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Óïðàâëåíèå ìíîãîìåðíûìè àâòîìàòè÷åñêèìè ñèñòåìàìè - êîíòðîëüíàÿ ðàáîòà

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:


1 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