Synthesis of sliding-mode controllers for nonlinear systems via extended linearization

In this article, a general synthesis method is proposed for the design of discontinuous feedback strategies leading to asymptotically stabilizing sliding regimes. The method is applicable to the class of nonlinear dynamical systems possessing constant equilibrium points. A family of nonlinear stabilizing sliding manifolds, parametrized by generic desired equilibrium point, is specified on the basis of the extended linearization approach. Some examples including simulations are presented for illustrative purposes. Editor: S. Zak     

A geometric approach to pulse-width modulated control in nonlineardynamical systems

The author demonstrates, under the assumption of high-frequency control switchings, the existence of an ideal equivalence among sliding regimes of variable-structure feedback control and pulse-width-modulated (PWM) control responses in nonlinear dynamical systems. This equivalence constitutes the basis for a geometric approach approach to PWM control loops design. An illustrate example of energy conversion in a lossless switched-controlled bilinear network is presented     

A dynamical variable structure control strategy in asymptoticoutput tracking problems

A dynamical discontinuous feedback strategy of the sliding mode type is presented for asymptotic output tracking problems in nonlinear dynamical systems. N. Fliess' (1989, 1990) generalized observability canonical form (GOCF) is used in the derivation of the dynamical variable structure feedback controller. For a large class of nonlinear systems, a truly effective smoothing of the sliding mode controlled responses is possible, while substantially reducing the chattering for the control output. For this reason, the technique is especially suitable for the control of some mechanical and electromechanical systems. An example, including simulations, is provided     

Nonlinear feedback regulator design for the Cuk converter

The method of extended linearization is used for designing stabilizing nonlinear proportional-integral (PI) feedback controllers which regulate to a constant set-point value either the average output inductor current, the average input inductor current, or the average transfer capacitor voltage of a pulse width modulation (PWM) controlled Cuk converter. The design is carried out on the basis of the frequency-domain Ziegler-Nichols method, applied to a family of transfer function models of the linearized average PWM controlled circuit, parametrized by constant operating equilibrium points     

Periodic sliding motions

A general geometric characterization is given for the global existence of sliding regimes, on compact manifolds, in nonlinear variable structure feedback systems. The characterization involves a set-theoretic inclusion condition to be satisfied by the control-dependent flow map acting on the compact region contained by the sliding manifold. A sign condition is derived on the volume integral of the divergence of the generating controlled vector field. The condition is a necessary, but not sufficient, condition for the existence of a sliding regime. The manifold invariance conditions, or ideal sliding conditions, are characterized in terms of volume-preserving evolution of the flow map associated with the sliding dynamics. An application of the general results to periodic sliding motions in R² was illustrated using some simple examples     

Flatness-based approach for the manipulation of a microscopic particle by optical tweezers

Based on the fact that optical tweezers (OT) constitute a flat system, with flat outputs given by the horizontal and vertical position coordinates of the geometric centre of the laser beam, a flatness-based control strategy for the manipulation of a microscopical particle is presented in this article. The control strategy is derived under the assumption that the particle is suspended in a frictionless medium, obtaining a simple controller with a relatively simple stability analysis. The control strategy is tested by tracking a straight line, an elliptic curve, and carrying out the rest-to-rest transfer manoeuvre task by using a smooth trajectory.     

The differential algebraic approach in nonlinear dynamical feedbackcontrolled landing maneuvers

A differential algebraic approach is proposed for the synthesis of a dynamical feedback controller regulating a spacecraft smooth descent toward the surface of a planet which exhibits nonnegligible atmospheric resistance. An exact linearization-based controller is synthesized using Fliess' generalized observability canonical form of the controller system. The smooth controlled trajectory is regulated by means of assumed amplitude modulated thrusting capabilities of the spacecraft. The robustness of the regulator is tested in the presence of significant unmodelled spatial changes in the coefficient of atmospheric resistance. A simulation example is provided     

Nonlinear variable structure systems in sliding mode: the generalcase

The problem of inducing local sliding regimes on smooth state-space surfaces of nonlinear single-input-single-output controlled systems is addressed in full generality. The notion of relative degree, in its more general form, is used to establish the most salient features of nonlinear controlled systems undergoing sliding motions, including their characteristic disturbance rejection properties. It is shown that the simplest possible structure at infinity must be exhibited by nonlinear systems undergoing sliding motions on the zero level set of the output feedback function     

Adaptive Controller for Single-Link Flexible Manipulators Based on Algebraic Identification and Generalized Proportional Integral Control

In this paper, we propose a fast online closed-loop identification method combined with an output-feedback controller of the generalized proportional integral (GPI) type for the control of an uncertain flexible robotic arm with unknown mass at the tip, including a Coulomb friction term in the motor dynamics. A fast nonasymptotic algebraic identification method developed in continuous time is used to identify the unknown system parameter and update the designed certainty equivalence GPI controller. In order to verify this method, several informative simulations and experiments are shown.     

Static and dynamic sliding mode control schemes for a permanent magnet stepper motor

In this paper, the sliding mode control of a permanent magnet (PM) stepper motor is addressed from the perspective of differentially flat systems. Flat systems naturally allow for de-coupled linearization directly leading to static and dynamic discontinuous feedback control alternatives. Implementation results of the proposed sliding mode control schemes on an experimental set-up are given to illustrate the developments.