Page 153 - Modern Control Systems

Section 2.9 The Simulation of Systems Using Control Design Software 127
«(/) >•</)
Step System Output
input | G(s)
•> t
(a)

t = T: user-supplied time vector
y(t) = output response at t or
G(s) = sys
T = simulation time t = Tflna,: simulation final time
(optional)

][

[y,T]=step(sys,t)
FIGURE 2.73
The step function. (b)

% This script computes the step
% response of the traction motor
% wheel velocity
%
num=[5400]; den=[2 2.5 5402]; sys=rf(num,den);
t=[0:0.005:3];
[y,t]=step(sys,t);
Jlffi i Hizi plot(t,y),grid
xlabel(Time (s)')
1
0 ylabel('Wheel velocity )
0 0.5 1.0 1.5 2.0 2.5 3.0
Time (s)
(a) (b)

FIGURE 2.74 (a) Traction motor wheel velocity step response, (b) m-file script.

If the only objective is to plot the output,y(t), we can use the step function with-
out left-hand arguments and obtain the plot automatically with axis labels. If we
need y{f) for any purpose other than plotting, we must use the step function with
left-hand arguments, followed by the plot function to plot y(t). We define t as a row
vector containing the times at which we wish the value of the output variable y(t).
We can also select t — /g nai, which results in a step response from t — 0 to t — ffmai
and the number of intermediate points are selected automatically.
The step response of the electric traction motor is shown in Figure 2.74. As
expected, the wheel velocity response, given by y(t), is highly oscillatory. Note
that the output is y(t) s o)(t). m