
to simulate the response of the system dx=dt ¼x þu when the input is given by u ¼u(t) ¼
sin 25t, t 0. The initial condition x(0) ¼0. Compute
^
u
nþ1=2
and
^
u
nþ1
based on linear
extrapolation through the points (t
n1
, u
n1
) and (t
n
, u
n
). Plot the exact solution and the
simulated response on the same graph.
8.6 ADDITIONAL METHODS OF APPROXIMATING CONTINUOUS-TIME
SYSTEM MODELS
Several additional methods for simulating the dynamics of continuous-time systems are presented in
this section. Explanations of each are followed by the application of the methods to a linear
continuous-time system to produce the z-domain transfer function, difference equations, and ...