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Chapter 4 System Analysis
Xmath Control Design Module 4-18 ni.com
Step Response
The response of a system to a unit step input is one of the most commonly
used measures of how well a given control system’s output tracks the
system input. A unit step is a time signal which is zero up until the
beginning of the time period of interest, and one thereafter. This indicator
is popular because it is easy to compute and interpret. It also is
mathematically possible to calculate the response to any input if the
response to a unit step is known. The performance measures associated
with the step response are as follows:
• Delay time (t
d
)—The time required for the response to reach half its
final value.
• Rise time (t
r
)—The time required for the response to rise from 10%
of its final value to 90% of its final value.
• Peak time (t
p
)—The time required for the response to reach the peak
value of its first overshoot.
• Maximum overshoot (M
p
)—The response value which most exceeds
unity, expressed as a percent.
• Settling time (t
s
)—The time required for the response to reach 5% of
its final value.
These performance measures are obtained easily with a few lines of
MathScript, as demonstrated in Example 4-9. For a plot of these
performance measures, refer to Figure 4-6.
step( )
Y = step(Sys,T)
The step( ) function computes the unit step response of a dynamic
system over a time period which can be specified with the optional time
vector
T. If T is not specified, step( ) computes a default time vector
using
deftimerange( ).
The output,
Y, is a PDM where domain is the time vector and dependent
matrices have row size equal to the number of inputs and column size equal
to the number of outputs.
Example 4-9 Performance Measurements for a Step Response
Y = step(Sys, 0:.1:15);
plot (Y,{x_lab = "Time (sec)",
ylab = "Amplitude", xinc=1, yinc=.1})