I've implemented a model of a ball-on-plate plant and am controlling it over a network. Below is the open loop output when excited by successive sinusoidal inputs with increasing frequencies. I know that the plant is open loop unstable, and it is cool that this figure so nicely captures the instability.

What I'd like to know is if there is other information that I can glean about the plant from the relationship between the input and the output state.

(The state is clipped at 3.1 units.)

Green reference signal and blue observed system state

  • $\begingroup$ What happens at t = 5000 (s?) $\endgroup$ Dec 3 '15 at 16:09
  • $\begingroup$ The frequency of the reference input changes and the state of the simulation is reset to zero. (There are 10 cycles at each frequency and the plot is truncated just as the third region is beginning). $\endgroup$
    – Remy
    Dec 3 '15 at 21:17
  • $\begingroup$ Gotcha, you should separate those plots if the simulation is reset. $\endgroup$ Dec 3 '15 at 21:19
  • $\begingroup$ Ok. Will do in the future. $\endgroup$
    – Remy
    Dec 3 '15 at 21:20

The natural frequency of your system is obvious from your graph. From that you can get a relationship between mass and stiffness (using a second order model). If you look at the growth in amplitude of your natural frequency (use a high-pass filter to remove the input signal) you should see the rate of growth in the characteristic frequency. That is related to the system damping ratio. A text on vibration (e.g., http://www.newport.com/Fundamentals-of-Vibration/140234/1033/content.aspx) can help with the specific parameters.


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