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     

Robust flat filtering DSP based control of the boost converter

The article deals with the design and implementation of a flat filter tracking digital controller for a boost dc-dc power converter. A highly perturbed switched boost converter circuit is shown to be efficiently controlled, in a trajectory tracking task for its non-minimum phase output, by means of a suitable linear filter, here addressed as a flat filter. Flat filtering is a natural robust version of generalized proportional integral control (GPIC) by which the effects of arbitrary time varying exogenous disturbances, unknown endogenous nonlinearities and un-modeled dynamics can be jointly attenuated in a conceptually similar fashion to observer-based active disturbance rejection control (ADRC) and algebraic identification based model free control (MFC) but: a) without using extended state observers and b) respecting the original system order in a time-varying simplified model while avoiding algebraic estimation techniques. The proposed control technique based on the TMS320F28335 digital signal processor chip is tested by means of realistic simulations and experimental setup.     

Robust sigma–delta generalised proportional integral observer based control of a ‘buck’ converter with uncertain loads

This article describes the design of an observer based robust linear output feedback controller for the regulation and output reference trajectory tracking tasks in switched ‘buck’ converter circuits feeding a completely unknown time-varying load. The state-dependent perturbation effects of the unknown load resistance are on-line estimated by means of a generalised proportional integral (GPI) observer, which represents the dual counterpart of GPI controllers introduced in Fliess, Márquez, Delaleau and Sira-Ramírez (Fliess, M., Márquez, R., Delaleau, E., and Sira-Ramírez, H. (2002), ‘Correcteurs Proportionnels-intégraux Géneralisés’, ESAIM: Control, Optimisation and Calculus of Variations, 7, 23–41). The reconstructed perturbation complements the controller in a cancellation effort which allows the core of the feedback controller to become a traditional proportional derivative (PD) controller. The designed average feedback controller is then implemented via a sigma–delta-modulator, which effectively translates the designed continuous average feedback control input signal into a discrete valued switched input signal driving the converter's input switch and preserving all relevant features of the average design. The Appendix collects some generalities about GPI observers.     

Robust residual generation for linear fault diagnosis: an algebraic setting with examples

We are generating residuals for linear fault diagnosis and isolation which are 1. robust with respect to a large variety of additive disturbances,

2. working in closed-loop, even with uncertain parameters.

Several examples with their computer simulations, including a concrete case-study of a two mass system, are enlightening our viewpoint. Our methods, which are mainly of algebraic flavour (module theory, differential algebra, and operational calculus), are borrowed from recent works on control and identification.     

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     

ADAPTIVE DYNAMICAL INPUT–OUTPUT LINEARIZATION OF DC TO DC POWER CONVERTERS: A BACKSTEPPING APPROACH

Dynamical adaptive regulation of pulse-width-modulation (PWM) controlled power supplies is proposed using a suitable combination of average dynamical input–output linearization and the ‘backstepping’ controller design method. Nonlinear average models of dc to dc power supplies are not transformable to parametric pure nor parametric strict feedback canonical forms by means of parameter-independent state co-ordinate transformation. A more direct approach is therefore proposed for implementing the fundamental ideas related to the so called ‘non-overparametrized’ adaptive backstepping algorithm which avoids explicit transformations to the above mentioned canonical forms. Dynamical adaptive feedback controllers are developed for the regulation of the input-inductor current towards desirable constant values. The validity of the proposed approach, regarding control objectives and robustness with respect to unmodelled, yet unmatched, and bounded stochastic perturbation inputs, is tested through digital computer simulations. © 1997 by John Wiley & Sons, Ltd.     

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     

Stability of active disturbance rejection control for uncertain systems: A Lyapunov perspective

In this work, we introduce a simple stability analysis to justify, under some suitable assumptions, the active disturbance rejection control method, used in the feedback regulation of a substantially uncertain plant. A criterion is obtained that allows us to define under what conditions closed‐loop stability can be assured. When the plant is mostly unknown, the criterion allows us to guarantee exponential convergence for the output‐feedback regulation problem, in the presence of a constant external perturbation, and practical stability when the external perturbation and the tracking reference signal are both time‐varying. In the latter case, the confinement error can be made as small as desired. To carry out the corresponding stability analysis, we derive the tracking error equation, and the observation error equation. To decouple these error equations, we use the Sylvester equation. Finally, we applied the direct Lyapunov method to analyze the corresponding convergence of the observation error and of the tracking error. Copyright © 2017 John Wiley & Sons, Ltd.