Modern Control Engineering

Section 10–5 / State Observers 775

MATLAB Program 10–10

A = [0 1 0;0 0 1;-6 -11 -6];

B = [0;0;1];

J = [-2+j2sqrt(3) -2-j2sqrt(3) -6];

K = acker(A,B,J)

K =

90.0000 29.0000 4.0000

Abb = [0 1;-11 -6];

Aab = [1 0];

L = [-10 -10];

Ke = acker(Abb',Aab',L)'

Ke =

14

5

Equation (10–99) now becomes

(A MATLAB computation of this Keis given in MATLAB Program 10–10.)

= B

89

- 154

14

5

RB

0

1

R =B

14

5

R

Ke= bB

0

- 11

1

- 6

R

2

+ 20 B

0

- 11

1

- 6

R + 100 B

1

0

0

1

RrB

1

0

0

1

R

• 1
  B

0

1

R

Referring to Equations (10–88) and (10–89), the equation for the minimum-order observer can
be given by

(10–100)

where

Noting that

the equation for the minimum-order observer, Equation (10–100), becomes

or

B

h 2

h 3

R = B

- 14

- 16

1

- 6

RB

h 2

h 3

R +B

- 191

- 260

Ry+ B

0

1

Ru

+B

0

- 6

R- B

14

5

R 0 ry+bB

0

1

R - B

14

5

R 0 ru

B

h 2

h 3

R = B

- 14

- 16

1

- 6

RB

h 2

h 3

R +bB

- 14

- 16

1

- 6

RB

14

5

R

Abb-Ke Aab= B

0

- 11

1

- 6

R -B

14

5

R[1 0]=B

- 14

- 16

1

- 6

R

H= xb-Ke y=xb-Ke x 1

H=AAbb-Ke AabBH+CAAbb-Ke AabBKe+Aba-Ke AaaDy+ABb-Ke BaBu