Carlos Aguilar-Ibañez

The trajectory tracking problem for an unmanned four-rotor system: flatness-based approach

In this article we present a flatness-based controller that solves the trajectory tracking problem for an unmanned four-rotor aircraft. A simple version of the dynamical system obtained from a suitable coordinate transformation of the Euler–Lagrange model of the system is used. This model, combined with a suitable input saturation nonlinearity, also avoids the inconvenient system singularities. The corresponding tracking error is shown to be globally asymptotically stable but only locally exponentially stable, while the controller maintains the four-rotor system motions inside a feasible region. Numerical simulations are presented to assesses the effectiveness of the proposed control strategy.

Stable optimal control applied to a cylindrical robotic arm

In this paper, an asymptotically stable optimal control is proposed for the trajectory tracking of a cylindrical robotic arm. The proposed controller uses the linear quadratic regulator method and its Riccati equation is considered as an adaptive function. The tracking error of the proposed controller is guaranteed to be asymptotically stable. A simulation shows the effectiveness of the proposed algorithm.

The Lyapunov direct method for the stabilisation of the ball on the actuated beam

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A linear differential flatness approach to controlling the Furuta pendulum

The aim of this work is to motivate the use of linear flatness, or controllability, to design a feedback control law for the rather challenging mechanism known as the ‘Furuta pendulum’. This is achieved by introducing three feedback controller design options for the stabilization and rest-to-rest trajectory tracking tasks: a direct pole placement approach, a hierarchical high-gain approach and a generalized proportional integral approach synthesized on the basis of measured inputs and outputs.

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.

The direct Lyapunov method for the stabilisation of the Furuta pendulum

A nonlinear controller for the stabilisation of the Furuta pendulum is presented. The control strategy is based on a partial feedback linearisation. In a first stage only the actuated coordinate of the Furuta pendulum is linearised. Then, the stabilising feedback controller is obtained by applying the Lyapunov direct method. That is, using this method we prove local asymptotic stability and demonstrate that the closed-loop system has a large region of attraction. The stability analysis is carried out by means of LaSalles invariance principle. To assess the controller effectiveness, the results of the corresponding numerical simulations are presented.

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction.

Control of the Furuta Pendulum by using a Lyapunov function

A Lyapunov based control approach is proposed for the stabilization of the under actuated Furuta pendulum. First, by a suitable partial feedback linearization that allows to linearize only the actuated coordinate of the system, it proceeds to find a candidate Lyapunov function, and them, a stabilizing controller is derived from the obtained candidate function. The proposed closed-loop system is locally and asymptotically stable around the unstable vertical equilibrium rest, with a computable domain of attraction

Dual PD Control Regulation with Nonlinear Compensation for a Ball and Plate System

The normal proportional derivative (PD) control is modified to a new dual form for the regulation of a ball and plate system. First, to analyze this controller, a novel complete nonlinear model of the ball and plate system is obtained. Second, an asymptotic stable dual PD control with a nonlinear compensation is developed. Finally, the experimental results of ball and plate system are provided to verify the effectiveness of the proposed methodology.

CONTROL OF THE CHUA'S SYSTEM BASED ON A DIFFERENTIAL FLATNESS APPROACH

In this paper, we present a flatness based control approach for the stabilization and tracking problem, for the well-known Chua chaotic circuit, that includes an additional input. We introduce two feedback controller design options for the set-point stabilization and the trajectory tracking problem: a direct pole placement approach, and Generalized Proportional Integral (GPI) approach based only on measured inputs and outputs.