Characterizing the Dynamics of the Watt Governor System Under Harmonic Perturbation and Gaussian Noise

We investigate the disturbance on the dynamics of a Watt governor system model due to the addition of a harmonic perturbation and a Gaussian noise, by analyzing the numerical results using two distinct methods for the nonlinear dynamics characterization: (i) the well-known Lyapunov spectrum, and (ii) the 0-1 test for chaos. The results clearly show that for tiny harmonic perturbations only the smallest stable periodic structures (SPSs) immersed in chaotic domains are destroyed, whereas for intermediate harmonic perturbation amplitudes there is the emergence of quasiperiodic motion, with the existence of typical Arnold tongues and, the consequent distortion of the SPSs embedded in the chaotic region. For large enough harmonic perturbations, the SPSs immersed in chaotic domains are suppressed and the dynamics becomes essentially chaotic. Regarding the noise perturbations, it is able to suppress periodic motion even if tiny noise intensities are considered, as analyzed by a periodic attractor subject to different noise intensities. The threshold of noise amplitude for chaos generation in periodic structures is reported by both methods. Additionally, we investigate the robustness of the 0-1 test for chaos characterization in both noiseless and noise cases, and for the first time, we compare the Lyapunov exponents and 0-1 test methods in the parameter-planes. Our findings are generic due to their remarkable agreement with results previously reported for dynamical systems in other contexts.

Extensive Numerical Study and Circuitry Implementation of the Watt Governor Model

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 astonishingly well in 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.

El concepto realimentación y sus significado en el ámbito pedagógico

RESUMEN: Este artículo comprende un estudio minucioso sobre el concepto de realimentación. Se describe su desarrollo histórico, su presencia en diversas disciplinas científicas —en particular en las CC. Sociales—, analizando su influencia en el orden de las ideas y los métodos, lo que le ha llevado a convertirse en una de las principales metáforas científicas de la actualidad. Su incorporación al lenguaje pedagógico, por vía de las corrientes sistémicas y cibernéticas, merece un estudio crítico, en el que se describan los niveles a los que opera, su relación con otros conceptos y procesos, y su posición central en las modernas teorías de la educación; con especial hincapié en las aportaciones del Dr. Sanvisens.SUMMARY: The purpose of this paper is to analyze the concept feedback. From Watt «Governor» (1790) and the initial theoretical work developed by J. Maxwell (1868), including the cybernetics concepts developed in the fifties, in this paper we revise the conceptual influences and the methodological and thecnological applications in different disciplines, with special attention to the Social Sciences field. The feedback concept is related with other concepts such as: The Systems Dynamic's, the Biofeedback thecnics, the sociological systemic models, the family therapy... Thorough discussion is deserved to the application of this concept in the Educational Theory field. Specifically we analyze the contributions made by the humanistic cybernetic proposed by A. Sanvisens.