Consider an asymptotically stable first-order system: y = ay+bu. The coefficients a and b are
real-valued and, furthermore, a < 0 due to asymptotic stability. You have available the test data
from a "sine wave" experiment (the dependent variable has converged its steady-state sinusoidal
response in the measurement). The results of the test is shown below:
Sine wave test results
Input and output
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
0.1
0.2
- Input sinusoid
-Output sinudoid
0.3
Time (second)
0.4
0.5
0.6
Use this information to estimate a and b. Hints: first determine the frequency (in rad/s) of the input
sinusoid (the output sinusoid has the same frequency); the magnitude and phase of the frequency
response function can be determined at this frequency from the relative magnitudes and phases.
Fig: 1