Consider an asymptotically stable first-order system: y = ay+bu. The coefficients a and b are real-valued...

Transcribed Image Text:

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 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. 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 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.