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?
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1 Answer
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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.
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$\begingroup$ Should I include the PID controller block into the system which is going to be linearized? $\endgroup$ Mar 14, 2015 at 0:14
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$\begingroup$ I think that should be a separate question. Come back once you have the linearized equations. $\endgroup$– holmeskiMar 14, 2015 at 4:17
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$\begingroup$ 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
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$\begingroup$ A nice resource on the argument: mne.ksu.edu/static/nlc/…. $\endgroup$ Mar 17, 2015 at 15:58