11.状態空間でのシステム結合

11.≧ែ✵㛫䛷䛾䝅䝇䝔䝮⤖ྜ
ᩍ⛉᭩ 6.5,6.6
┤ิ⤖ྜ䛾ሙྜ(1)
z ఏ㐩㛵ᩘ⾲⌧䛷䛿䛂┤ิ⤖ྜ = ఏ㐩㛵ᩘ䛾᥃䛡⟬䛃䛷䛒䛳䛯䚹
䛷䛿䚸䛭䜜䜢≧ែ✵㛫䛷⾲䛩䛸䛹䛖䛺䜛䛷䛒䜝䛖䛛?
z ┤ิ⤖ྜ (䜹䝇䜿䞊䝗᥋⥆)
u1
y1
u2
y2
62
61
:
z
=
:
=
=
=
+
+
+
=
=
+
+
䜢⪃៖䛩䜛䛸䚸
+
=
+
=
:
=
=
+
+
+
+
+
+
=
+
=
+
䜘䛳䛶䚸┤ิ⤖ྜ⣔䛿
┤ิ⤖ྜ䛾ሙྜ(2)
z 61䛸62䛿䛭䜜䛮䜜༢⊂䛷䛿ྍไᚚ䞉ྍほ 䛸䛩䜛䚹
z 1ධຊ1ฟຊ⣔䛾ሙྜ䚸 61䛾ఏ㐩㛵ᩘG1(s)䛸62䛾ఏ㐩㛵ᩘG2(s) 䛜䚸
( )
( )
,
=
=
( )
( )
䛸䛺䜛䛸䛝(䛭䜜䛮䜜᪤⣙䛸௬ᐃ)䚸᥃䛡⟬䛷ᴟ䝊䝻┦ẅ䛩䜛䛺䜙䚸≧ែ✵㛫䛷䛾┤
ิ⤖ྜ⣔䛿୙ྍไᚚ䛛୙ྍほ 䚹
( )䛸 ( )䛜ᴟ䝊䝻┦ẅ䛩䜛䛺䜙䚸┤ิ⤖ྜ⣔䛿୙ྍไᚚ䚹
z
z
( )䛸 ( )䛜ᴟ䝊䝻┦ẅ䛩䜛䛺䜙䚸┤ิ⤖ྜ⣔䛿୙ྍほ 䚹
୪ิ⤖ྜ䛾ሙྜ(1)
z ఏ㐩㛵ᩘ䛷䛿䚸䛂୪ิ⤖ྜ = ఏ㐩㛵ᩘ䛾㊊䛧⟬䛃
u1
u
u2
z
=
y1
61
+
y2 +
62
=
䛚䜘䜃
=
+
y
:
=
=
+
+
:
=
=
+
+
䜘䜚䚸⤖ྜ⣔䛿䚸
=
=
+
+
+
୪ิ⤖ྜ䛾ሙྜ(2)
z 61䛸62䛿䛭䜜䛮䜜༢⊂䛷䛿ྍไᚚ䞉ྍほ 䛸䛩䜛䚹
z 1ධຊ1ฟຊ⣔䛾ሙྜ䚸 61䛾ఏ㐩㛵ᩘG1(s)䛸62䛾ఏ㐩㛵ᩘG2(s) 䛜䚸
( )
( )
,
=
=
( )
( )
䛸䛺䜛䛸䛝(䛭䜜䛮䜜᪤⣙䛸௬ᐃ)䚸㊊䛧⟬䛧䛶㏻ศ䛧䛯䛸䛝䛻ḟඖ䛜䛚䛱䜜䜀䚸୙ྍ
ไᚚ䛛䛴୙ྍほ 䚹
z 䛴䜎䜚䚸 ( )䛸 ( )䛻ඹ㏻ᅉᏊ䛜䛒䜛䛺䜙䜀䚸୪ิ⤖ྜ⣔䛿䚸ྍไᚚ䛷䜒ྍ
ほ 䛷䜒䛺䛔䚹
ฟຊ䝣䜱䞊䝗䝞䝑䜽⣔䛾ሙྜ(1)
z ฟຊ䝣䜱䞊䝗䝞䝑䜽⣔ (䝉䞁䝃䞊䝎䜲䝘䝭䜽䝇௜䛝):
u
+
z
u1
–
y2
y1
61
y
:
u2
62
=
=
䛚䜘䜃
䛾⤖ྜ⣔䛾≧ែኚᩘ⾲⌧䛿䚸
:
=
=
=
=
+
+
=
+
=
=
=
+
+
=
+
䜘䜚䚸䛣
ฟຊ䝣䜱䞊䝗䝞䝑䜽⣔䛾ሙྜ(2)
z 61䛸62䛿䛭䜜䛮䜜༢⊂䛷䛿ྍไᚚ䞉ྍほ 䛸䛩䜛䚹
z 1ධຊ1ฟຊ⣔䛾ሙྜ䚸 61䛾ఏ㐩㛵ᩘG1(s)䛸62䛾ఏ㐩㛵ᩘG2(s) 䛜䚸
( )
( )
,
=
=
( )
( )
䛸䛺䜛䛸䛩䜛(䛭䜜䛮䜜᪤⣙䛸௬ᐃ)䚹
z 䛭䛾䛸䛝䚸 ( )䛸 ( )䛻ඹ㏻ᅉᏊ䛜䛒䜛䛺䜙䜀䚸䛣䛾ฟຊ䝣䜱䞊䝗䝞䝑䜽⣔䛿䚸
ྍไᚚ䛷䜒ྍほ 䛷䜒䛺䛔䚹