Óïðàâëåíèå ìíîãîìåðíûìè àâòîìàòè÷åñêèìè ñèñòåìàìè ÌÎÑÊÎÂÑÊÈÉ ÃÎÑÓÄÀÐÑÒÂÅÍÍÛÉ ÎÒÊÐÛÒÛÉ ÓÍÈÂÅÐÑÈÒÅÒ ÔÀÊÓËÜÒÅÒ ÈÍÔÎÐÌÀÒÈÊÈ È ÐÀÄÈÎÝËÅÊÒÐÎÍÈÊÈ ÊÀÔÅÄÐÀ ÈÍÔÎÐÌÀÒÈÊÈ È ÐÀÄÈÎÝËÅÒÐÎÍÈÊÈ Êîíòðîëüíàÿ ðàáîòà ïî óïðàâëåíèþ ìíîãîìåðíûìè àâòîìàòè÷åñêèìè ñèñòåìàìè Âûïîëíèëà: Ðàòíèêîâà Ñ.À. Çàî÷íàÿ ôîðìà îáó÷åíèÿ Êóðñ V Ñïåöèàëüíîñòü 210100 ¹ çà÷åòíîé êíèæêè 6001053 Ïðîâåðèë ïðåïîäàâàòåëü: Ðàáîòà ñäàíà ____________________ Ïîäïèñü ëèöà, ïðèíÿâøåãî ðàáîòó ____ Ïîäïèñü ñòóäåíòà ______________ Âîëîêîëàìñê 2004 ã. Èñõîäíûå äàííûå Ñòðóêòóðíàÿ ñõåìà îáúåêòà óïðàâëåíèÿ – ñèñòåìà àâòîìàòè÷åñêîãî óïðàâëåíèÿ âòîðîãî ïîðÿäêà ñ îäíîìåðíûì âåêòîðîì ū-âõîäíûõ âîçäåéñòâèé è îäíîìåðíûì âåêòîðîì y-âûõîäíûõ ïåðåìåííûõ ïðèâåäåíà íà ðèñóíêå: (ñ1 ñ2 ) ū ν ∫ Ä S x y α11 α12 α21 α22 R α11 = 18 α12 = 5 α21 = – 3 α22 = 12 β1 = 1 β2 = – 2 c1 = – 1 c2 = 9 Çàäàíèå 1. Çàïèñàòü óðàâíåíèå îáúåêòà â âåêòîðíîé ôîðìå; 2. Èññëåäîâàòü îáúåêò óïðàâëåíèÿ íà óñòîé÷èâîñòü; 3. Èññëåäîâàòü îáúåêò óïðàâëåíèÿ íà óïðàâëÿåìîñòü; 4. Èññëåäîâàòü îáúåêò óïðàâëåíèÿ íà íàáëþäàåìîñòü. Âûïîëíåíèå ðàáîòû 1 – 2 (– 1 9) ∫ ū ν Ä – Sxy 18 5 – 3 12 R Óðàâíåíèå îáúåêòà â âåêòîðíîé ôîðìå ν = ν1 • u ν2 – 2u x = x1 x2 ν = 1 • u – 2 S = ν – R x = ⌠Sdt R = 18 5 – 3 12 y = (– 1 9) • x = (– 1 9) • x1 = – x1 + 9x2 x2 dx/dt = SS = 1 • u – 18 5 • x – 2 – 3 12 dx/dt = Ax + Du – óðàâíåíèå îáúåêòà Y = Cx + Du – óðàâíåíèå âûõîäíûõ ïåðåìåííûõ D = 0 u = u1 x = x1 y = y1 x2 A = 18 5 B = 1 C = (– 1 9) – 3 12 – 2 Èññëåäîâàíèå îáúåêòà óïðàâëåíèÿ íà óñòîé÷èâîñòü det (A – pE) = 0 18 5 – p 0 = 18 – p 5 – 3 12 0 p – 3 12 – p 18 – p 5 – 3 12 – p = (18 – p) (12 – p) – 5 • (– 3) = 216 – 18p – 12p + p2 + 15 = p2 – 30p + 231 p2 – 30p + 231 = 0 p1 = (900 + √–24) / 2 = 15 + √6 j p2 = (900 – √–24 ) / 2 = 15 – √6 j Rep1 > 0 Rep2 > 0, ñëåäîâàòåëüíî ñèñòåìà íåóñòîé÷èâà. Èññëåäîâàíèå îáúåêòà óïðàâëåíèÿ íà óïðàâëÿåìîñòü dx/dt = Ax + Bu Ïîðÿäîê n = 2 Ìàòðèöà óïðàâëÿåìîñòè: R = (BAB) A • B = 18 5 • 1 = 18 • 1 + 5 • (– 2) = 8 – 3 12 – 2 – 3 • 1 + 12 • (– 2) – 2 R = 1 8 – 2 – 27 1 8 = 1 • (–27) – 8 • (– 2) = – 27 + 16 = – 11≠ 0 – 2 – 27 Ñëåäîâàòåëüíî r =2 = n Îáúåêò óïðàâëÿåì. Èññëåäîâàíèå íà íàáëþäàåìîñòü HT = C CA C • A = (– 1 9) • 18 5 = –1•18+9•(–3) –1•5+9•12 = (– 45 103) – 3 12 HT = – 1 9 – 45 103 – 1 9 = – 103 + 405 = 302 ≠ 0, ñëåäîâàòåëüíî r = 2 = n – 45 103