Human brain capabilities to control are undeniable, but embedding that capacity in an algorithm for the control of a dynamic system has proven limited by natural human bounds such as the reaction time, which restricts the number of industrial applications using a human in the loop. Thus, the authors of this paper propose a new procedure to scale linear systems in time, which makes human control of dynamic systems not only feasible but also comfortable. The scaling method comprises moving poles and zeros of a transfer function proportionally to a scaling factor. Thus, a person controls the scaled version of the system, while the computer acquires his/her reactions, then a neural network learns those reactions. This network controls both scaled and original systems. The new control strategy controls slow and fast systems, as well as stable and unstable systems, achieving high performance for all conditions. Appropriate time scaling, and practice, facilitate the control of any dynamic system.

In this paper, we present two algorithms for approximating a period given a discrete data set. These algorithms superimpose two consecutive sections of the data for several candidate periods. The first algorithm counts the number of shuffling points per candidate period, whereas the second algorithm computes a distance between points when sorted by time. The best candidate period maximizes the number of shuffling points in the first algorithm, whereas the second algorithm minimizes the distance between points. The experimental validation with noiseless data demonstrates that the relative error for the estimations is less than half of the sampling period and shows that this error does not depend on the harmonic content, as normally occurs with algorithms that estimate a period. The application of the algorithms demonstrates that they properly track the frequency of a power grid and accurately estimate the period of a Van der Pol oscillator, which serves to confirm their applicability to real-time problems.Keywords: Frequency estimation, frequency measurement, periodic functions, power system monitoring, signal reconstruction. RESUMENEn este artículo se presentan dos algoritmos para estimar el periodo de una señal, dado un conjunto de datos discretos, estos algoritmos superponen dos secciones de datos a varios periodos. El primer algoritmo cuenta el número de puntos que se mezclan por cada periodo, mientras el segundo, calcula la distancia entre los puntos cuando se ordenan por tiempo. De esta manera, el mejor candidato para periodo maximiza el número de puntos que se mezclan en el primer algoritmo, mientras que en el segundo, minimiza la distancia entre puntos. La validación experimental con señales sin ruido, demuestra que el error relativo de las estimaciones cae por debajo de la mitad del periodo de muestreo, y a su vez, muestra que ese error no depende del contenido armónico de la señal, como ocurre con los algoritmos para estimar periodo. La aplicación de los algoritmos demuestra que pueden seguir la frecuencia de un sistema de potencia y además, pueden aproximar el periodo de un oscilador Van der Pol, lo cual sirve para confirmar que estos algoritmos se pueden aplicar para solucionar problemas en tiempo real.Palabras clave: estimación de frecuencia, medida de frecuencia, funciones periódicas, monitoreo de sistemas de potencia y reconstrucción de señales.

The purpose of this study is to minimize the arc length for the path described by the model of a robot platform when the path is constrained to have smooth transitions given by sigmoid functions. The optimization required a proof of stability for the resulting control law, the selection of the best sigmoid function among ten functions, and the definition of two gains necessary to parameterize the control law. The optimization was carried out by simulating the system under several kinematic and dynamical conditions, and the best sigmoid function was a hyperbolic tangent. Thus, the motion control first implied the simulation of a reference model to define an optimal path, and later the control of an actual robot platform, which followed the optimal path. The use of the optimized path reduced the complexity of the controller while allowing natural and intuitive paths for the robot platform.

Human-robot interaction requires the robot to recognize and convey emotions. Emotions also enhance adaptation by influencing deliberative actions. However, scientists traditionally relegate the emulation of emotions to high levels in multilevel architectures, where those emulated emotions collaborate with reasoning to come up with the best action. In contrast, in this research, we propose the use of emulated emotions at the lowest level of a cognitive architecture, for instance, robot motion control. Thus, the traditional definition of error used by a controller changes in order to include anticipation. The discrepancy between an anticipated ideal state and an anticipated robot state elicits an emotion. This simple emotion-inspired definition of the error improves the controller by more than 11% according to the definition of performance in this article, which argues that robot control architectures should use emulated emotions from their lowest levels.