Modern Control Engineering

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210 Chapter 5 / Transient and Steady-State Response Analyses

MATLAB Program 5–16

t = 0:0.05:3;

A = [0 1;-10 -5];

B = [0;0];

C = [0 0];

D = [0];

[y,x] = initial(A,B,C,D,[2;1],t);

x1 = [1 0]*x';

x2 = [0 1]*x';

plot(t,x1,'o',t,x1,t,x2,'x',t,x2)

grid

title('Response to Initial Condition')

xlabel('t Sec')

ylabel('State Variables x1 and x2')

gtext('x1')

gtext('x2')

Response to Initial Condition

t Sec

0 0.5 1 1.5 2 2.5 3

State Variables

x^1

and

x^2

3

− 3

− 2

− 1

0

1

2

x 1

x 2

Figure 5–33

Response curves to

initial condition.

EXAMPLE 5–10 Consider the following system that is subjected to the initial condition. (No external forcing

function is present.)

Obtain the response y(t)to the given initial condition.

y(0)=2, y#(0)=1, y$(0)=0.5

y%+8y$+17y# +10y= 0

Then the command “initial” can be used as shown in MATLAB Program 5–16 to obtain

the response to the initial condition. The response curves x 1 (t)andx 2 (t)are shown in

Figure 5–33. They are the same as those shown in Figure 5–32.

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