Modern Control Engineering

Section 10–8 / Quadratic Optimal Regulator Systems 805

MATLAB Program 10–23

% ---------- Unit-step response of designed system ----------

A = [0 1 0;0 0 1;0 -2 -3];

B = [0;0;1]

C = [1 0 0];

D = [0];

K = [100.0000 53.1200 11.6711];

k1 = K(1); k2 = K(2); k3 = K(3);

% ***** Define the state matrix, control matrix, output matrix,

% and direct transmission matrix of the designed systems as AA,

% BB, CC, and DD *****

AA = A - B*K;

BB = B*k1;

CC = C;

DD = D;

t = 0:0.01:8;

[y,x,t] = step (AA,BB,CC,DD,1,t);

plot(t,x)

grid

title('Response Curves x1, x2, x3, versus t')

xlabel('t Sec')

ylabel('x1,x2,x3')

text(2.6,1.35,'x1')

text(1.2,1.5,'x2')

text(0.6,3.5,'x3')

Response Curves x1,x2,x3 versus t

x1,

x2,

x^3

5

• 2

1

4

2

0

• 1

3

t Sec

051 2 3 486 7

x 3

x (^2) x 1
Figure 10–40
Response curves x 1
versust, x 2 versust,
andx 3 versust.