  In this work we carry out extensive numerical study of a
Watt-centrifugal-governor system model, and we also implement an electronic
circuit by analog computation to experimentally solve the model. Our numerical
results show the existence of self-organized stable periodic structures (SPSs)
on parameter-space of the largest Lyapunov exponent and isospikes of time
series of the Watt governor system model. A peculiar hierarchical organization
and period-adding bifurcation cascade of the SPSs are observed, and this
self-organized cascade accumulates on a periodic boundary. It is also shown
that the periods of these structures organize themselves obeying the solutions
of Diophantine equations. In addition, an experimental setup is implemented by
a circuitry analogy of mechanical systems using analog computing technique to
characterize the robustness of our numerical results. After applying an active
control of chaos in the experiment, the effect of intrinsic experimental noise
was minimized such that, the experimental results are in astonishing well
agreement with our numerical findings. We can also mention as another
remarkable result, the application of analog computing technique to perform an
experimental circuitry analysis in real mechanical problems.
