Stability analysis of the extended state observers by Popov criterion

AbstractThe analysis and design of the extended state observer (ESO) involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper establishes the sufficient conditions for absolute stability of the ESO. Based on this study, a methodology to estimate several nonlinear functions in dynamics systems is proposed

Controlling a DC Motor through Lypaunov-like Functions and SAB Technique

In this paper, state adaptive backstepping and Lyapunov-like function methods are used to design a robust adaptive controller for a DC motor. The output to be controlled is the motor speed. It is assumed that the load torque and inertia moment exhibit unknown but bounded time-varying behavior, and that the measurement of the motor speed and motor current are corrupted by noise. The controller is implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform and experimental results agree with theory

Two-Valued Control for a Second-Order Plant with Additive External Disturbance

In this work a two-valued state feedback control for a plant of second order with known constant coefficients and an additive bounded disturbance is designed. In this controller the control signal can take only two possible values. The controller design is based on Lyapunov-like function method, achieving the convergence of the tracking error to a user-defined residual set. A boundedness condition for the user-defined reference signal is defined, which is necessary to allow out-put tracking. The developed scheme avoids large commutation rate of the control input. The controller design and stability analysis have important contributions with respect to closely related controllers based on the direct Lyapunov method, namely, (i) conditions to guarantee the expected convergence of the tracking error are established. These conditions are imposed on the reference signal and the extreme values of the control input. The stability analysis is developed by means of the Lyapunov-like function method and the Barbalat's Lemma and includes (ii) the bounded nature of the Lyapunov function, (iii) the monotonic convergence of the Lyapunov function to a residual set, and (iv) the asymptotic convergence of the tracking error to a residual set of user-defined size

Técnica ZAD aplicada a un convertidor "buck": análisis de estabilidad y de transición al caos

En este trabajo se presentan algunos resultados obtenidos al analizar el convertidor buck controlado mediante un modulador de anchura de pulsos (PWM) centrado. El ciclo de trabajo se calcula obligando a que una salida, definida como una ecuación diferencial de primer orden en el error de tensión, tenga promedio cero en cada ciclo. Los resultados obtenidos han mostrado que la técnica garantiza frecuencia de conmutación fija y una variedad de fenómenos no lineales como bifurcaciones y caos, en la medida en que el parámetro asociado a la dinámica de primer orden, varía. Estos fenómenos han sido estudiados en el presente trabajo de forma analítica y numérica. Finalmente a nivel de simulación se ha hecho uso de la técnica Time Delay Auto Synchronization para controlar el sistema.Peer Reviewe

Estudio de factibilidad para la creación de una institución educativa para el trabajo y desarrollo humano afro

174 Páginas.​Este proyecto recoge las necesidades de los residentes afro y desplazados del barrio Britalia, es así como nace la Fundación Forfuturo como institución educativa para el Trabajo y Desarrollo Humano, con la intencionalidad de ofrecerles capacitación en gastronomía y belleza enfocados en la cultura, costumbres e identidad afro; programas al alcance de sus capacidades económicas y con los cuales obtendrán el título de Técnico Laboral por competencias en Gastronomía y Técnico Laboral por competencias en cuidado de manos y pies, peluquería y maquillaje, con los cuales podrán acceder a un empleo en el sector y así mejorar su calidad de vida. ​

Bounding the output error in a buck power converter using perturbation theory

We show the main results obtained when applying the average theory to Zero Average Dynamic control technique in a buck power converter with pulse-width modulation (PWM). In particular, we have obtained the bound values for output error and sliding surface. The PWM with centered and lateral pulse configurations were analyzed. The analytical results have confirmed the numerical and experimental results already obtained in previous publications. Moreover, through an important lemma, we have generalized the theory for any stable second-order system with relative degree 2, using properties related to transformations and stability of linear systems.Peer Reviewe

Controller Design for a Second-Order Plant with Uncertain Parameters and Disturbance: Application to a DC Motor

This paper shows the controller design for a second-order plant with unknown varying behavior in the parameters and in the disturbance. The state adaptive backstepping technique is used as control framework, but important modifications are introduced. The controller design achieves mainly the following two benefits: upper or lower bounds of the time-varying parameters of the model are not required, and the formulation of the control and update laws and stability analysis are simpler than closely related works that use the Nussbaum gain method. The controller has been developed and tested for a DC motor speed control and it has been implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform. The motor speed converges to a predefined desired output signal

Performance Analysis of a Peak-Current Mode Control with Compensation Ramp for a Boost-Flyback Power Converter

High voltage gain power converters are very important in photovoltaic applications mainly due to the low output voltage of photovoltaic arrays. This kind of power converters includes three or more semiconductor devices and four or more energy storage elements, making the dynamical analysis of the controlled system more difficult. In this paper, the boost-flyback power converter is controlled by peak-current mode with compensation ramp. The closed-loop analysis is performed to guarantee operation conditions such that a period-1 orbit is attained. The converter is considered as a piecewise linear system, and the closed-loop stability is determined by using the monodromy matrix, obtained by the composition of the saltation matrixes with the solutions of the dynamical equations in the linear intervals. The largest eigenvalue of the monodromy matrix gives the stability of the period-1 orbit, and a deep analysis using bifurcation diagrams let us reach a conclusion about the loss of the stability, which is experimentally verified. To avoid overcompensation effects, the minimum value required by the compensation ramp is obtained, and the minimum and maximum values of the load resistance are found too. The system has a good transient response under disturbances in the load and in the input voltage