Estabilidad de ecuaciones diferenciales estocásticas lineales anticipativas

En el presente trabajo se dan condiciones suficientes para la estabilidad e inestabilidad en media cuadrática de soluciones de ecuaciones diferenciales estocásticas lineales en el sentido de Skorohod (i.e., la integral estocástica involucrada es definida a través de la descomposición en caos de Itô-Wiener). Aquí el coeficiente de deriva considerado tiene una descomposición en caos de orden 1, y el de difusión es determinista y cuadrado integrable. El análisis realizado se basa, principalmente, en estimar las normas en L2 de los núcleos en la descomposición en caos de la solución fuerte de dichas ecuaciones

Nested Saturation Function Control of a Magnetic Levitation System

The trajectory tracking task of a magnetic levitation system connected to a beam mechanism is solved by means of a nested saturation control with a feedforward term. The flatness property of the system allows to use the nested saturation control technique and the feedforward control to stabilize the output tracking error around the equilibrium. The closed-loop error dynamics is proven to be locally exponentially stable. Numerical simulations prove the effectiveness of the proposal

Active Disturbance Rejection Strategy for Distance and Formation Angle Decentralized Control in Differential-Drive Mobile Robots

The important practical problem of robust synchronization in distance and orientation for a class of differential-drive mobile robots is tackled in this work as an active disturbance rejection control (ADRC) problem. To solve it, a kinematic model of the governed system is first developed based on the distance and formation angle between the agents. Then, a special high-order extended state observer is designed to collectively estimate the perturbations (formed by longitudinal and lateral slipping parameters) that affect the kinematic model. Finally, a custom error-based ADRC approach is designed and applied assuming that the distance and orientation between the agents are the only available measurements. The proposed control strategy does not need time-derivatives of the reference trajectory, which increases the practical appeal of the proposed solution. The experimental results, obtained in laboratory conditions with a set of differential-drive mobile robots operating in a leader–follower configuration, show the effectiveness of the proposed governing scheme in terms of trajectory tracking and disturbance rejection

Modelado y control de un sistema de levitación magnética basado en un cojinete magnético activo

Abstract In this paper, we present the design, modeling as well as the implementation of a magnetic levitation system, consisting on a single-degree of freedom pendular beam, which is driven by means of an active magnetic bearing. The analysis includes the state space representation and, after a tangent linearization process, its transfer function is obtained. In addition, the characteristics of the device such as the electronic instrumentation and mechanical design are described. In particular, it is shown the design procedure of the electromagnetic actuator used, as well as its characterization to determine the proportional constant of the electromagnetic force with respect to a current input. Finally, some numerical simulations and experimental results of the implementation of some classic controllers in stabilization task are shown.Resumen En este trabajo se presenta el diseño, modelado e implementación de un sistema de levitación magnética de un grado de libertad, que consiste en una viga actuada por un cojinete magnético activo en configuración pendular. Se obtiene su representación en espacio de estado y, tras una linealización tangente, su función de transferencia correspondiente. Se describen las características del dispositivo experimental, su instrumentación electrónica y mecanismo, particularmente el procedimiento de diseño del actuador electromagnético empleado, así como su caracterización para determinar la constante de proporcionalidad de la fuerza electromagnética. Finalmente, se muestra la simulación numérica e implementación experimental de esquemas clásicos de control para estabilizar en el punto de equilibrio del sistem

Robust flat filtering control of a two degrees of freedom helicopter subject to tail rotor disturbances

This article deals with modelling and a flatness-based robust trajectory tracking scheme for a two degrees of freedom helicopter, which is subject to four types of tail rotor disturbances to validate the control scheme robustness. A mathematical model of the system, its differential flatness and a differential parametrization are obtained. The flat filtering control is designed for the system control with a partially known model, assuming the non-modelled dynamics and the external disturbances (specially the tail rotor ones) to be rejected by means of an extended state model (ultra-local model). Numerical and experimental assessments are carried out on a characterized prototype whose yaw angle (ψ), given by the z axis, is in free form, while the pitch angle (θ), which results from rotation about the y axis, is mechanically restricted. The proposed controller performance is tested through a set of experiments in trajectory tracking tasks with different disturbances in the tail rotor, showing robust behaviour for the different disturbances. Besides, a comparison study against a widely used controller of LQR type is carried out, in which the proposed controller achieves better results, as illustrated by a performance index

Robust Flat Filtering Control of a Two Degrees of Freedom Helicopter Subject to Tail Rotor Disturbances

This article deals with modelling and a flatness-based robust trajectory tracking scheme for a two degrees of freedom helicopter, which is subject to four types of tail rotor disturbances to validate the control scheme robustness. A mathematical model of the system, its differential flatness and a differential parametrization are obtained. The flat filtering control is designed for the system control with a partially known model, assuming the non-modelled dynamics and the external disturbances (specially the tail rotor ones) to be rejected by means of an extended state model (ultra-local model). Numerical and experimental assessments are carried out on a characterized prototype whose yaw angle (ψ), given by the z axis, is in free form, while the pitch angle (θ), which results from rotation about the y axis, is mechanically restricted. The proposed controller performance is tested through a set of experiments in trajectory tracking tasks with different disturbances in the tail rotor, showing robust behaviour for the different disturbances. Besides, a comparison study against a widely used controller of LQR type is carried out, in which the proposed controller achieves better results, as illustrated by a performance index

Design Procedure of a Low-Cost System for Energy Replenishment in a Quadrotor UAV through a Battery Exchange Mechanism

This paper describes the design and construction of an energy replenishment service station for a quadrotor. The prototype includes a small number of actuators, making it a low-cost solution. The system consists of three batteries: two charged and one discharged (within the quadrotor). Once the quadrotor lands, the battery with the highest charge is selected, which is then exchanged for the discharged battery. In order to perform this action, position control is used, in which the desired value depends on the location of the sensor that detects the highest voltage. In addition, the system has a mechanical design that facilitates the coupling of the unmanned aerial vehicle (UAV) with the structure for battery exchange, ensuring that the discharged battery is always in the same position. Furthermore, the design of a mechanism to release and hold the battery placed in the quadrotor is presented, which works by means of voltage and force sensors that identify the instant that the battery is discharged and when the UAV has landed on the exchange platform, thus initiating the exchange process. Likewise, the criteria for selecting the elements used, acquiring and processing signals, and routines for changing batteries are detailed

Design Strategy for Low-Power Consumption in Solar Trackers

The new energy generation technologies that transform the solar energy, require a high accuracy for the tracking of the solar vector path, which increases the system energy consumption and reduces the entire system performance. From an optimization approach, a novel design strategy for low-power trackers is proposed, which consists of two main stages, a first for the physical tracker design optimization, and a second for the design of the tracker behavior. For the validation of the proposed design strategy, the implementation is presented through the development of a solar tracker prototype. For the implementation of the second stage, three Tracking Error Minimization Strategies (TEMS) are proposed (PI, GPI, and cascade control), and four Energy Saving Strategies (ESS) are proposed. The presented experimental results show that the saving energy strategy can reduce the energy consumption in up to 27.2771% in tracking tasks with an absolute maximum tracking error of 0.08°, and obtaining a low-power prototype tracker with 5.4749 Wh energy consumption. The proposed design strategy allows the design of solar trackers with a balance between the energy consumption and the tracking error

Adaptive Active Disturbance Rejection Control of Solar Tracking Systems with Partially Known Model

In this article, the trajectory tracking control of a solar tracking system is tackled by means of an adaptive active disturbance rejection control scheme. The state and disturbance estimation system is based on the combination of a time varying identification system and an adaptive observer. The stability and robustness of the controller is mathematically tested by means of the second method of Lyapunov, and its effectiveness is experimentally tested in a robotic test bed, achieving both lower energy consumption and better tracking results with respect to a PID-based controller

Position Measurements Using Magnetic Sensors for a Shape Memory Alloy Linear Actuator

This article presents the design and implementation of a linear actuator based on NiTi Shape Memory Alloys with temperature and position measurements based on a magnetic sensor array and a set of thermistors. The position instrumentation is contact free to avoid friction perturbations; the position signal conditioning is carried out through the calculation of the response of each magnetic sensor, selecting the closest sensor to ensure accurate results on the full range of movement. Experimental results validate the accuracy of the position sensing with a competitive behaviour