Rafael Castro-Linares

On robust regulation via sliding mode for nonlinear systems

Abstract A robust control scheme for the output tracking of nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. It is shown that if perturbations and/or uncertainties appear on the system, the sliding mode controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.

Adaptive passivity of nonlinear systems using time-varying gains

In this paper, an adaptive controller with time-varying gains is proposed to solve the problem of making a single-input single-output (SISO) nonlinear system, with explicit linear parametric uncertainty, equivalent to a passive system. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to two examples, a third order nonlinear system and a model of a magnetic levitation system, to show the controller methodology design.

On fractional extensions of Barbalat Lemma

a b s t r a c t This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory.

Control of a flexible joint robot manipulator via a non-linear control-observer scheme

A non-linear controller-observer scheme for the output tracking of a class of non-linear singularly perturbed systems based on a two-time scale sliding-mode technique and a high gain estimator, is presented. An analysis of stability of the resultant closed-loop system is given. The proposed scheme is applied to the model of a two degrees of freedom flexible joint robot to show the controller-observer methodology proposed.

Direct passivity of a class of MIMO non-linear systems using adaptive feedback

In this paper, an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi-input multi-output (MIMO) non-linear system, with explicit linear parametric uncertainty, equivalent to a passive system. These results are an extension of those obtained by the authors for the SISO case. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to models of dynamical MIMO systems, to illustrate the controller design methodology.

Adaptive passivation with time‐varying gains of mimo nonlinear systems

This paper addresses the adaptive passivation of multi‐input multi‐output (MIMO) non‐linear systems,with unknown parameters. The class of MIMO non‐linear systems considered here has an explicit linear parametric uncertainty and it is made equivalent to a passive system by means of an adaptive controller with adaptive laws specially designed, which include suitable time‐varying gains. The solution presented here is an extension of that obtained by the authors for single‐input single‐output (SISO) systems. The proposed algorithm was applied, at simulation level, to models of dynamical MIMO systems, to exemplify the controller design methodology and to observe the adaptive system behavior.

Sliding Mode Control and State Estimation for a Class of Nonlinear Singularly Perturbed Systems

This paper is concerned with the design of a controller-observer scheme for the exponential stabilization of a class of singularly perturbed nonlinear systems. The controller design uses a sliding mode technique and is divided in two phases: slow feedback control and fast feedback control so that a final composite control is obtained. Assuming that only the fast state is available and the systems output is a function of the slow state, an observer design is presented. A stability analysis is also made to provide sufficient conditions for the ultimate boundedness of the full order closed-loop system when the slow state is estimated by means of the observer. An application to the model of a permanent magnet stepper motor is given to show the controller-observer methodology and stability analysis.

Bi-causal solutions to the disturbance decoupling problem for time-delay nonlinear systems

In this paper, the disturbance decoupling problem for a class of single-input single-output nonlinear systems with multiple delays in the input and the state is studied. Based on a pioneering mathematical frame, a bicausal compensator that solves the problem is considered, giving necessary and sufficient conditions for the existence of such a compensator.

Modeling and controller design of a magnetic levitation system

In this paper, the nonlinear mathematical model with five DOFs of a magnetic levitation system is developed and analyzed. Then a second order sliding mode controller is proposed to regulate the levitation to a desired position, stabilize the other 4 DOFs in the nonlinear system and compensate the unknown increments on the load. Simulation results are presented to show the effectiveness of the proposed controller.

Robust trajectory tracking control of a quadrotor helicopter

In this paper, a nonlinear controller endowed with a disturbances estimator, based on the Immersion and Invariance control technique, is proposed. This nonlinear controller is applied to the six degrees of freedom dynamics of the quadrotor helicopter to achieve regulation and trajectory tracking. The proposed estimator can reconstruct constant disturbances entering additively to the dynamic model. An experimental evaluation was carried out in order to show the performance of the proposed controller.