This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo system, having one, two, and three parameters, were experimentally identified using both the classic least squares and the least squares of orthogonal distances. The models with two and three parameters were identified through numerical routines. The servo system model with a single parameter only considered the input gain. In this particular case, the analytical conditions for finding the critical points and for determining the existence of a minimum were presented, and the estimate of the input gain was obtained by solving a simple quadratic equation whose coefficients depended on measured data. The results showed that as opposed to the least squares method, the least squares of orthogonal distances method experimentally produced consistent estimates without regard for the classic persistency-of-excitation condition. Moreover, the parameter estimates of the least squares of orthogonal distances method produced the best tracking performance when they were used to compute a trajectory-tracking controller.
La electrocoagulación (EC) es un proceso electroquímico para desestabilizar contaminantes presentes en el agua mediante la aplicación de energía eléctrica, a través de electrodos sumergidos en el agua. Uno de los factores que afectan el proceso de EC es el suministro de la energía eléctrica, ésta se cuantifica mediante la densidad de corriente, que relaciona la corriente aplicada y el área de los electrodos. Diferentes autores sugieren que, para obtener un mejor desempeño en el proceso de EC, la densidad de corriente se debe mantener constante. Sin embargo, debido a la variación en la resistividad del agua, existirán cambios en la densidad de corriente aplicada, disminuyendo la eficiencia de remoción de contaminantes. Con el objetivo de mantener constante a la tensión en una celda de electrocoagulación, este trabajo se presenta el modelado, diseño y simulación de controladores Proporcional Integral Derivativo (PID) y Proporcional Derivativo más un Observador Proporcional Integral Generalizado (PD+GPI por sus siglas en inglés) para la regulación de la tensión eléctrica en el proceso de electrocoagulación para el tratamiento de aguas grises mediante un convertidor CD-CD tipo Buck.
Electrocoagulation is an electrochemical process used to treat wastewater and water contaminated with heavy metals. This method destabilizes contaminants that are suspended, emulsified or dissolved in wastewater by applying electrical current through electrodes and then removing them by filtration. In this work we present a turbidity, dissolved oxygen and pH measurement system for the influent and effluent of the gray water treatment process by the electrocoagulation method. The treatment process is carried out via batch and the measurement system allows to know the initial and final levels of the variables through a human machine interface (HMI) designed in LabVIEW. Twelve experimental tests were performed varying the treatment time and applied voltage in the electrocoagulation process to analyze the rate of change of the measured variables and its behavior regarding time and voltage. The applied direct current voltages were 10 V, 15 V and 20 V during 30 min, 60 min, 90 min and 120 min.
This paper shows a proposal for a control scheme for the trajectory tracking problem in a Two Degree of Freedom Helicopter (2DOFH). For this purpose, a control scheme based on a feedback linearization combined with a Generalized Proportional Integral (GPI) controller is used. In order to implement linearization by feedback, it is required to know and have access to all the physical 2DOFH parameters, however, angular velocity and viscous friction are often not available. Commonly, state observers are used to know the angular velocity, however, estimating friction results out to be more complex. Therefore, we propose the use of a Convolutional Neural Network (CNN) to estimate viscous friction and angular velocity. The variables estimated by the CNN are entered into both the GPI and feedforward controllers. Thus, the system is brought to a linear representation that directly relates the GPI control to the dynamics of perturbations and non-model parameters. Finally, results of numerical simulations are shown that validate the robustness of our scheme in the presence of disturbances in the tail rotor, as well as the advantages of using a feedforward control based on a CNN. INDEX TERMSFriction estimation, Neural networks, Non-linear system, Tail rotor disturbance, Two degrees of freedom helicopter. Hence, different experimental prototypes have been developed to study helicopter dynamics [13]-[15]. One of the most popular consists of a Two Degree of Freedom Helicopter (2DOFH), which recreates the dynamic behavior of the helicopter in its pitch (θ) and yaw (ψ) rotations [15], [16].
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