Alberto Luviano-Juárez

Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum.

An Active Disturbance Rejection Control (ADRC) scheme is proposed for a trajectory tracking problem defined on a nonfeedback linearizable Furuta Pendulum example. A desired rest to rest angular position reference trajectory is to be tracked by the horizontal arm while the unactuated vertical pendulum arm stays around its unstable vertical position without falling down during the entire maneuver and long after it concludes. A linear observer-based linear controller of the ADRC type is designed on the basis of the flat tangent linearization of the system around an arbitrary equilibrium. The advantageous combination of flatness and the ADRC method makes it possible to on-line estimate and cancels the undesirable effects of the higher order nonlinearities disregarded by the linearization. These effects are triggered by fast horizontal arm tracking maneuvers driving the pendulum substantially away from the initial equilibrium point. Convincing experimental results, including a comparative test with a sliding mode controller, are presented.

A Robust Linear Field-Oriented Voltage Control for the Induction Motor: Experimental Results

A field-oriented armature-input-voltage output-feedback control approach is proposed for the robust linear controller design on an induction motor. The scheme simultaneously solves an angular-velocity reference-trajectory tracking task and a flux magnitude regulation in the presence of arbitrary time-varying load torques and unknown nonlinearities. The field-oriented input-voltage scheme is combined with linear high-gain asymptotic observers, of the generalized proportional-integral type, and linear active-disturbance-rejection output-feedback controllers. The linear observers online estimate, in a simultaneous manner, the output phase variables and the lumped effects of the following: 1) unknown time-varying load torques and unmodeled frictions and 2) rather complex state-dependent nonlinearities present in the electric and magnetic circuits. The field-oriented part of the scheme uses the classical flux observer or simulator. The proposed control laws naturally decouple, while linearizing, the extended second-order dynamics for the angular velocity and the squared flux magnitude. The proposed control scheme is here tested on an experimental induction motor setup.

SYNCHRONIZATION OF CHAOTIC OSCILLATORS BY MEANS OF GENERALIZED PROPORTIONAL INTEGRAL OBSERVERS

The problem of synchronization of chaotic oscillators, using state observers, is handled through the use of a simplified perturbed linear integration model of the chaotic system output dynamics. The linear simplified model of the chaotic system does not entitle approximate linearizations, nor state coordinate transformations, but, simply, a pure linear integration model with additive unknown but bounded perturbation inputs lumping all the output dynamics nonlinearities. An extended linear state observer (here addressed as Generalized Proportional Integral (GPI) observer) is proposed for the accurate estimation of the phase variables and the perturbation input of the nonlinear output dynamics. The effectiveness of the approach is tested in the synchronization of two study cases: The Genesio–Tesi chaotic system and the Rossler oscillator. As an application of the estimation process, a coding–decoding process involving encrypted messages, in transmitted phase variables, is implemented using a Rossler chaotic system.

Algebraic Identification and Estimation Methods in Feedback Control Systems: Sira-Ramírez/Algebraic Identification and Estimation Methods in Feedback Control Systems

Algebraic Identification and Estimation Methods in Feedback Control Systems presents a model-based algebraic approach to online parameter and state estimation in uncertain dynamic feedback control systems. This approach evades the mathematical intricacies of the traditional stochastic approach, proposing a direct model-based scheme with several easy-to-implement computational advantages. The approach can be used with continuous and discrete, linear and nonlinear, mono-variable and multi-variable systems. The estimators based on this approach are not of asymptotic nature, and do not require any statistical knowledge of the corrupting noises to achieve good performance in a noisy environment. These estimators are fast, robust to structured perturbations, and easy to combine with classical or sophisticated control laws.This book uses module theory, differential algebra, and operational calculus in an easy-to-understand manner and also details how to apply these in the context of feedback control systems. A wide variety of examples, including mechanical systems, power converters, electric motors, and chaotic systems, are also included to illustrate the algebraic methodology.Key features:Presents a radically new approach to online parameter and state estimation.Enables the reader to master the use and understand the consequences of the highly theoretical differential algebraic viewpoint in control systems theory.Includes examples in a variety of physical applications with experimental results.Covers the latest developments and applications.Algebraic Identification and Estimation Methods in Feedback Control Systems is a comprehensive reference for researchers and practitioners working in the area of automatic control, and is also a useful source of information for graduate and undergraduate students.

Robust Trajectory Tracking of a Delta Robot Through Adaptive Active Disturbance Rejection Control

This paper describes the adaptive control design to solve the trajectory tracking problem of a Delta robot with uncertain dynamical model. This robot is a fully actuated, parallel closed-chain device. The output-based adaptive control was designed within the active disturbance rejection framework. An adaptive nonparametric representation for the uncertain section of the robot model was obtained using an adaptive least mean squares procedure. The adaptive algorithm was designed without considering the velocity measurements of the robot joints. Therefore, a simultaneous observer-identifier scheme was the core of the control design. A set of experimental tests were developed to prove the performance of the algorithm presented in this paper. Some reference trajectories were proposed which were successfully tracked by the robot. In all the experiments, the adaptive scheme showed a better performance than the regular proportional-integral-derivative (PID) controller with feed-forward actions as well as a nonadaptive active disturbance rejection controller. A set of numerical simulations was developed to show that even under five times faster reference trajectories, the adaptive controller showed better results than the PID controller.

Robust GPI controller for trajectory tracking for induction motors

In this article, we propose a field oriented control scheme of two stages. The first stage keeps the tracking of the angular velocity and simultaneously, regulates the flux modulus by means of the stator currents. These designed current signals are used as reference trajectories for the second stage. Both stages use observer based controllers of Generalized Proportional Integral (GPI) nature. The trajectory tracking task is defined on the angular velocity of a complete model of an induction motor subject to a completely unknown, but bounded, load torque perturbation input. The robustness is tested under deviation of system parameter, additive unknown perturbations and high frequency measurement noises in the closed loop system. A numerical simulation verifies the effectiveness of the proposed scheme.

Diagnosis for a class of non-differentially flat and Liouvillian systems

In this chapter, we tackle the diagnosis problem for non-differentially flat and Liouvillian systems by using the concept of differential transcendence degree of a differential field extension, as well as, we consider the algebraic observability concept of the variable which models the failure presence for the solvability of the diagnosis problem. The construction of a reduced-order uncertainty observer to estimate the fault variable is the main ingredient in our approach. Finally, we present a simulation example dealing with a ship in smooth landing to illustrate the effectiveness of the suggested approach.

Control lineal robusto de sistemas no lineales diferencialmente planos

In this arcicle, a linear observer-linear controller approach is proposed for the robust trajectory tracking task in a large class of nonlinear differentially flat systems, including multi-variable nonlinear flat systems. A non-phenomenological model of the input-to-flat-output dynamics is proposed which only retains the orders of the Kronecker integration subsystems and, the control input gain matrix, as key controller design elements. The additive influence of the rest of the nonlinear state dependent dynamics, including exogenous unknown perturbation inputs, is considered as unknown but uniformly absolutely bounded disturbance that is shown to be algebraically observable and it can, hence, be approximately determined, to any desired degree of accuracy, by means of a set of linear observers with suitable, self-updating, time-polynomial internal models of the unknown disturbances. The controller design task is reduced to that of canceling the additive disturbances while imposing a desired linear dynamics, via estimated state feedback, obtained from the proposed observer itself. A convincing simulation example dealing with rather complex nonlinear physical system is provided. Two experimental implementations on laboratory prototype systems are also reported.

Algebraic parameter identification for induction motors

In this article, we propose a fast, on-line, algebraic identification scheme for the determination of some relevant induction motor parameters. The estimated values, given by the algebraic identification methodology, are here tested in a self-tuning output feedback control, subject to constant perturbation load torques while solving a reference trajectory tracking task. An output feedback controller of the classical, Field Oriented, Proportional Integral (PI) type, is proposed for the perturbed output trajectory tracking problem. Experimental results validate the effectiveness of the proposed approach.

Robust disturbance rejection control of a biped robotic system using high-order extended state observer☆

This study addressed the problem of robust control of a biped robot based on disturbance estimation. Active disturbance rejection control was the paradigm used for controlling the biped robot by direct active estimation. A robust controller was developed to implement disturbance cancelation based on a linear extended state observer of high gain class. A robust high-gain scheme was proposed for developing a state estimator of the biped robot despite poor knowledge of the plant and the presence of uncertainties. The estimated states provided by the state estimator were used to implement a feedback controller that was effective in actively rejecting the perturbations as well as forcing the trajectory tracking error to within a small vicinity of the origin. The theoretical convergence of the tracking error was proven using the Lyapunov theory. The controller was implemented by numerical simulations that showed the convergence of the tracking error. A comparison with a high-order sliding-mode-observer-based controller confirmed the superior performance of the controller using the robust observer introduced in this study. Finally, the proposed controller was implemented on an actual biped robot using an embedded hardware-in-the-loop strategy.