Rubén Garrido-Moctezuma

Output feedback trajectory stabilization of the uncertainty DC servomechanism system

This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.

Improved MPPT adaptive incremental conductance algorithm

In this work we study a new Improved Adaptive Incremental Conductance (IAIC) algorithm proposed originally by A. Morales-Acevedo for maximum power point tracking (MPPT). The maximum power point is searched by means of an adaptive correction of the DC-DC converter duty cycle which is determined by the sum of the incremental and the instantaneous conductance at a given time. The operating principle is first presented and then the performance evaluation is made using a MATLAB/SEVIULINK model of a photovoltaic system to be connected to the grid. This new algorithm helps in reducing possible power over-impulses during solar radiation transient periods. In addition, it has a good behavior under steady state conditions because oscillations around the maximum power point are reduced. The IAIC algorithm is also better than the conventional adaptive incremental conductance (AIC) algorithm since the MPPT tracking efficiency is higher for the former than for the latter. The IAIC algorithm is highly efficient (above 99.6%), it is simpler than the AIC algorithm and it can be implemented easily using a low cost micro-controller.

On the linear active disturbance rejection control of the Furuta pendulum

This article studies, an Active Disturbance Rejection Control scheme, using a Generalized PI disturbance observer based control applied to the stabilization problem of the Furuta pendulum. The control scheme assumes a limited knowledge of the system and uses a simplified model of the Furuta pendulum modeled as a disturbed chain of two integrators. The control scheme is experimentally tested, showing good performance. A comparison study with respect to a linear control scheme is also carried out.

Active disturbance rejection control of singular differentially flat systems

A possible limitation of differentially flat systems stems from the possibility of gain singularities on open or closed regions of the flat output phase space. The evasion of control gain singularity poses an important theoretical problem even under the scope of Active Disturbance Rejection Control. In this article, we illustrate an interesting example of controlling a singular flat system, the inertia wheel pendulum, using the combined benefits of ADR control and flatness as applied to a carefully chosen flat tangent linearization model of the singular system.

On the linear Active Disturbance Rejection Control of the inertia wheel pendulum

In this article, an Active Disturbance Rejection Control (ADRC) scheme, using a Generalized PI disturbance observer based control is applied to the stabilization problem of the Inertia wheel pendulum. The control scheme assumes a limited knowledge of the underactuated system and relies on a simplified model regarded as a perturbed chain of two integrators with a stable zero dynamics. The control scheme is experimentally tested, showing good performance. A comparison study with respect to a linear control scheme is also carried out.

Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case

This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass. The motion of the inverted pendulum is restricted to an admissible set. The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), exerting a force on the radially moving mass. The controller design procedure, which follows a traditional Lyapunov-based approach, tailors the energy behavior of the system described in Euler-Lagrange terms.

Linear robust Generalized Proportional Integral Control of a ball and beam system for trajectory tracking tasks

In this article, the ball and beam trajectory tracking problem is tackled using a robust Generalized Proportional Integral (GPI) Controller. The controller is developed on the basis of the tangent linearized system model around the equilibrium point. The approximate linearized system is differentially flat, and hence, controllable. Flatness reveals that the resulting linearized system has an interesting cascade property which allows the simplification of the controller design. Experimental results are included to show the effectiveness of the controller in trajectory tracking and disturbance rejection control.

Flat filtering: A classical approach to robust control of nonlinear systems

Flat filtering constitutes a reinterpretation of Generalized Proportional Integral Control (GPIC) in the form of robust Classical Compensation Networks (CCN). Roughly speaking, any linear controllable system can be output regulated with the help of a well tuned filter and a suitable cascaded linear combinations of the internal states of such filter. Here, it is shown that such classical tool is also capable of efficiently handling control tasks on perturbed nonlinear systems, including unknown nonlinearities and un-modeled dynamics.

Stabilization on a Physical Pendulum with Moving Mass

An asymptotic PD controller with gravity compensation to attenuate the oscillation of a poorly damping physical pendulum system is presented. The active vibration-damping element is a mass that moves along the pendulum arm. The stability analysis was carried out using the traditionally Lyapunov method in conjunction with LaSalle’s theorem. The closed-loop asymptotic stability performance was tested with some numerical simulations.