Antonio Estrada

Integral Sliding Mode Control for Nonlinear Systems With Matched and Unmatched Perturbations

We consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state-dependent drift and input matrix. The general case of both, matched and unmatched disturbances affecting the system is addressed. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms, which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified. A simulation of the proposed technique, applied to a dynamically feedback linearized unicycle, illustrates its effectiveness, even in presence of nonholonomic constraints.

Technical communique: Quasi-continuous HOSM control for systems with unmatched perturbations

The control of nonlinear systems subject to unmatched perturbations is studied. A new design algorithm is proposed in this paper. This control scheme is based on the block control and quasi-continuous HOSM techniques. The proposed method provides for the finite time exact tracking of the desired signal in spite of unmatched perturbations. The proposed control design is tested in a simulation example.

Integral HOSM Semiglobal Controller for Finite-Time Exact Compensation of Unmatched Perturbations

The present technical note studies a class of nonlinear systems with unmatched perturbations. The combination of integral high-order sliding modes with the hierarchical quasi-continuous controller is proposed allowing finite-time exact compensation of unmatched perturbations with semiglobal convergence features for both regulation and tracking.

Global and exact HOSM differentiator with dynamic gains for output-feedback sliding mode control

In this paper we introduce a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains to solve the problem of trajectory tracking via output-feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Uniform global stability and robust exact tracking are guaranteed employing the proposed HOSM based exact differentiator. The obtained results are not restricted to first-order sliding mode control feedback, but applies for second order sliding mode algorithms (twisting, super-twisting and variable gain super-twisting) as well as quasi-continuous HOSM finite-time controllers. Simulations with an aircraft pitch-control application illustrate the claimed properties, even in the presence of measurement noise.

Global exact differentiator based on higher-order sliding modes and dynamic gains for globally stable output-feedback control

In this paper, we propose a global exact differentiator with dynamic gains based on higher-order sliding modes to solve the problem of global trajectory tracking via output-feedback for a class of uncertain nonlinear plants with disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Differently from some previous works in the literature, no hybrid switching scheme is necessary to state global stability using only input-output information. For the first time, uniform global exponential stability and ultimate exact tracking are guaranteed exclusively employing higher-order sliding modes based exact differentiators. Numerical simulations are presented to validate the analysis and show the effectiveness of the proposed method.

Cascaded-based stabilization of time-varying systems using second-order sliding modes

We present a result on stabilization of strict feedback systems with unknown disturbances based on the so-called twisting algorithm, a second-order sliding mode controller for the double integrator. The novelty of the note relies in the stability analysis of the closed-loop system and the relaxation of stability conditions (we do not assume boundedness of trajectories). The proof of the main result is constructed along similar lines as for well-established theorems for nonlinear time-varying systems in cascade, with continuous right-hand sides. Although we restrict our analysis to second-order systems, the purpose of this note is to settle the basis for a methodological stability analysis approach for higher-order systems in strict feedback form, under the influence of uncertain perturbations. An illustrative example is provided.

Output-feedback generalization of Variable Gain Super-Twisting Sliding Mode Control via global HOSM differentiators

In this paper, an output-feedback version of the Variable Gain Super-Twisting Sliding Mode Control is proposed for uncertain plants with arbitrary relative degree. This extension is achieved by using global HOSM (higher-order sliding modes) differentiators with dynamic gains. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator, since the disturbances may be state-dependent and time-varying. The proposed control scheme guarantees global stability with robust exact tracking. As the control signal is continuous the proposed scheme alleviates the chattering phenomenon. Numerical simulations illustrate the theoretical results.

Optimal disturbance rejection via integral sliding mode control for uncertain systems in regular form

This paper considers the problem of using an integral sliding mode strategy to reduce the disturbance terms acting on nonlinear systems in regular form. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it can guarantee the minimization of the disturbance terms. Simulation examples shows the effectiveness of the proposal.

Exact compensation of unmatched perturbation via quasi-continuous HOSM

This paper studies nonlinear systems control when unmatched perturbations are present. A new control scheme, based on block control and quasi-continuous HOSM techniques, is proposed. The proposed method assures exact finite time tracking, for the desired signal, regardless of unmatched perturbations. The proposed control design is tested through a simulation example.

Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

ABSTRACT In this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.