Hebertt Sira-Ramírez

Differentially flat systems

Introduction Linear Time-Invariant SISO Systems Linear Time-Invariant MIMO Systems Time-Varying Linear Systems Discrete-Time Linear Systems Infinite Dimensional Linear Systems SISO Nonlinear Systems Multivariable Nonlinear Systems Mobile Robots Flatness and Optimal Trajectories Optimal Planning with Constraints Non-Differentially Flat Systems

Non-linear estimation is easy

Non-linear state estimation and some related topics like parametric estimation, fault diagnosis and perturbation attenuation are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with online estimations, illustrate our viewpoint.

On the dynamical sliding mode control of nonlinear systems

The consequences of the differential algebraic approach in the sliding mode control of nonlinear single-input single-output systems are reviewed in tutorial fashion. Input-dependent sliding surfaces, possibly including time derivatives of the input signal, are shown to arise naturally from elementary differential algebraic results pertaining to the Fliesss Generalized Controller Canonical Forms of nonlinear systems. This class of switching surfaces generally leads to chattering-free dynamically synthesized sliding regimes, in which the highest time derivative of the input signal undergoes all the bang-bang type discontinuities. Examples illustrating the obtained results are also included.

Differential geometric methods in variable-structure control

This article presents a differential geometric approach for the design of sliding modes in non-linear variable-structure feedback systems. Coordinate-free characterizations of local existence conditions for sliding regimes, and a geometric reformulation of some of its most salient features are presented. The approach uses basic notions from differential geometry involving vector fields, distributions and 1-forms. Both single- and multiple-input cases are treated with some illustrative examples.

Non-linear discrete variable structure systems in quasi-sliding mode

Abstract The problem of inducing convergent quasi-sliding regimes on smooth state-space surfaces of non-linear single-input single output discrete-time controlled systems is addressed in full generality. A suitable extension of the notion of relative degree is used in establishing the most salient features of quasi-sliding motions in non-linearly controlled systems. Several examples are given.

Sliding mode control of DC-to-DC power converters via extended linearization

The method of extended linearization is proposed for the systematic solution of sliding mode controller design in DC-to-DC power converters of the boost and the buck-boost type. A nonlinear sliding surface with suitable stabilizing properties is synthesized on the basis of the extension of a linear sliding design carried out for the parametrized average linear incremental model of the converter. The obtained feedback strategies lead to asymptotically stable sliding modes with remarkable self-scheduling properties. Simulation examples are presented for illustrative purposes. >

SYNCHRONIZATION OF CHAOTIC SYSTEMS: A GENERALIZED HAMILTONIAN SYSTEMS APPROACH

A reapproach to chaotic systems synchronization is presented from the perspective of passivity-based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector fields. The synchronization and lack of synchronization of several well-studied chaotic systems is reexplained in these terms.

Closed-loop Parametric Identification for Continuous-time Linear Systems via New Algebraic Techniques

A few years ago the present authors launched a new approach to parametric identification of linear continuous-time systems [11]. Its main features may be summarised as follows: closed-loop identification is permitted thanks to the real-time identification scheme; the robustness with respect to noisy data is obtained without knowing the statistical properties of the corrupting noises.

On Some Nonlinear Current Controllers for Three-Phase Boost Rectifiers

Several flatness-based current controllers for three-phase three-wire boost rectifiers are compared. For this purpose, the flatness of a rectifier model is shown, and a trajectory planning algorithm that nominally achieves voltage regulation in finite time is given. The main focus lies on the inner loop current controllers. On one hand, linearization-based controllers using exact feedback linearization, exact feedforward linearization, and input-output linearization are discussed. On the other hand, two passivity-based approaches are compared. The first one is the energy shaping and damping injection method, and the other one uses exact tracking error dynamics passive output feedback. Furthermore, a reduced-order load observer is given, and a method that allows the prevention of invalid switching patterns is presented. The presented control algorithms are tested by simulations on a switched model.

On the Control of the Permanent Magnet Synchronous Motor: An Active Disturbance Rejection Control Approach

This brief presents an active disturbance rejection control scheme for the angular velocity trajectory tracking task on a substantially perturbed, uncertain, and permanent magnet synchronous motor. The presence of unknown, time varying, and load-torque inputs, unknown system parameters, and the lack of knowledge of the initial shafts angular position, prompts a high-gain generalized proportional integral (GPI) observer-based active disturbance rejection (ADR) controller. This controller is synthesized on the basis of the differential flatness of the system and the direct measurability of the systems flat outputs, constituted by the motors angular displacement and the d-axis current. As a departure from many previous treatments, the d-q-axis currents model is here computed on the basis of the measured displacement and not on the basis of the unknown position. The proposed high-gain GPI observer-based ADR controller is justified in terms of a singular perturbation approach. The validity and robustness of the scheme are verified by means of realistic computer simulations, using the MATLAB/SIMULINK-PSIM package.