Multistep variable methods for exact integration of perturbed stiff linear systems

A family of real and analytical functions with values within the ring of M(m, R) is introduced. The solution for linear systems of differential equations is expressed as a series of Φ-functions. This new multistep method is defined for variable-step and variable-order, maintains the good properties of the Φ-function series method. It incorporates to compute the coefficients of the algorithm a recurrent algebraic procedure, based in the existing relation between the divided differences and the elemental and complete symmetrical functions. In addition, under certain hypotheses, the new multistep method calculates the exact solution of the perturbed problem. The new method is implemented in a computational algorithm which enables us to resolve in a general manner some physics and engineering IVP’s modeled by means systems of differential equations. The good behaviour and precision of the method is evidenced by contrasting the results with other-reputed algorithms and even with methods based on Scheifele’s G-functions.This work has been supported by GRE09-13 project of the University of Alicante and the project of the Generalitat Valenciana GV/2011/032

Accurate integration of forced and damped oscillators

The new methods accurately integrate forced and damped oscillators. A family of analytical functions is introduced known as T-functions which are dependent on three parameters. The solution is expressed as a series of T-functions calculating their coefficients by means of recurrences which involve the perturbation function. In the T-functions series method the perturbation parameter is the factor in the local truncation error. Furthermore, this method is zero-stable and convergent. An application of this method is exposed to resolve a physic IVP, modeled by means of forced and damped oscillators. The good behavior and precision of the methods, is evidenced by contrasting the results with other-reputed algorithms implemented in MAPLE

Output-feedback proportional-integral-derivative-type control with multiple saturating structure for the global stabilization of robot manipulators with bounded inputs

"An output-feedback proportional integral derivative-type control scheme for the global regulation of robot manipulators with constrained inputs is proposed. It guarantees the global stabilization objective-avoiding input saturation-releasing the feedback not only from the exact knowledge of the system structure and parameter values but also from velocity measurements. With respect to previous approaches of the kind, the proposed controller is expressed in a generalized form whence multiple saturating structures may be adopted, thus enlarging the degree of design flexibility. Furthermore, experimental tests on a two-degree-of-freedom direct-drive manipulator corroborate the efficiency of the proposed scheme.

A generalized scheme for the global adaptive regulation of robot manipulators with bounded inputs

"In this work, a generalized adaptive control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. It gives rise to various families of bounded controllers with adaptive gravity compensation. Compared with the adaptive approaches previously developed in a bounded-input context, the proposed scheme guarantees the adaptive regulation objective: globally, avoiding discontinuities in the control expression as well as in the adaptation auxiliary dynamics, preventing the inputs to reach their natural saturation bounds, and imposing no saturation-avoidance restriction on the control gains. Experimental results corroborate the efficiency of the proposed adaptive scheme.

Output-feedback adaptive control for the global regulation of robot manipulators with bounded inputs

"In this paper, an output-feedback adaptive scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. Compared to the previous output-feedback adaptive approaches developed in a bounded-input context, the proposed free-of-velocity feedback controller guarantees the adaptive regulation objective: globally, avoiding discontinuities throughout the scheme, preventing the inputs to reach their natural saturation bounds, and imposing no saturation-avoidance restriction on the control gains. Moreover, the developed scheme is not restricted to the use of a specific saturation function to achieve the required boundedness, but may involve any one within a set of smooth and non-smooth (Lipschitz-continuous) bounded passive functions that include the hyperbolic tangent and the conventional saturation as particular cases. Experimental results corroborate the efficiency of the proposed scheme.

Output-feedback adaptive SP-SD-Type control with an extended continuous adaptation algorithm for the global regulation of robot manipulators with bounded inputs

"In this work, an output-feedback adaptive SP-SD-type control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. Compared with the output-feedback adaptive approaches previously developed in a bounded-input context, the proposed velocity-free feedback controller guarantees the adaptive regulation objective globally (i.e. for any initial condition), avoiding discontinuities throughout the scheme, preventing the inputs from reaching their natural saturation bounds and imposing no saturation-avoidance restrictions on the choice of the P and D control gains. Moreover, through its extended structure, the adaptation algorithm may be configured to evolve either in parallel (independently) or interconnected to the velocity estimation (motion dissipation) auxiliary dynamics, giving an additional degree of design flexibility. Furthermore, the proposed scheme is not restricted to the use of a specific saturation function to achieve the required boundedness, but may involve any one within a set of smooth and non-smooth (Lipschitz-continuous) bounded passive functions that include the hyperbolic tangent and the conventional saturation as particular cases. Experimental results on a 3-degree-of-freedom manipulator corroborate the efficiency of the proposed scheme

Implementation of Model Reference Adaptive Control in a Dehydration System

[EN] In this article, the use of Model Reference Adaptive Control (MRAC) is proposed as a technique to regulate a system with input delay. As a case study, a thermal system represented by a cabin dehydrator is considered. The analysis of the selected system is carried out to determine the equations that describe its behavior, and a reference signal is designed, which is essential for the proper operation of the control algorithm. The identification of the parameters of the thermal system and the tuning of the adaptation gain are performed. The theory of Lyapunov is used to evaluate the stability of the system and design the control. The performance of the proposed control is compared with other methods using the performance index (L2 norm).[ES] En este artículo se propone el uso del Control Adaptable por Modelo de Referencia (MRAC) como técnica para regular un sistema con retardo en la entrada, como caso de estudio se considera un sistema térmico representado por un deshidratador de cabina. Se realiza el análisis del sistema seleccionado para determinar las ecuaciones que describen su comportamiento, y se diseña una señal de referencia, esencial para el correcto funcionamiento del algoritmo de control. Se realiza la identificación de los parámetros del sistema térmico y la sintonización de la ganancia de adaptación. Para evaluar la estabilidad del sistema y diseñar el control se utiliza la teoría de Lyapunov. El desempeño del control propuesto se compara con otros métodos empleando el índice de desempeño (norma L2).Sánchez-Sánchez, P.; Cebada Reyes, JG.; Montiel Martínez, A.; Reyes Cortés, JF. (2023). Implementación del control adaptable por modelo de referencia en un sistema de deshidratación. Revista Iberoamericana de Automática e Informática industrial. 21(1):39-51. https://doi.org/10.4995/riai.2023.19172395121

Seismic model analysis by means of a series method

La respuesta desde la Mecánica Estructural a los fenómenos sísmicos, hace necesario mejorar el cálculo de las estructuras así como su análisis. Para ello los métodos especialmente basados en el análisis estático no lineal necesitan tener una mayor precisión. El análisis no lineal se puede abordar mediante modelos discretos o continuos. Los modelos discretos representan la estructura a través de un número finito de grados de libertad; en este caso las ecuaciones de movimiento son ecuaciones diferenciales ordinarias que se resuelven por métodos numéricos. En este trabajo se muestra una aplicación del método de series ɸ-funciones para calcular la respuesta ante un terremoto de las estructuras modeladas mediante sistemas SDOF (Single Degree Of Freedom system) y 2DOF (Two Degree Of Freedom systems). Además, en el caso de SDOF, el método se ha aplicado tomando como la frecuencia forzada la frecuencia natural de vibración. La solución de los modelos sísmicos se ha obtenido mediante la generación de un algoritmo numérico y su implementación computacional. El método de series ɸ-funciones integra osciladores forzados y es una adaptación de los métodos de Scheifele, con la ventaja de integrar, sin error de truncamiento, el problema perturbado con sólo las dos primeras ɸ-funciones. El cálculo de coeficientes de la serie se efectúa por recurrencias algebraicas sencillas en las que se implica la función de perturbación. El buen comportamiento y precisión del método de series ɸ-funciones se ilustra cuando se contrasta con otros métodos de integración ya conocidos e implementados en MAPLE, comparándose también con los métodos clásicos de Ingeniería de Estructuras.The seismic events have attracted interest and the need to improve the structures and their analysis to sustain this type of oscillation. To do this, new methods especially those based on static non-linear analysis need to have increased accuracy. The non-linear analysis can be approached by means of discrete or continuous models. The discrete models represent the structure through a finite number of degrees of freedom; in this case the equations of motion are ordinary differential equations which are solved by numerical methods. This paper shows an application of the ɸ-functions series method to calculate the response of structures, modeled as both SDOF(Single Degree Of Freedom system) and 2DOF (Two Degree Of Freedom systems) systems, to an earthquake. Furthermore, in the case of SDOF, the method has been applied taking as the forcing frequency the natural frequency of vibration. The solution of the seismic models has been obtained by the generation of the numerical algorithm and its computational implementation. The ɸ-functions series method integrates forced oscillators and it is an adaptation of Scheifele's methods, with the advantage of integrating, without truncation error, the perturbed problem with just the first two ɸ-functions. The calculation of series coefficients is effected by simple algebraic recurrences in which the perturbation function is takes part. The good precision of ɸ-functions series method is illustrated when contrasted with other methods of integration already known and implemented in MAPLE and even with classic methods of Structural Engineering

La evolución climática a largo plazo y evaluación de la seguridad

El concepto de almacenamiento geológico profundo para residuos radiactivos de alta actividad basa una parte importante de su seguridad a largo plazo en el comportamiento del medio geológico. De aquí que los estudios de seguridad post-clausura de tales almacenamientos deban contemplar la necesidad de cuantificar los procesos susceptibles de intervenir en la liberación y el transporte de los radionucleidos desde el propio almacenamiento hasta la biosfera, y las modificaciones importantes que esta última pueda sufrir debido tanto a factores naturales como antropogénicos, durante los periodos de tiempo del orden de cientos de miles de años en que se cifra la duración de la liberación de radionucleido

Fiscal Policy Stance Reaction to the Financial/Economic Crisis in the EMU: The Case of Slovenia

The article evaluates the current economic crisis’ impact on changes in the adoption of fiscal policy measures for 16 euro-area countries in the 2004–2012 period and compares those changes with fiscal policy measures introduced in Slovenia. In general, the results suggest that the adopted fiscal policy measures in most euro-area countries were more expansionary in the period before the current economic crisis started. The evaluation of the fiscal stance in Slovenia suggests expansionary and pro-cyclical fiscal behaviour during the 2005–2008 period, whereas the response of the fiscal authorities in Slovenia in 2011 and 2012 due to fiscal consolidation was more restrictive and pro-cyclical. Finally, we emphasize that inconsistent fiscal policy without structural reforms also being carried out may lead to a further deterioration of the fiscal position and macroeconomic situation of euro-area countries, including during a period of cyclical recovery