I have a inverted inertia wheel pendulum. I suppose that if I have a wheel with larger inertia at its top, the system would be more stable.

How can I prove or disprove my conjecture?


1 Answer 1


Linearize the system around the operating point you're interested in. Look at the eigenvalues of the A and B matrices that represents the linearized system. Then compare the eigenvalues using from systems with different wheel sizes.

  • $\begingroup$ Should I include the PID controller block into the system which is going to be linearized? $\endgroup$ Mar 14, 2015 at 0:14
  • $\begingroup$ I think that should be a separate question. Come back once you have the linearized equations. $\endgroup$
    – holmeski
    Mar 14, 2015 at 4:17
  • $\begingroup$ Could you also work out the physics to create the state-space representation, convert that to a transfer function and then observe the root locus plots? $\endgroup$ Mar 16, 2015 at 21:26
  • $\begingroup$ A nice resource on the argument: mne.ksu.edu/static/nlc/…. $\endgroup$ Mar 17, 2015 at 15:58

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