɦɟɧɟɧɢɟ
ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɦɨɞɟɥɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚ (Ⱦɶɹɤɨɧɨɜ, Ʉɪɭɝɥɨɜ, 2002).
4) th=thd2thc(model) – ɮɭɧɤɰɢɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɞɢɫɤɪɟɬɧɨɣ ɦɨɞɟɥɢ model ɜ ɧɟɩɪɟɪɵɜɧɭɸ ɦɨɞɟɥɶ th.
5) [num, den]=th2tf(th) – ɮɭɧɤɰɢɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɦɨɞɟɥɢ th ɬɟɬɚ-ɮɨɪɦɚɬɚ ɜ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ, ɝɞɟ
[num, den] – ɦɚɬɪɢɰɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɱɢɫɥɢɬɟɥɹ ɢ ɡɧɚɦɟɧɚɬɟɥɹ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ.
6) compare(prom, model) – ɮɭɧɤɰɢɹ ɩɪɨɜɟɪɤɢ ɚɞɟɤɜɚɬɧɨɫɬɢ ɦɨɞɟɥɢ. ȼ ɫɥɭɱɚɟ ɩɪɢɜɟɞɟɧɧɨɣ ɮɨɪɦɵ ɡɚɩɢɫɢ
ɜɵɞɚɟɬ ɨɬɞɟɥɶɧɨɟ ɨɤɧɨ ɫ ɝɪɚɮɢɤɚɦɢ ɜɵɯɨɞɨɜ ɨɛɴɟɤɬɚ ɢ ɦɨɞɟɥɢ ɢ ɩɪɨɰɟɧɬ ɚɞɟɤɜɚɬɧɨɫɬɢ ɦɨɞɟɥɢ.
ɉɨ ɪɟɡɭɥɶɬɚɬɚɦ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɩɪɨɜɟɪɤɢ ɛɵɥɚ ɜɵɛɪɚɧɚ ɦɨɞɟɥɶ ɫ ɩɚɪɚɦɟɬɪɚɦɢ [na nb nk] = [2 2 0],
ɞɥɹ ɤɨɬɨɪɨɣ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɟ ɨɬɤɥɨɧɟɧɢɟ (ɋɄɈ) ɧɟ ɩɪɟɜɵɲɚɟɬ 1,4 %. ɋɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɞɚɧɧɨɣ
ɦɨɞɟɥɢ ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɮɨɪɦɭɥɨɣ
Wmatlab(p) = (0,1269*p2 + 0,3595*p + 0,4553)/(p2 + 0,2003*p + 0,0249).
(3)
ɉɪɢɧɢɦɚɹ ɜɨ ɜɧɢɦɚɧɢɟ ɬɨɬ ɮɚɤɬ, ɱɬɨ ɱɢɫɥɢɬɟɥɶ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ (3) ɯɚɪɚɤɬɟɪɢɡɭɟɬ
ɜɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ, ɜɵɡɜɚɧɧɵɟ ɢɡɦɟɧɟɧɢɟɦ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ, ɨɫɬɚɜɢɦ ɜ ɱɢɫɥɢɬɟɥɟ ɬɨɥɶɤɨ
ɫɜɨɛɨɞɧɵɣ ɱɥɟɧ, ɩɨɥɭɱɢɜ ɨɤɨɧɱɚɬɟɥɶɧɵɣ ɜɢɞ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɦɨɞɟɥɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ (4).
Wmatlab (p) = 0,4553/(p2 + 0,2003*p + 0,0249) = 18,29/(40,16*p2 + 8,04*p + 1).
(4)
Ɋɟɡɭɥɶɬɚɬɵ ɫɪɚɜɧɟɧɢɹ ɜɵɯɨɞɨɜ ɨɛɴɟɤɬɚ ɢ ɩɨɥɭɱɟɧɧɨɣ ɦɨɞɟɥɢ ɫɪɟɞɫɬɜɚɦɢ Autocont ɩɨɤɚɡɵɜɚɸɬ,
ɱɬɨ ɞɢɧɚɦɢɱɟɫɤɚɹ ɨɲɢɛɤɚ ɧɟ ɩɪɟɜɵɲɚɟɬ 3 %. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɝɨɜɨɪɢɬɶ ɨ ɩɪɢɦɟɧɢɦɨɫɬɢ ɩɨɥɭɱɟɧɧɨɣ
ɦɨɞɟɥɢ ɜ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɨɣ ɷɬɚɥɨɧɧɨɣ ɦɨɞɟɥɢ ɞɥɹ ɚɞɚɩɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ.
4. Ɂɚɤɥɸɱɟɧɢɟ
ɉɨ ɪɟɡɭɥɶɬɚɬɚɦ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞɵ, ɱɬɨ ɪɚɡɪɚɛɨɬɚɧɧɚɹ
ɦɟɬɨɞɢɤɚ ɹɜɥɹɟɬɫɹ ɩɪɢɦɟɧɢɦɨɣ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɨɞɟɥɟɣ ɢɫɫɥɟɞɭɟɦɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ,
ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɪɢɟɦɥɟɦɭɸ ɬɨɱɧɨɫɬɶ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ, ɜɦɟɫɬɟ ɫ ɬɟɦ, ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɨɣ ɜ
ɪɟɚɥɢɡɚɰɢɢ. ɉɨɥɭɱɟɧɧɵɟ ɩɪɢ ɩɨɦɨɳɢ ɞɚɧɧɨɣ ɦɟɬɨɞɢɤɢ ɦɨɞɟɥɢ ɩɥɚɧɢɪɭɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜ ɞɚɥɶɧɟɣɲɟɦ
ɜ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɵɯ ɷɬɚɥɨɧɧɵɯ ɦɨɞɟɥɟɣ ɜ ɤɨɧɬɭɪɚɯ ɚɞɚɩɬɚɰɢɢ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ
ɞɵɦɨɨɛɪɚɡɨɜɚɧɢɹ ɩɪɢ ɯɨɥɨɞɧɨɦ ɤɨɩɱɟɧɢɢ.
Ʌɢɬɟɪɚɬɭɪɚ
Ȼɚɥɚɤɢɪɟɜ ȼ.ɋ., Ⱦɭɞɧɢɤɨɜ ȿ.Ƚ., ɐɢɪɥɢɧ Ⱥ.Ɇ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɢɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɨɦɵɲɥɟɧɧɵɯ ɨɛɴɟɤɬɨɜ ɭɩɪɚɜɥɟɧɢɹ. Ɇ., ɗɧɟɪɝɢɹ, 232 ɫ., 1967.
ȼɢɫɤɨɜ Ⱥ.ɘ. ɉɨɜɵɲɟɧɢɟ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɯɨɥɨɞɧɨɝɨ ɤɨɩɱɟɧɢɹ ɪɵɛɵ ɩɭɬɟɦ ɧɟɩɪɟɪɵɜɧɨɝɨ
ɤɨɧɬɪɨɥɹ ɜɧɭɬɪɟɧɧɢɯ ɫɜɨɣɫɬɜ ɩɨɥɭɮɚɛɪɢɤɚɬɚ. Ⱦɢɫɫ. ... ɤɚɧɞ. ɬɟɯɧ. ɧɚɭɤ. Ɇɭɪɦɚɧɫɤ, 187 ɫ., 2002.
Ƚɨɜɨɪɭɯɢɧ ȼ., ɐɢɛɭɥɢɧ Ȼ. Ʉɨɦɩɶɸɬɟɪ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɢɫɫɥɟɞɨɜɚɧɢɢ. Ɇ., ȼɵɫɲɚɹ ɲɤɨɥɚ, 633 ɫ., 2000.
Ⱦɶɹɤɨɧɨɜ ȼ., Ʉɪɭɝɥɨɜ ȼ. MATLAB. Ⱥɧɚɥɢɡ, ɢɞɟɧɬɢɮɢɤɚɰɢɹ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦ. ɋɩɟɰɢɚɥɶɧɵɣ
ɫɩɪɚɜɨɱɧɢɤ. ɋɉɛ, ɉɢɬɟɪ, 448 ɫ., 2002.
ȿɝɨɪɟɧɤɨɜ Ⱦ.Ʌ., Ɏɪɚɞɤɨɜ Ⱥ.Ʌ., ɏɚɪɥɚɦɨɜ ȼ.ɘ. Ɉɫɧɨɜɵ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɨɫɬɪɨɟɧɢɟ
ɢ ɚɧɚɥɢɡ ɦɨɞɟɥɟɣ ɫ ɩɪɢɦɟɪɚɦɢ ɧɚ ɹɡɵɤɟ MATLAB. Ɇ., ɂɧɮɨɪɦɚɬɢɤɚ ɢ ɤɨɦɩɶɸɬɟɪɵ, 189 ɫ., 1997.
Ʌɶɸɧɝ Ʌ. ɂɞɟɧɬɢɮɢɤɚɰɢɹ ɫɢɫɬɟɦ. Ɍɟɨɪɢɹ ɞɥɹ ɩɨɥɶɡɨɜɚɬɟɥɹ. Ɇ., ɇɚɭɤɚ, Ƚɥ. ɪɟɞ. ɮɢɡ.-ɦɚɬ. ɥɢɬ., 432 ɫ.,
1991.
Ɇɚɫɥɨɜ Ⱥ.Ⱥ., ɍɲɚɤɨɜ ɋ.ɂ. ɉɚɤɟɬ ɚɧɚɥɢɡɚ / ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɪɟɚɥɶɧɨɦ ɜɪɟɦɟɧɢ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ / ɪɟɝɭɥɢɪɨɜɚɧɢɹ "AutoCont II". ɇɚɭɤɚ – ɩɪɨɢɡɜɨɞɫɬɜɭ, ʋ 2, ɫ.55-57, 2000.
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