Modern Control Engineering

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Example Problems and Solutions 251

Solution.A possible MATLAB program based on Equations (5–58) and (5–60) is given by MAT-

LAB program 5–26. The response curve obtained here is shown in Figure 5–65. (Notice that this

problem was solved by use of the command “initial” in Example 5–16. The response curve obtained

here is exactly the same as that shown in Figure 5–34.)

MATLAB Program 5–26

t = 0:0.05:10;

A = [0 1 0;0 0 1;-10 -17 -8];

B = [2;1;0.5];

C=[1 0 0];

[y,x,t] = step(A,B,CA,CB,1,t);

plot(t,y)

grid;

title('Response to Initial Condition')

xlabel('t (sec)')

ylabel('Output y')

A–5–17. Consider the following characteristic equation:

Determine the range of Kfor stability.

Solution.The Routh array of coefficients is

s^4

s^3

s^2

s^1

s^0

1

K

K- 1

K

1 -

K^2

K- 1

1

1

1

1

1

0

s^4 +Ks^3 +s^2 +s+ 1 = 0

Figure 5–65
Response y(t) to
the given initial
condition.

Output

y

t (sec)

Response to Initial Condition

0.5

1

1.5

2

2.5

0

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