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Система автоматизированного предупреждения опасных ситуаций при заходе самолета на посадку перед началом снижения по глиссаде..pdf

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ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɍȾɄ 656.7.052
ɋɂɋɌȿɆȺ ȺȼɌɈɆȺɌɂɁɂɊɈȼȺɇɇɈȽɈ ɉɊȿȾɍɉɊȿɀȾȿɇɂə
ɈɉȺɋɇɕɏ ɋɂɌɍȺɐɂɃ ɉɊɂ ɁȺɏɈȾȿ ɋȺɆɈɅȿɌȺ ɇȺ ɉɈɋȺȾɄɍ
ɉȿɊȿȾ ɇȺɑȺɅɈɆ ɋɇɂɀȿɇɂə ɉɈ ȽɅɂɋɋȺȾȿ
Ⱥ.ɂ. ȿɊȿɆɂɇ, Ƚ.ɇ. ɅȿȻȿȾȿȼ, ɂ.Ⱥ. ɑȿɏɈȼ
(Ɋɚɛɨɬɚ ɜɵɩɨɥɧɟɧɚ ɩɪɢ ɩɨɞɞɟɪɠɤɟ ɊɎɎɂ, ɝɪɚɧɬɨɜ ʋ15-08-00043 ɢ ʋ16-08-00070)
ȼ ɫɬɚɬɶɟ ɩɪɟɞɥɨɠɟɧ ɩɨɞɯɨɞ ɤ ɨɪɝɚɧɢɡɚɰɢɢ ɧɟɩɪɟɪɵɜɧɨɝɨ ɩɪɨɝɧɨɡɢɪɭɸɳɟɝɨ ɤɨɧɬɪɨɥɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɡɚɯɨɞɚ
ɧɚ ɩɨɫɚɞɤɭ ɩɪɢ ɝɢɩɨɬɟɡɟ ɨɛ ɨɩɬɢɦɚɥɶɧɨɦ ɩɨɜɟɞɟɧɢɢ ɩɪɢ ɭɫɬɪɚɧɟɧɢɢ ɨɩɚɫɧɵɯ ɫɢɬɭɚɰɢɣ, ɩɪɢɜɟɞɟɧɨ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ
ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɢ ɤɨɧɬɪɨɥɹ, ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɛɚɡɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɚ ɬɚɤɠɟ ɩɪɨɰɟɞɭɪɚ
ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɚɧɧɨɝɨ ɩɪɨɰɟɫɫɚ. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɤɚɡɚɥɨ, ɱɬɨ ɩɪɢ ɧɟɚɤɬɢɜɧɨɦ
ɤɨɧɬɪɨɥɟ, ɡɧɚɱɢɬɟɥɶɧɨ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɮɭɧɤɰɢɹ ɪɢɫɤɚ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɪɟɡɭɥɶɬɚɬɨɜ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨɥɭɱɟɧɨ ɪɟɲɟɧɢɟ ɨ ɜɵɛɨɪɟ ɩɨɪɨɝɚ ɞɥɹ ɮɭɧɤɰɢɢ ɪɢɫɤɚ. Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɩɪɢ ɞɨɩɭɳɟɧɢɹɯ ɨ
ɫɬɚɰɢɨɧɚɪɧɨɦ ɨɩɬɢɦɚɥɶɧɨɦ ɭɩɪɚɜɥɟɧɢɢ ɢ ɭɩɪɨɳɟɧɧɨɣ ɞɢɧɚɦɢɤɟ ɩɨɥɟɬɚ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɨɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ, ɦɟɬɨɞ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɮɭɧɤɰɢɹ ɪɢɫɤɚ,
ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɟ ɨɩɬɢɦɚɥɶɧɵɯ ɪɟɝɭɥɹɬɨɪɨɜ.
ȼȼȿȾȿɇɂȿ
ȼɚɠɧɟɣɲɢɦ ɜɨɩɪɨɫɨɦ ɷɤɫɩɥɭɚɬɚɰɢɢ ɚɜɢɚɰɢɨɧɧɨɣ ɬɟɯɧɢɤɢ ɹɜɥɹɟɬɫɹ ɨɛɟɫɩɟɱɟɧɢɟ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɥɟɬɚ, ɧɚ ɤɨɬɨɪɭɸ ɧɟɝɚɬɢɜɧɨ ɜɥɢɹɟɬ ɪɹɞ ɮɚɤɬɨɪɨɜ. ɋɪɟɞɢ ɧɢɯ ɝɥɚɜɧɨɟ ɦɟɫɬɨ ɡɚɧɢɦɚɟɬ ɱɟɥɨɜɟɱɟɫɤɢɣ ɮɚɤɬɨɪ, ɤɨɝɞɚ ɜ ɨɫɨɛɵɯ ɤɪɢɬɢɱɟɫɤɢɯ ɫɢɬɭɚɰɢɹɯ ɷɤɢɩɚɠ ɧɟ ɭɫɩɟɜɚɟɬ ɫɪɟɚɝɢɪɨɜɚɬɶ ɢ ɩɪɟɞɨɬɜɪɚɬɢɬɶ ɚɜɚɪɢɸ.
ɉɨɷɬɨɦɭ ɜ ɩɨɦɨɳɶ ɥɟɬɱɢɤɭ ɧɚ ɛɨɪɬɭ ɫɚɦɨɥɟɬɚ ɞɨɥɠɧɵ ɛɵɬɶ ɭɫɬɚɧɨɜɥɟɧɵ ɬɟɯɧɢɱɟɫɤɢɟ
ɫɪɟɞɫɬɜɚ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɤɨɧɬɪɨɥɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɥɟɬɚ, ɧɟɩɪɟɪɵɜɧɨ ɜɵɩɨɥɧɹɸɳɢɟ ɮɭɧɤɰɢɢ
ɩɪɟɞɭɩɪɟɠɞɟɧɢɹ ɢ ɩɪɟɞɨɬɜɪɚɳɟɧɢɹ ɨɩɚɫɧɵɯ ɫɢɬɭɚɰɢɣ, ɞɥɹ ɱɟɝɨ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɧɟɨɛɯɨɞɢɦɨ
ɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɢɯ ɪɚɡɜɢɬɢɟ.
Ɉɞɧɚɤɨ ɞɥɹ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɬɨɱɧɨɝɨ ɩɪɨɝɧɨɡɚ ɭɩɪɚɜɥɹɟɦɨɝɨ ɩɨɥɟɬɚ ɧɭɠɧɨ ɡɧɚɬɶ ɢ ɭɱɢɬɵɜɚɬɶ ɨɫɨɛɟɧɧɨɫɬɢ ɫɚɦɨɝɨ ɭɩɪɚɜɥɟɧɢɹ, ɜɨɡɦɨɠɧɨɫɬɢ ɟɝɨ ɪɚɡɥɢɱɧɵɯ ɫɩɨɫɨɛɨɜ, ɜ ɬɨɦ ɱɢɫɥɟ ɪɭɱɧɨɝɨ ɢɥɢ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ, ɷɤɫɬɪɟɧɧɨɝɨ ɢɥɢ ɲɬɚɬɧɨɝɨ, ɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɷɬɨɝɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɯ
ɞɥɹ ɩɪɟɞɨɬɜɪɚɳɟɧɢɹ ɨɩɚɫɧɨɫɬɢ.
ɉɪɢɧɰɢɩɢɚɥɶɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɩɪɟɞɥɨɠɟɧɧɨɝɨ ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɨɞɯɨɞɚ ɹɜɥɹɟɬɫɹ ɨɫɭɳɟɫɬɜɥɟɧɢɟ ɩɪɨɝɧɨɡɚ ɩɪɢ ɝɢɩɨɬɟɡɟ ɨɛ ɨɩɬɢɦɚɥɶɧɨɦ ɭɫɬɪɚɧɟɧɢɢ ɭɝɪɨɡɵ ɩɨ ɧɚɡɧɚɱɟɧɧɨɦɭ ɢɧɬɟɝɪɚɥɶɧɨɦɭ ɤɪɢɬɟɪɢɸ. Ɉɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɧɚɯɨɞɢɬɫɹ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ [1–4], ɩɨɡɜɨɥɹɸɳɟɝɨ ɩɪɢ ɭɩɪɨɳɚɸɳɟɦ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɨ ɞɢɧɚɦɢɤɟ ɩɨɥɟɬɚ ɨɫɭɳɟɫɬɜɢɬɶ ɬɪɚɞɢɰɢɨɧɧɨɟ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɟ ɨɩɬɢɦɚɥɶɧɵɯ ɪɟɝɭɥɹɬɨɪɨɜ – ȺɄɈɊ [2–4].
Ʉɪɨɦɟ ɬɨɝɨ, ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɡɚɦɟɱɚɬɟɥɶɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɟɡɚɦɟɱɟɧɧɨɣ ɦɧɨɝɢɦɢ ɢɫɫɥɟɞɨɜɚɬɟɥɹɦɢ, ɹɜɥɹɟɬɫɹ ɫɩɨɫɨɛɧɨɫɬɶ ɨɰɟɧɢɬɶ ɫ ɩɨɦɨɳɶɸ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ Ȼɟɥɥɦɚɧɚ ɬɟɤɭɳɭɸ ɮɭɧɤɰɢɸ ɪɢɫɤɚ, ɤɨɬɨɪɚɹ ɨɛɥɚɞɚɟɬ ɩɪɨɝɧɨɡɢɪɭɸɳɢɦɢ
ɮɭɧɤɰɢɹɦɢ.
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɮɨɪɦɢɪɭɟɬɫɹ ɢ ɪɟɲɚɟɬɫɹ ɡɚɞɚɱɚ ɧɟɩɪɟɪɵɜɧɨɝɨ ɤɨɧɬɪɨɥɹ ɡɚɯɨɞɚ ɫɚɦɨɥɟɬɚ ɧɚ ɩɨɫɚɞɤɭ ɩɟɪɟɞ ɧɚɱɚɥɨɦ ɫɧɢɠɟɧɢɹ ɩɨ ɝɥɢɫɫɚɞɟ, ɱɬɨ ɨɬɧɨɫɢɬɫɹ ɤ ɨɞɧɨɦɭ ɢɡ ɨɬɜɟɬɫɬɜɟɧɧɵɯ
ɪɟɠɢɦɨɜ ɩɨɥɟɬɚ. Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɢ ɫɥɟɞɭɸɳɟɣ ɩɨɫɬɚɧɨɜɤɟ.
ɉɈɋɌȺɇɈȼɄȺ ɁȺȾȺɑɂ
1. Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɩɪɨɞɨɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɫɚɦɨɥɟɬɚ ɩɪɢ ɭɩɪɚɜɥɟɧɢɢ ɜɵɫɨɬɨɣ ɩɨɥɟɬɚ ɩɨ
ɡɚɞɚɧɧɨɣ ɩɪɨɝɪɚɦɦɟ m1(x) ɟɟ ɢɡɦɟɧɟɧɢɹ, ɢɦɟɸɳɟɣ ɜɢɞ ɤɭɫɨɱɧɨ-ɥɢɧɟɣɧɨɣ ɮɭɧɤɰɢɢ ɩɪɢ ɡɚɯɨɞɟ
ɧɚ ɩɨɫɚɞɤɭ ɢ ɩɨɤɚɡɚɧɧɨɣ ɧɚ ɪɢɫ. 1:
90
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Hɉ
­
°° H ɉ , ɩɪɢ ɯ ≥ θ
,
m1 ( x ) = ®
H
ɉ
°θ , ɩɪɢ ɯ <
°¯ ɯ
θ
ɝɞɟ
(1)
ɇɉ – ɡɚɞɚɧɧɚɹ ɜɵɫɨɬɚ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɩɨɥɟɬɚ ɩɟɪɟɞ ɫɧɢɠɟɧɢɟɦ ɩɨ ɝɥɢɫɫɚɞɟ;
ș – ɡɚɞɚɧɧɵɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɬɪɚɟɤɬɨɪɢɢ ɩɪɢ ɫɧɢɠɟɧɢɢ ɩɨ ɝɥɢɫɫɚɞɟ;
ɯ – ɬɟɤɭɳɚɹ ɞɚɥɶɧɨɫɬɶ ɞɨ ɡɚɞɚɧɧɨɣ ɬɨɱɤɢ ɩɪɢɡɟɦɥɟɧɢɹ ɧɚ ȼɉɉ.
Ɋɢɫ. 1. ɉɪɨɝɪɚɦɦɚ ɢɡɦɟɧɟɧɢɹ ɜɵɫɨɬɵ ɩɨɥɟɬɚ ɩɪɢ ɩɨɫɚɞɤɟ
ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɬɪɟɛɭɟɦɚɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ m2(x) ɹɜɥɹɟɬɫɹ ɤɭɫɨɱɧɨ-ɩɨɫɬɨɹɧɧɨɣ
ɮɭɧɤɰɢɟɣ.
Hɉ
­
°° 0 , ɩɪɢ ɯ ≥ θ
,
m 2 ( x) = ®
°− Vθ , ɩɪɢ ɯ < H ɉ
°¯
θ
(2)
ɝɞɟ V – ɡɚɞɚɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɫɤɨɪɨɫɬɶ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɩɨɥɟɬɚ.
Ɉɬɜɟɬɫɬɜɟɧɧɵɦ ɦɨɦɟɧɬɨɦ ɜɵɩɨɥɧɟɧɢɹ ɩɪɨɝɪɚɦɦɵ ɹɜɥɹɟɬɫɹ ɧɚɱɚɥɨ ɫɧɢɠɟɧɢɹ ɩɨ ɝɥɢɫɫɚɞɟ – ɩɪɢ ɨɬɫɬɚɜɚɧɢɢ ɢɥɢ ɨɩɟɪɟɠɟɧɢɢ ɬɨɱɤɚ ɩɪɢɡɟɦɥɟɧɢɹ ɫɦɟɳɚɟɬɫɹ, ɱɬɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɩɚɫɧɨɫɬɶ
ɩɪɢ ɨɝɪɚɧɢɱɟɧɧɨɣ ɞɥɢɧɟ ȼɉɉ ɢ ɡɧɚɱɢɬɟɥɶɧɨɣ ɞɥɢɧɟ ɩɪɨɛɟɝɚ ɫɚɦɨɥɟɬɚ.
2. ɇɚ ɞɚɧɧɨɦ ɷɬɚɩɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɡɚɞɚɧɵ ɭɩɪɨɳɟɧɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ
ɩɪɨɞɨɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ.
­
° y 1 = y 2 ,
y2 = H 0
°
f ( x) = ® y 2 = −a ⋅ y 2 + b ⋅ U , y 2 = 0 ,
°
H
° x = −V ,
ɯ ( 0) > ɉ
θ
¯
ɝɞɟ
y1 – ɬɟɤɭɳɟɟ ɮɚɤɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɜɵɫɨɬɵ,
y2 – ɬɟɤɭɳɚɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ,
x – ɬɟɤɭɳɚɹ ɞɚɥɶɧɨɫɬɶ ɞɨ ɬɨɱɤɢ ɩɪɢɡɟɦɥɟɧɢɹ,
U – ɫɢɧɬɟɡɢɪɭɟɦɵɣ ɫɢɝɧɚɥ ɭɩɪɚɜɥɟɧɢɹ,
a ɢ b – ɡɚɞɚɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɢ ɭɩɪɨɳɟɧɧɨɣ ɞɢɧɚɦɢɤɟ ɩɨɥɟɬɚ.
91
(3)
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɐɟɥɶɸ ɭɩɪɨɳɟɧɢɹ ɹɜɥɹɟɬɫɹ ɩɨɥɭɱɟɧɢɟ ɩɪɨɫɬɨɣ ɢ ɩɪɢɝɨɞɧɨɣ ɞɥɹ ɬɟɯɧɢɱɟɫɤɨɣ ɪɟɚɥɢɡɚɰɢɢ
ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɮɨɪɦɵ ɜɵɱɢɫɥɟɧɢɹ ɮɭɧɤɰɢɢ ɪɢɫɤɚ ɤɚɤ ɝɥɚɜɧɨɣ ɡɚɞɚɱɢ, ɩɨɧɢɦɚɹ ɩɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɩɨɫɥɟɞɭɸɳɟɝɨ ɫɢɧɬɟɡɚ ɡɚɤɨɧɚ ɭɩɪɚɜɥɟɧɢɹ ɜɵɫɨɬɨɣ ɩɨɥɟɬɚ ɫ ɩɨɦɨɳɶɸ ɛɨɥɟɟ ɩɨɥɧɨɣ
ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɨɛɴɟɤɬɚ.
3. Ɂɚɞɚɧɚ ɤɜɚɞɪɚɬɢɱɧɚɹ ɮɨɪɦɚ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɮɭɧɤɰɢɨɧɚɥɚ J ɤɚɱɟɫɬɜɚ ɩɨɫɚɞɤɢ, ɭɱɢɬɵɜɚɸɳɚɹ ɲɬɪɚɮɵ ɡɚ ɨɲɢɛɤɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɨ ɩɨɥɨɠɟɧɢɸ (y1 – m1) ɢ ɩɨ ɫɤɨɪɨɫɬɢ (y2 – m2), ɚ ɬɚɤɠɟ
ɲɬɪɚɮ ɡɚ ɤɜɚɞɪɚɬ ɭɩɪɚɜɥɟɧɢɹ, ɞɥɹ ɤɨɬɨɪɨɝɨ ɩɪɹɦɨɟ ɨɝɪɚɧɢɱɟɧɢɟ ɩɨ ɦɨɞɭɥɸ ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ.
T
[
]
J = min ³ 0,5 l1 ⋅ ( y1 − m1 ) 2 + 0,5 l 2 ⋅ ( y 2 − m2 ) 2 + 0,5 U 2 dt ,
(4)
0
ɝɞɟ l1, l2 – ɤɨɷɮɮɢɰɢɟɧɬɵ ɲɬɪɚɮɨɜ ɡɚ ɨɲɢɛɤɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ, ɤɨɬɨɪɵɟ ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɨɩɢɫɵɜɚɸɬɫɹ ɫɩɟɰɢɚɥɶɧɵɦ ɨɛɪɚɡɨɦ.
Ɋɢɫ. 2. Ʉɚɪɬɢɧɚ ɢɡɦɟɧɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ ɮɭɧɤɰɢɢ ɲɬɪɚɮɨɜ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɞɚɥɶɧɨɫɬɢ
ȿɟ ɩɨɜɟɞɟɧɢɟ ɢɦɢɬɢɪɭɟɬ ɧɚɪɚɫɬɚɧɢɟ ɜɨɥɧɟɧɢɹ ɢ ɬɪɟɜɨɝɢ ɭ ɥɟɬɱɢɤɚ ɩɨ ɦɟɪɟ ɩɪɢɛɥɢɠɟɧɢɹ
ɤ ɦɨɦɟɧɬɭ ɧɚɱɚɥɚ ɫɧɢɠɟɧɢɹ ɩɨ ɝɥɢɫɫɚɞɟ.
l1 = r1 ⋅ f ( x, y1 ),
l2 = r2 ⋅ f ( x, y1 ),
(5)
1
f ( x) =
1+
(x −
Hɉ
θ
) + ( y1 − m1 )
2
,
2
d2
ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬɵ r1, r2, d ɞɨɥɠɧɵ ɛɵɬɶ ɭɬɨɱɧɟɧɵ ɢ ɧɚɡɧɚɱɟɧɵ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ
ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ, ɚ f(x,y1) – ɫɩɟɰɢɚɥɶɧɚɹ ɮɭɧɤɰɢɹ, ɩɨɤɚɡɚɧɧɚɹ ɧɚ ɪɢɫ. 2.
4. Ɍɪɟɛɭɟɬɫɹ ɩɪɨɜɟɫɬɢ ɫɢɧɬɟɡ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɢ, ɝɥɚɜɧɨɟ, ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɮɨɪɦɵ ɩɪɨɝɧɨɡɢɪɭɸɳɟɣ ɮɭɧɤɰɢɢ ɪɢɫɤɚ, ɩɨɞɬɜɟɪɞɢɜ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɩɪɟɞɥɨɠɟɧɧɨɝɨ ɩɨɞɯɨɞɚ ɫ ɩɨɦɨɳɶɸ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ.
92
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɋȿɒȿɇɂȿ ɁȺȾȺɑɂ ɋɂɇɌȿɁȺ ɈɉɌɂɆȺɅɖɇɈȽɈ ɍɉɊȺȼɅȿɇɂə
ɂ ɎɍɇɄɐɂɂ ɊɂɋɄȺ ɋ ɉɈɆɈɓɖɘ ɆȿɌɈȾȺ ȺɄɈɊ
ɋɨɝɥɚɫɧɨ ɞɢɧɚɦɢɱɟɫɤɨɦɭ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɸ ɭɫɥɨɜɢɸ ɨɩɬɢɦɚɥɶɧɨɫɬɢ ɪɟɲɟɧɢɹ ɞɚɧɧɨɣ
ɡɚɞɚɱɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɥɟɞɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ Ȼɟɥɥɦɚɧɚ ɜ ɱɚɫɬɧɵɯ ɩɪɨɢɡɜɨɞɧɵɯ.
ª
º
«
»
« 0,5r ( y − m ) 2 + 0,5r ( y − m ) 2 ∂ε
»
ε
∂ε
∂
1
1
1
2
2
2
(− ay2 + bU ) + 0,5U 2 » = min F ( y1 , y2 , x ) , (6)
y2 +
−
= minU «
+
H
∂t
∂y1
∂y2
«
»
( x − ɉ ) 2 + ( y1 − m1 ) 2
« 1+
»
θ
«¬
»¼
d2
ɝɞɟ
ε(y1,y2) – ɢɫɤɨɦɚɹ ɮɭɧɤɰɢɹ Ȼɟɥɥɦɚɧɚ;
F(y1,y2,x) – ɩɪɚɜɚɹ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ Ȼɟɥɥɦɚɧɚ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɮɭɧɤɰɢɢ
ɪɢɫɤɚ ɜ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɮɨɪɦɟ.
Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɮɭɧɤɰɢɢ Ȼɟɥɥɦɚɧɚ İ ɡɚɞɚɞɢɦɫɹ ɬɪɚɞɢɰɢɨɧɧɨɣ ɞɥɹ ȺɄɈɊ ɤɜɚɞɪɚɬɢɱɧɨɣ
ɮɨɪɦɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɨɪɞɢɧɚɬ y1 ɢ y2, ɧɟ ɭɱɢɬɵɜɚɹ ɜ ɧɟɣ ɤɨɨɪɞɢɧɚɬɭ x, ɬ. ɤ. ɨɧɚ ɦɟɧɹɟɬɫɹ
ɨɬɞɟɥɶɧɨ ɢ ɧɟɡɚɜɢɫɢɦɨ ɨɬ y1, y2 ɢ ɭɩɪɚɜɥɟɧɢɹ U.
ε = β 1 y1 + β 2 y 2 + 0,5γ 1 y1 2 + 0,5γ 2 y 2 2 + ψ y1 y 2 ,
(7)
ɝɞɟ ȕ1, ȕ2, Ȗ1, Ȗ2, ȥ – ɤɨɷɮɮɢɰɢɟɧɬɵ, ɤɨɬɨɪɵɟ ɧɚɞɥɟɠɢɬ ɨɩɪɟɞɟɥɢɬɶ.
Ⱦɚɥɟɟ, ɩɨ ɢɡɜɟɫɬɧɨɣ ɩɪɨɰɟɞɭɪɟ ɫɢɧɬɟɡɚ ɜɵɱɢɫɥɢɦ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɮɭɧɤɰɢɣ Ȼɟɥɥ∂ε
∂ε
ɦɚɧɚ
ɢ
ɢ ɩɨɞɫɬɚɜɢɦ ɢɯ ɜ ɭɪɚɜɧɟɧɢɟ (6).
∂y1
∂y 2
∂ε
∂ε
= β 1 + γ 1 y1 + ψ y 2 ,
= β 2 + γ 2 y 2 + ψ y1 ,
∂y 1
∂y 2
ª
º
«
»
« 0,5r ( y − m )2 + 0,5r ( y − m )2
»
∂ε
1
1
1
2
2
2
−
= minU «
+ (β1 + γ 1 y1 +ψ y 2 ) y2 + ( β 2 + γ 2 y2 +ψ y1 )(−ay2 + bU ) + 0,5U 2 » . (8)
H
∂t
«
»
( x − ɉ ) 2 + ( y1 − m1 ) 2
« 1+
»
θ
d2
¬«
¼»
ȼɵɞɟɥɹɹ ɢɡ ɜɵɪɚɠɟɧɢɹ (8) ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɤɨɛɤɚɯ ɱɥɟɧɵ, ɡɚɜɢɫɹɳɢɟ ɨɬ ɭɩɪɚɜɥɟɧɢɹ U,
ɧɚɯɨɞɢɦ ɟɝɨ ɨɩɬɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Û.
∂
(β 2 + ψ y1 + γ 2 y 2 ) bU + 0,5U 2 = 0 ; U = − b (β 2 + ψ y1 + γ 2 y 2 ) .
∂U
[
]
(9)
ɂɡ ɮɨɪɦɭɥɵ (9) ɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɫɢɧɬɟɡɚ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ
ɨɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬɵ ɮɭɧɤɰɢɢ Ȼɟɥɥɦɚɧɚ ȕ2, ȥ ɢ Ȗ2. Ⱦɥɹ ɢɯ ɧɚɯɨɠɞɟɧɢɹ ɩɪɟɞɫɬɚɜɢɦ ɥɟɜɭɸ ɢ ɩɪɚɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ ɜ ɜɢɞɟ ɫɬɟɩɟɧɧɨɝɨ ɩɨɥɢɧɨɦɚ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɢ
ɩɪɢɪɚɜɧɹɟɦ ɦɧɨɠɢɬɟɥɢ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɫɬɟɩɟɧɹɯ ɞɪɭɝ ɞɪɭɝɭ. ɉɨɥɶɡɭɹɫɶ ɫɬɚɧɞɚɪɬɧɵɦ
∂ε
ɩɪɢɟɦɨɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɫɨɫɬɨɹɧɢɢ, ɤɨɝɞɚ
= 0 , ɦɨɠɧɨ ɩɪɢɛɥɢɠɟɧ∂t
93
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ɧɨ ɩɨɥɭɱɢɬɶ ɫɥɟɞɭɸɳɭɸ
y1, y2, y22, y1y2.
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɫɢɫɬɟɦɭ
ɚɥɝɟɛɪɚɢɱɟɫɤɢɯ
ɭɪɚɜɧɟɧɢɣ
­
r1 − b 2ψ 2
°
2 2
°0,5 r2 + ψ − aγ 2 − 0,5 b y2
°
r1m1 + b 2ψβ 2
®
°
γ 1 − aψ − b 2γ 2ψ
°
° r m − β + a β + b 2γ β
1
2
2 2
¯ 2 2
ɞɥɹ
ɦɧɨɠɢɬɟɥɟɣ
ɩɪɢ
= 0,
= 0,
= 0, ,
(10)
= 0,
= 0.
Ɍɨɝɞɚ ɢɡ ɭɪɚɜɧɟɧɢɹ (1) ɫɢɫɬɟɦɵ (10) ɧɚɣɞɟɦ ȥ:
ψ=
r1
b
.
(11)
ɂɡ ɭɪɚɜɧɟɧɢɹ (2) ɫɢɫɬɟɦɵ (10) ɨɩɪɟɞɟɥɢɦ Ȗ2 ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
γ2 =
− a + a 2 + b 2 ⋅ (r2 + 2ψ )
b
2
≈
b r2 + 2ψ − a
b2
.
(12)
ɂɡ ɭɪɚɜɧɟɧɢɹ (3) ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ȕ2:
β 2 = − m1
r1
b
.
(13)
ɉɨɥɭɱɟɧɧɵɯ ɨɰɟɧɨɤ (11–13) ɧɟɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɜɫɟɣ ɩɪɚɜɨɣ ɱɚɫɬɢ
ɭɪɚɜɧɟɧɢɹ Ȼɟɥɥɦɚɧɚ F, ɩɨɷɬɨɦɭ ɢɡ ɭɪɚɜɧɟɧɢɣ (4) ɢ (5) ɫɢɫɬɟɦɵ (10) ɞɨɨɩɪɟɞɟɥɢɦ
Ȗ1 ɢ ȕ1.
γ 1 = bψ 2ψ , β 1 = r2 m 2 −
r1 m1 2
.
b ψ
(14)
ɇɭɠɧɨ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɫɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɨɛ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɫɨɫɬɨɹɧɢɢ ɜ
ɩɨɥɭɱɟɧɧɵɯ ɮɨɪɦɭɥɚɯ (11–14) ɛɵɥɚ ɨɩɭɳɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ l1 ɢ l2 ɨɬ ɞɚɥɶɧɨɫɬɢ x, ɩɨɷɬɨɦɭ ɧɚɣɞɟɧɧɵɟ ɨɰɟɧɤɢ ɹɜɥɹɸɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦɢ, ɚ ɫɚɦ ɨɩɬɢɦɚɥɶɧɵɣ ɪɟɝɭɥɹɬɨɪ – ɫɬɚɰɢɨɧɚɪɧɵɦ.
ȼ ɡɚɤɥɸɱɟɧɢɟ ɷɬɨɝɨ ɪɚɡɞɟɥɚ ɩɨɞɫɬɚɜɢɦ ɩɨɥɭɱɟɧɧɵɟ ɨɰɟɧɤɢ (11–14) ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (8). Ⱥɧɚɥɢɡɢɪɭɹ ɡɧɚɱɢɦɨɫɬɶ ɨɬɞɟɥɶɧɵɯ ɫɥɚɝɚɟɦɵɯ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɢ ɩɪɟɧɟɛɪɟɝɚɹ ɱɚɫɬɶɸ
ɢɡ ɧɢɯ, ɜɜɢɞɭ ɢɯ ɦɚɥɨɫɬɢ ɞɥɹ ɪɟɲɚɟɦɨɣ ɡɚɞɚɱɢ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ
F = 0,5 l1 ( y1 − m1 ) 2 + 0,5 l2 ( y2 m2 )2 − 0,5U 2 + y1 y2 (γ 1 − aψ ) + y2 ( β1 − aβ 2 ) + y22 (ψ − aγ 2 ) ≈
≈
0,5 r1 ( y1 − m1 ) 2 + 0,5 r2 ( y2 − m2 )2
− 0,5U 2 + ( y1 − m1 )( y2 − m2 )(γ 1 − aψ ).
Hɉ 2
(x −
) + ( y1 − m1 ) 2
θ
1+
d2
94
(15)
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ɉɨɫɥɟɞɧɟɟ ɫɥɚɝɚɟɦɨɟ ɜ ɮɨɪɦɭɥɟ (15) ɹɜɥɹɟɬɫɹ ɧɨɜɵɦ ɪɟɡɭɥɶɬɚɬɨɦ ɢ ɨɬɪɚɠɚɟɬ ɢɧɬɟɪɟɫɧɵɣ ɮɚɤɬ – ɟɫɥɢ ɡɧɚɤɢ ɨɬɤɥɨɧɟɧɢɣ (y1 – m1) ɢ (y2 – m2) ɩɨ ɩɨɥɨɠɟɧɢɸ ɢ ɫɤɨɪɨɫɬɢ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵ (ɚ ɷɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɢɬɭɚɰɢɢ ɭɦɟɧɶɲɟɧɢɹ ɨɲɢɛɨɤ), ɬɨ ɮɭɧɤɰɢɹ ɪɢɫɤɚ ɩɚɞɚɟɬ, ɢ
ɧɚɨɛɨɪɨɬ – ɩɪɢ ɫɨɜɩɚɞɟɧɢɢ ɡɧɚɤɨɜ ɪɢɫɤ ɪɚɫɬɟɬ, ɬ. ɤ. ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜɨɡɪɚɫɬɚɸɬ ɦɨɞɭɥɢ
ɨɲɢɛɨɤ, ɡɧɚɱɢɬ, ɮɨɪɦɭɥɚ (15) ɨɬɪɚɠɚɟɬ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɪɟɲɚɟɦɨɣ ɡɚɞɚɱɢ, ɟɫɥɢ ɦɧɨɠɢɬɟɥɶ
(Ȗ1 – aȥ) ɩɨɥɨɠɢɬɟɥɟɧ. ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ ɷɬɨ ɡɚɜɢɫɢɬ ɨɬ ɩɪɚɜɢɥɶɧɨɫɬɢ ɧɚɡɧɚɱɟɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
ɲɬɪɚɮɨɜ r1 ɢ r2.
ɄɈɆɉɖɘɌȿɊɇɈȿ ɆɈȾȿɅɂɊɈȼȺɇɂȿ ɉɊɈɐȿɋɋɈȼ
ɍɉɊȺȼɅȿɇɂə ɂ ɄɈɇɌɊɈɅə ɉɊɂ ɁȺɏɈȾȿ ɇȺ ɉɈɋȺȾɄɍ
Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɩɪɨɜɨɞɢɥɨɫɶ ɜ ɫɪɟɞɟ Matlab. Ȼɥɨɤ-ɫɯɟɦɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 3.
Ɋɢɫ. 3. ɋɯɟɦɚ ɩɪɨɝɪɚɦɦɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɡɚɯɨɞɚ ɧɚ ɩɨɫɚɞɤɭ ɜ ɫɪɟɞɟ Matlab
ȼ ɫɯɟɦɟ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 3, ɢɦɟɸɬɫɹ ɞɜɟ ɭɤɪɭɩɧɟɧɧɵɟ ɩɨɞɫɢɫɬɟɦɵ: psi ɢ
Sypsystem, ɤɨɬɨɪɵɟ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3, ɚ ɢ ɧɚ ɪɢɫ. 3, ɛ.
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Ɋɢɫ. 3, a. ɋɯɟɦɚ ɩɨɞɩɪɨɝɪɚɦɦɵ psi ɩɨ ɜɵɱɢɫɥɟɧɢɸ ȥ
Ɋɢɫ. 3, ɛ. ɋɯɟɦɚ ɩɨɞɩɪɨɝɪɚɦɦɵ Subsystem1
Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɜɨɞɢɥɨɫɶ ɞɥɹ ɬɪɟɯ ɫɥɭɱɚɟɜ:
– ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɭɩɪɚɜɥɟɧɢɹ ɩɪɢ U = 0;
– ɩɪɢ ɧɟɩɪɟɪɵɜɧɨɦ ɨɩɬɢɦɚɥɶɧɨɦ ɭɩɪɚɜɥɟɧɢɢ Û;
– ɩɪɢ ɡɚɞɟɪɠɤɟ ɭɩɪɚɜɥɟɧɢɹ ɩɨɫɥɟ ɩɪɨɥɟɬɚ ɧɚɞ ɬɨɱɤɨɣ ɧɚɱɚɥɚ ɫɧɢɠɟɧɢɹ.
ȼ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɛɵɥɢ ɧɚɡɧɚɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɩɚɪɚɦɟɬɪɵ: a = 0,25; b = 0,1;
Hɉ = 400 ɦ; V = 80 ɦ/c; ș = 0,06; y1(0) = 450; y2(0) = 0; x(0) = 10000 ɦ; r1 = 25; r2 = 5.
ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɪɨɰɟɫɫ ɫɬɚɛɢɥɢɡɚɰɢɢ ɜɵɫɨɬɵ y1 ɨɤɨɥɨ ɬɪɟɛɭɟɦɨɝɨ ɡɧɚɱɟɧɢɹ
Hɉ = 400 ɦ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ U = 0, ɩɨɷɬɨɦɭ ɮɭɧɤɰɢɹ ɪɢɫɤɚ F ɧɟɢɡɛɟɠɧɨ ɪɚɫɬɟɬ, ɤɚɤ ɩɨɤɚɡɚɧɨ
ɧɚ ɪɢɫ. 4.
Ɋɢɫ. 4. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɪɢɫɤɚ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɚɤɬɢɜɧɵɯ ɞɟɣɫɬɜɢɣ ɩɪɢ y1(0) = 500 ɦ
ɇɚ ɝɪɚɮɢɤɟ ɭɤɚɡɚɧ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t0 =
x(0) −
Hɉ
θ = 23 c , ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɧɚɱɚɥɭ
V
ɧɟɨɛɯɨɞɢɦɨɝɨ ɫɧɢɠɟɧɢɹ ɩɨ ɝɥɢɫɫɚɞɟ, ɜɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɦɚɤɫɢɦɭɦ ɮɭɧɤɰɢɢ ɪɢɫɤɚ ɜɨɡɧɢɤɚɟɬ
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ɜ ɧɚɱɚɥɟ ɭɫɬɪɚɧɟɧɢɹ ɨɲɢɛɤɢ ( y1 (0) − H ɉ ) ɢ ɜ ɬɨɱɤɟ ɧɚɱɚɥɚ ɫɧɢɠɟɧɢɹ, ɤɚɤ ɩɨɤɚɡɚɧɨ
ɧɚ ɪɢɫ. 5 ɢ 6.
Ɋɢɫ. 5. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɜɵɫɨɬɵ y1
ɢ ɡɚɞɚɧɧɨɣ ɩɪɨɝɪɚɦɦɵ m1 ɩɨɥɟɬɚ ɩɪɢ ɨɩɬɢɦɚɥɶɧɨɦ ɭɩɪɚɜɥɟɧɢɢ
Ɋɢɫ. 6. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɮɭɧɤɰɢɢ ɪɢɫɤɚ ɩɪɢ ɨɩɬɢɦɚɥɶɧɨɦ ɭɩɪɚɜɥɟɧɢɢ
ȼɢɞɧɨ, ɱɬɨ ɮɭɧɤɰɢɹ ɪɢɫɤɚ ɜɟɫɶɦɚ ɦɚɥɚ, ɢ ɫɢɝɧɚɥ ɩɪɟɞɭɩɪɟɞɢɬɟɥɶɧɨɣ ɬɪɟɜɨɝɢ ɧɟ ɬɪɟɛɭɟɬɫɹ. ȼ ɬɪɟɬɶɟɦ ɫɥɭɱɚɟ ɢɦɢɬɢɪɭɟɬɫɹ ɡɚɞɟɪɠɤɚ ɜ ɨɩɬɢɦɚɥɶɧɵɯ ɞɟɣɫɬɜɢɹɯ, ɤɨɝɞɚ ɧɚɱɚɥɨ ɚɤɬɢɜɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɩɨɡɠɟ ɦɨɦɟɧɬɚ ɧɚɱɚɥɚ ɫɧɢɠɟɧɢɹ ɧɚ Ʃt = 5 c, ɚ ɩɟɪɜɨɧɚɱɚɥɶɧɵɣ ɩɨɥɟɬ
ɩɪɨɢɫɯɨɞɢɥ ɧɚ ɠɟɥɚɟɦɨɣ ɜɵɫɨɬɟ Hɉ.
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Ɋɢɫ. 7. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɜɵɫɨɬɵ ɩɪɢ ɡɚɩɨɡɞɚɥɨɦ ɭɩɪɚɜɥɟɧɢɢ
ɇɚ ɪɢɫ. 7 ɜɢɞɧɨ, ɱɬɨ ɩɪɨɰɟɫɫ ɫɧɢɠɟɧɢɹ ɩɨ ɝɥɢɫɫɚɞɟ ɨɩɚɡɞɵɜɚɟɬ, ɩɨɷɬɨɦɭ ɮɭɧɤɰɢɹ ɪɢɫɤɚ
F ɧɚɱɢɧɚɟɬ ɛɵɫɬɪɨ ɜɨɡɪɚɫɬɚɬɶ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 8.
Ɋɢɫ. 8. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɮɭɧɤɰɢɢ ɪɢɫɤɚ ɩɪɢ ɡɚɩɨɡɞɚɥɨɦ ɭɩɪɚɜɥɟɧɢɢ
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɟɫɥɢ ɧɚɡɧɚɱɢɬɶ ɧɟɤɨɬɨɪɵɣ ɩɨɪɨɝ F0, ɩɪɟɜɵɲɟɧɢɟ ɤɨɬɨɪɨɝɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɢɝɧɚɥɭ ɩɪɟɞɭɩɪɟɞɢɬɟɥɶɧɨɣ ɬɪɟɜɨɝɢ, ɬɨ ɦɨɠɧɨ ɡɚɪɚɧɟɟ ɩɪɟɞɨɬɜɪɚɬɢɬɶ ɨɩɚɫɧɨɫɬɶ ɡɚɞɟɪɠɤɢ ɜ ɭɩɪɚɜɥɟɧɢɢ ɞɨ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɭɯɨɞɚ ɧɚ ɩɨɜɬɨɪɧɵɣ ɤɪɭɝ.
ɁȺɄɅɘɑȿɇɂȿ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɩɪɨɜɟɞɟɧɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ.
1. ɉɪɟɞɥɨɠɟɧ ɩɨɞɯɨɞ ɤ ɨɪɝɚɧɢɡɚɰɢɢ ɧɟɩɪɟɪɵɜɧɨɝɨ ɩɪɨɝɧɨɡɢɪɭɸɳɟɝɨ ɤɨɧɬɪɨɥɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɡɚɯɨɞɚ ɧɚ ɩɨɫɚɞɤɭ ɩɪɢ ɝɢɩɨɬɟɡɟ ɨɛ ɨɩɬɢɦɚɥɶɧɨɦ ɩɨɜɟɞɟɧɢɢ ɩɪɢ ɭɫɬɪɚɧɟɧɢɢ ɨɩɚɫɧɵɯ ɫɢɬɭɚɰɢɣ ɩɨ ɡɚɞɚɧɧɨɦɭ ɤɪɢɬɟɪɢɸ.
2. Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɢ ɤɨɧɬɪɨɥɹ ɨɫɧɨɜɚɧɨ ɧɚ ɛɚɡɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɩɪɢ ɷɬɨɦ ɧɨɜɢɡɧɚ ɩɨɞɯɨɞɚ ɫɨɫɬɨɢɬ:
– ɜ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɫɢɝɧɚɥɚ ɬɪɟɜɨɝɢ ɩɪɢ ɡɚɯɨɞɟ ɧɚ ɩɨɫɚɞɤɭ ɜ ɜɢɞɟ ɮɭɧɤɰɢɢ ɪɢɫɤɚ, ɪɚɜɧɨɣ
ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ Ȼɟɥɥɦɚɧɚ;
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– ɜ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɟɪɟɦɟɧɧɨɣ ɮɭɧɤɰɢɢ ɲɬɪɚɮɨɜ ɡɚ ɨɲɢɛɤɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɞɨ ɬɨɱɤɢ ɧɚɱɚɥɚ ɫɧɢɠɟɧɢɹ ɩɨ ɝɥɢɫɫɚɞɟ;
– ɜ ɮɨɪɦɭɥɟ ɜɵɱɢɫɥɟɧɢɹ ɮɭɧɤɰɢɢ ɪɢɫɤɚ ɟɫɬɶ ɫɥɚɝɚɟɦɨɟ, ɭɱɢɬɵɜɚɸɳɟɟ ɫɨɜɩɚɞɟɧɢɟ ɡɧɚɤɨɜ ɨɬɤɥɨɧɟɧɢɣ ɩɨ ɩɨɥɨɠɟɧɢɸ ɢ ɫɤɨɪɨɫɬɢ (ɪɢɫɤ ɪɚɫɬɟɬ) ɢɥɢ ɢɯ ɧɟɫɨɜɩɚɞɟɧɢɟ (ɪɢɫɤ ɩɚɞɚɟɬ), ɱɬɨ
ɨɬɜɟɱɚɟɬ ɮɢɡɢɱɟɫɤɨɦɭ ɫɦɵɫɥɭ ɪɟɲɚɟɦɨɣ ɡɚɞɚɱɢ.
1. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɤɚɡɚɥɨ, ɱɬɨ ɩɪɢ ɧɟɚɤɬɢɜɧɨɦ ɢɥɢ ɡɚɩɨɡɞɚɥɨɦ ɭɩɪɚɜɥɟɧɢɢ, ɮɭɧɤɰɢɹ ɪɢɫɤɚ ɫɢɥɶɧɨ ɪɚɫɬɟɬ, ɚ ɩɪɢ ɨɩɬɢɦɚɥɶɧɨɦ ɭɩɪɚɜɥɟɧɢɢ ɜɟɫɶɦɚ ɦɚɥɚ. ɉɨɷɬɨɦɭ ɦɨɠɧɨ ɧɚɡɧɚɱɢɬɶ ɧɟɤɨɬɨɪɵɣ ɩɨɪɨɝ, ɩɪɟɜɵɲɟɧɢɟ ɤɨɬɨɪɨɝɨ ɛɭɞɟɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɫɢɝɧɚɥɭ ɬɪɟɜɨɝɢ,
ɩɪɟɞɭɩɪɟɠɞɚɸɳɟɦɭ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɧɟɠɟɥɚɬɟɥɶɧɨɝɨ ɭɯɨɞɚ ɧɚ ɩɨɜɬɨɪɧɵɣ ɤɪɭɝ.
2. ɇɟɨɛɯɨɞɢɦɨ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ ɧɚ ɜɨɩɪɨɫ ɩɪɚɜɢɥɶɧɨɝɨ ɜɵɛɨɪɚ ɩɨɪɨɝɚ ɞɥɹ ɮɭɧɤɰɢɢ
ɪɢɫɤɚ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɞɥɹ ɷɬɨɝɨ ɪɟɡɭɥɶɬɚɬɚɦɢ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ.
3. ɇɚɣɞɟɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɩɪɢ ɞɨɩɭɳɟɧɢɹɯ ɨ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ ɨɩɬɢɦɚɥɶɧɨɝɨ ɪɟɝɭɥɹɬɨɪɚ ɭɩɪɚɜɥɟɧɢɹ ɭɩɪɨɳɟɧɧɨɣ ɞɢɧɚɦɢɤɟ ɩɨɥɟɬɚ ɢ ɜ ɜɢɞɟ ɩɟɪɟɦɟɧɧɨɣ ɮɭɧɤɰɢɢ
ɲɬɪɚɮɨɜ. ɉɨɷɬɨɦɭ ɧɟɨɛɯɨɞɢɦɨ ɩɭɬɟɦ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɬɨɱɧɢɬɶ ɩɚɪɚɦɟɬɪɵ ɫɢɧɬɟɡɚ, ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɜɟɥɢɱɢɧɭ ɩɨɪɨɝɚ ɩɪɟɞɭɩɪɟɞɢɬɟɥɶɧɨɣ ɬɪɟɜɨɝɢ.
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ
1. Ȼɟɥɥɦɚɧ Ɋ. Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ Ɇ.: Ɏɢɡɦɚɬɝɢɡ, 1961.
2. Ʌɟɬɨɜ Ⱥ.Ɇ. Ⱦɢɧɚɦɢɤɚ ɩɨɥɟɬɚ ɢ ɭɩɪɚɜɥɟɧɢɟ Ɇ.: ɇɚɭɤɚ, 1969.
3. Ɉɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɢ ɤɨɧɬɪɨɥɶ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɩɟɪɟɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜɨɡɞɭɲɧɵɯ ɢ
ɪɟɱɧɵɯ ɫɭɞɨɜ ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɢɯ ɦɚɪɲɪɭɬɨɜ // Ƚ.ɇ. Ʌɟɛɟɞɟɜ, ȼ.Ȼ. Ɇɚɥɵɝɢɧ, Ɍɢɧ ɉɯɨɧ ɑɠɨ,
Ɂɨ Ɇɢɧ Ɍɚɣɤ. ɇɨɜɵɟ ɬɟɯɧɨɥɨɝɢɢ, ɦɟɯɚɬɪɨɧɢɤɚ, ɚɜɬɨɦɚɬɢɡɚɰɢɹ ɭɩɪɚɜɥɟɧɢɹ. 2012. ʋ 12. ɋ. 50–53.
4.Ʌɟɛɟɞɟɜ Ƚ.ɇ., Ɍɢɧ ɉɯɨ Ⱦɠɨ. Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɚɹ ɫɢɫɬɟɦɚ ɭɩɪɚɜɥɟɧɢɹ ɢ ɤɨɧɬɪɨɥɹ
ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɨɩɭɬɧɨɝɨ ɢ ɩɨɩɟɪɟɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɝɪɭɩɩɵ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɩɪɢ ɡɚɯɨɞɟ ɧɚ ɩɨɫɚɞɤɭ // ȼɟɫɬɧɢɤ ɉɟɧɡɟɧɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 2014. ʋ 1. ɋ. 72–80.
THE SYSTEM OF AUTOMATED AVOIDANCE
OF HAZARDOUS SITUATIONS AT AIRCRAFT APPROACH
BEFORE GLIDESLOPE DESCENT
Eremin A.I., Lebedev G.N., Chekhov I.A.
The article presents the attitude to the organization of continuous predictive control of approach safety under the
hypothesis about the optimal behavior while eliminating dangerous situations. The task solution of the optimal control and
monitoring based on dynamic programming as well as a computer modeling procedure of the present process has been
given. Computer modeling showed that under an inactive or delayed control the risk function increases considerably. Some
attention was drawn to the problem of the correct choice of the threshold for the risk function, using the results of computer
simulation for this purpose. The solution of the problem was obtained under the assumptions of stationary optimal control
and simplified flight dynamics.
Key words: optimal control, dynamic programming method, risk function, analytical design of optimal regulators.
REFERENCES
1. Bellman R. Dynamic programming. Moscow. 1961.
2. Letov A.M. Flight Dynamics and Control. Moscow. 1969.
3. Lebedev G.N., Malygin V.B., Tin Phone Chzho, Zo Min Taik. Optimal control and safety
control of the transverse movement of aircraft and sea vessels crossing their routes. New technologies,
mechatronics, automation control. 2012. No. 12. Pp. 50–53.
4. Lebedev G.N., Tin Phone Chzho. Automated control system safety for associated motion
and crossing motion while landing aircraft. Bulletin of Penza State University. 2014. No. 1. Pp. 72–80.
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ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɋȼȿȾȿɇɂə ɈȻ ȺȼɌɈɊȺɏ
ȿɪɟɦɢɧ Ⱥɧɞɪɟɣ ɂɝɨɪɟɜɢɱ, ɢɧɠɟɧɟɪ ɜɬɨɪɨɣ ɤɚɬɟɝɨɪɢɢ ɎȽɍɉ «Ƚɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɧɚɭɱɧɨ-ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɢɧɫɬɢɬɭɬ ɚɜɢɚɰɢɨɧɧɵɯ ɫɢɫɬɟɦ», ɷɥɟɤɬɪɨɧɧɵɣ ɚɞɪɟɫ. E-mail:
aieremin@2100.gosniias.ru.
Ʌɟɛɟɞɟɜ Ƚɟɨɪɝɢɣ ɇɢɤɨɥɚɟɜɢɱ, ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɩɪɨɮɟɫɫɨɪ ɤɚɮɟɞɪɵ ɂɧɮɨɪɦɚɰɢɨɧɧɨ-ɢɡɦɟɪɢɬɟɥɶɧɵɟ ɫɢɫɬɟɦɵ ɅȺ Ɇɨɫɤɨɜɫɤɨɝɨ ɚɜɢɚɰɢɨɧɧɨɝɨ ɢɧɫɬɢɬɭɬɚ (ɇɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ), ɡɚɫɥɭɠɟɧɧɵɣ ɞɟɹɬɟɥɶ ɧɚɭɤɢ ɊɎ, ɷɥɟɤɬɪɨɧɧɵɣ
ɚɞɪɟɫ: kaf301@mai.ru.
ɑɟɯɨɜ ɂɝɨɪɶ Ⱥɧɚɬɨɥɶɟɜɢɱ, ɤɚɧɞɢɞɚɬ ɜɨɟɧɧɵɯ ɧɚɭɤ, ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ ɆȽɌɍ ȽȺ, ɷɥɟɤɬɪɨɧɧɵɣ ɚɞɪɟɫ: i.chehov@mstuca.aero.
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