System ID with 3 Modes

After implementing a pole placement controller controller that placed the poles for the first two modes of SAMII's flexible base and realizing that this controller made the third mode unstable, I set out to curve fit a wider frequency range of my data to get a model that included the third mode of the flexible base.  This was the first time in my system i.d. work where the phase error needed to be included explictly.  The overall error function that I was minimizing was the sum of the squared magnitude error in dB and a phase weight times the sum of the squared phase error in degrees.  The results for various values of the phase weight are shown below along with seperate plots for the chosen value of phase weight=0.
Bode plot for the hydraulic actuator with various phase weights

This figure shows a Bode plot for the hydraulic actuator.  The black line is experimental data and the colored lines are from optimization curve fits with various values of the phase weight (0-0.5).
Bode plot for the fliexible base with various phase weights

This figure shows a Bode plot for the flexible base.  The black line is experimental data and the colored lines are from optimization curve fits with various values of the phase weight (0-0.5).
Bode plot for the hydraulic actuator with phase weight=0.1.

This figure shows a Bode plot for the hydraulic actuator.  The blue line is experimental swept sine data and black circles are experimental fixed sine data.  The red line is the output of an optimization with phase weight =0.1.
Bode plot for the flexible base with phase weight=0.1.

This figure shows a Bode plot for the flexible base.  The blue line is experimental swept sine data and black circles are experimental fixed sine data.  The red line is the output of an optimization with phase weight =0.1.
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