National Instruments 370760B-01

86 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ

spacing in the input signal pdm. This means that the input pdm must be regularly

spaced. Stair-case input functions with relatively few data points will often give

erroneous results. The input signal should be interpolated (with interp) before being

multiplied with the Dynamic System. The function defTimeRange will calculate a

default integrationstep size and form the required time vector. This can be useful in

creating an input pdm or as an input to interp. Note that the initial state is speciﬁed

within the Xmath Dynamic System.

Discrete time Dynamic Systems do not require an additional command as the time

increment is contained within the Dynamic System data object. The time step in the

input pdm must of course match the discrete system sample time.

Xmath also provides severalcore functions for common time response calculations: step

calculates the unit step response; impulse calculates the impulse response; and initial

calculates the unforced response from initial conditions speciﬁed within the Dynamic

System or provided as input arguments. In each of these functions the user may specify

a time to override the default selected bydefTimeRange.

Time response calculations are illustrated in the following example. Severalof the

functions discussed in the previous sections are also used.

# Create a second order lightly damped system.

sys = 5/makepoly([1,1,5],"s")

# Create an input signal with a step to +1 at

# 1 second and a step to -1 at 5 seconds. A

# 10 second signal is created.

u = gstep([0:0.05:10],[0;1;5],[0;1;-1])

# Calculate the time response.

y0 = sys*u

# Repeat this calculation with an initial

# condition of [-1;0]. Note that this is

# only meaningful for a specified realization

# and Xmath forces us to choose one. Here we

# choose that returned as the abcd default