7/21/2019 State Space Design Continuous

1/37

!"#"$ &'#($ )$&*+,

-.,"/.00#1*0*"2 3#"/*45 61&$/7#1*0*"2 3#"/*45

7/21/2019 State Space Design Continuous

2/37

!"#"$ &'#($ )$&*+,

8*7$,5

-.,"/.00#10$ (#,,.,*(#0 9./3

#0:#2& (.,"/.0#10$

;" *& .1&$/7#10$ *9 #,) ?=&> @#7$ ,. (.33., 9#("./&

*& "@$ (@#/#("$/*&A( '.02,.3*#0

7/21/2019 State Space Design Continuous

3/37

!"#"$ &'#($ )$&*+,

8*7$,5

61$/7#10$ (#,,.,*(#0 9./3

#0:#2& .1&$/7#10$

;" *& (.,"/.00#10$ *9 #,) ?=&> @#7$ ,. (.33., 9#("./&

*& "@$ (@#/#("$/*&A( '.02,.3*#0

7/21/2019 State Space Design Continuous

4/37

!"#"$ &'#($ )$&*+,

7/21/2019 State Space Design Continuous

5/37

B@$ "/#,&9./3#A.,5

*& "@$ &*3*0#/*"2 "/#,&9./3#A.,

!"#"$ &'#($ )$&*+,

C *& "@$ $DE*7#0$,($

"/#,&9./3#A.,

7/21/2019 State Space Design Continuous

6/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

?$H,*,+ "@$ 9.00.:*,+ (.,"/.0 0#:5

7/21/2019 State Space Design Continuous

7/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

?$H,*,+ "@$ 9.00.:*,+ (.,"/.0 0#:5

I$ .1"#*,5

:*(@ @#& "@$ 9.00.:*,+ (@#/#("$/*&A( $DE#A.,5

)$"

;9 "@$ &2&"$3 *& (.,"/.00#10$ :$ (#, /$0.(#"$ #00 "@$ &2&"$3 '.0$&

7/21/2019 State Space Design Continuous

8/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

-0.&$) J0..' (@#/#("$/*&A( $DE#A.,5

)$"

K*,) &E(@ "@#"

?$&*/$) (@#/#("$/*&A( $DE#A.,5

)$" L

1 2

1 2 1( ) n n n

n ns s s s s! ! ! ! !

" "

"

= + + + + +!

C/.10$35

;" *& $#&*$/ 9/.3 "@$ (.,"/.00#10$ (#,,.,*(#0 9./3

1 2

1 2 1

n n n

n ns s s s! ! ! !

" "

"

+ + + + +!

7/21/2019 State Space Design Continuous

9/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"K/.3 "@$ (.,"/.00#10$ (#,,.,*(#0 9./35

M&*,+ "@$ &"#"$ 9$$)1#(F5

I$ .1"#*,5

7/21/2019 State Space Design Continuous

10/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

B@$ &2&"$35

@#& "@$ (@#/#("$/*&A( '.02,.3*#05

)$" L ( ) ( ) ( ) ( )1 21 1 2 2 1 1n n n n n n ns a k s a k s a k s a k! ! ! !+ + + + + + + + +!

7/21/2019 State Space Design Continuous

11/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

( ) ( ) ( ) ( )1 2 1 2

1 2 1 1 1 2 2 1 1

n n n n n n

n n n n n ns s s s s a k s a k s a k s a k! ! ! ! " " " "

" " "+ + + + + = + + + + + + + + +! !

M&*,+ "@$ )$&*/$) (@#/#("$/*&A( $DE#A.,51 2

1 2 1( ) n n n

n ns s s s s! ! ! ! !

" "

"

= + + + + +!

NDE#0*,+

B@E&O :$ .1"#*,

[ ]1 1 2 2 1 1n n n na a a a! ! ! ! " "" " " "!

7/21/2019 State Space Design Continuous

12/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"C/.($)E/$5

6/*+*,#0 &'#($5

-.,"/.00#10$ (#,,.,*(#0 9./3

$DE*7#0$,($ "/#,&9./3#A.,

-#0(E0#"$?$&*/$) (@#/#("$/*&A( $DE#A.,5

1 21 2 1( )

n n n

n ns s s s s! ! ! ! ! " "

"

= + + + + +!

!2&"$3 (@#/#("$/*&A( $DE#A.,5

1 2

1 2 1( ) n n n

n ns s a s a s a s a

! !

!" = + + + + +!

[ ]1 1 2 2 1 1n n n na a a a! ! ! ! " "" " " "!

$DE*7#0$,($ "/#,&9./3#A.,

7/21/2019 State Space Design Continuous

13/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

$DE*7#0$,($ "/#,&9./3#A., ". "@$ (.,"/.00#10$ 9./3

6/*+*,#0 &2&"$3 (.,"/.00#1*0*"2 3#"/*45

-.,"/.00#10$ 9./3 (.,"/.00#1*0*"2 3#"/*45

:*(@ #/$ /$0#"$) 12

;" /$&E0"&5

7/21/2019 State Space Design Continuous

14/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

$DE*7#0$,($ "/#,&9./3#A., ". "@$ (.,"/.00#10$ 9./3

6/*+*,#0 &2&"$3 (.,"/.00#1*0*"2 3#"/*45

-.,"/.00#10$ 9./3 (.,"/.00#1*0*"2 3#"/*45

:*(@ #/$ /$0#"$) 12

;" /$&E0"&5

-.,"/.00#1*0*"2

7/21/2019 State Space Design Continuous

15/37

!"#"$ 9$$)1#(F G '.0$ '0#($3$,"

7/21/2019 State Space Design Continuous

16/37

PE#)/#A( .'A3#0 /$+E0#"./

7/21/2019 State Space Design Continuous

17/37

PE#)/#A( .'A3#0 /$+E0#"./

7/21/2019 State Space Design Continuous

18/37

PE#)/#A( .'A3#0 /$+E0#"./

7/21/2019 State Space Design Continuous

19/37

PE#)/#A( .'A3#0 /$+E0#"./

7/21/2019 State Space Design Continuous

20/37

PE#)/#A( .'A3#0 /$+E0#"./

7/21/2019 State Space Design Continuous

21/37

!"#"$ $&A3#"./

6'$,J0..' &"#"$ $&A3#"./5

N&A3#A., $//./5

I$ .1"#*,

7/21/2019 State Space Design Continuous

22/37

!"#"$ $&A3#"./

;9 "@$ &2&"$3 *& .1&$/7#10$ "@$ $&A3#"./ (#, 1$ )$&*+,$) ". $&A3#"$

"@$ &2&"$3 &"#"$ #& DE*(F02 #& )$&*/$)

[ ]1 2 1n nl l l l != !

7/21/2019 State Space Design Continuous

23/37

!"#"$ $&A3#"./

B@$ '0#," &2&"$3

B@$ $&A3#"./

N&A3#A., $//./5

I$ .1"#*,

7/21/2019 State Space Design Continuous

24/37

K*,) &E(@ "@#"

!"#"$ $&A3#"./

N&A3#A., $//./ (@#/#("$/*&A( '.02,.3*#05

?$&*/$) (@#/#("$/*&A( $DE#A.,5

)$" L

C/.10$35

;" *& $#&*$/ 9/.3 "@$ .1&$/7#10$ (#,,.,*(#0 9./3

1 2

1 2 1

n n n

n ns a s a s a s a

! !

!+ + + + +!

)$"

[ ]1 2 1n nl l l l != !

)$"

7/21/2019 State Space Design Continuous

25/37

!"#"$ $&A3#"./C/.($)E/$5

6/*+*,#0 &'#($5

61&$/7#10$ (#,,.,*(#0 9./3

$DE*7#0$,($ "/#,&9./3#A.,

-#0(E0#"$?$&*/$) (@#/#("$/*&A( $DE#A.,5

!2&"$3 (@#/#("$/*&A( $DE#A.,5

1 2

1 2 1( ) n n n

n ns s a s a s a s a

! !

!" = + + + + +!

$DE*7#0$,($ "/#,&9./3#A.,

7/21/2019 State Space Design Continuous

26/37

!"#"$ $&A3#"./

$DE*7#0$,($ "/#,&9./3#A.,

7/21/2019 State Space Design Continuous

27/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

B@$ (.,"/.0 0#:5 B@$ $&A3#"./

= l1

l2 ! l

n!1 l

n

"#$

%&'

7/21/2019 State Space Design Continuous

28/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

B@$ (.,"/.0 0#:5

7/21/2019 State Space Design Continuous

29/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

B@$ &E1&A"EA., .9 "@$ (.,"/.0 0#: *, "@$ &2&"$3 '0#," #,)$&A3#"./ $DE#A.,& 2*$0)&

7/21/2019 State Space Design Continuous

30/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

7/21/2019 State Space Design Continuous

31/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

7/21/2019 State Space Design Continuous

32/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

7/21/2019 State Space Design Continuous

33/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

7/21/2019 State Space Design Continuous

34/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

7/21/2019 State Space Design Continuous

35/37

-.,,$(A., .9 &"#"$ 9$$)1#(F #,) &"#"$ $&A3#"./

7/21/2019 State Space Design Continuous

36/37

Q2#'E,.7 &"#1*0*"2 "@$./$3

7/21/2019 State Space Design Continuous

37/37

Q2#'E,.7 &"#1*0*"2 "@$./$3