Javier Aracil

Stability indices for the global analysis of expert control systems

The stability of rule-based expert control systems is studied. A control structure with a nonlinear plant and a nonlinear controller, designed on the basis of logical rules incorporating the experience of designers and human operators, is considered. Two classes of indices are presented: one related to the relative stability of the equilibrium point at the origin, and the other to the global stability of the system. These indices can be used for the analysis and design of expert control systems. Some examples are included to illustrate the approach. >

A new swing-up law for the Furuta pendulum

In this paper the swing-up problem for the Furuta pendulum is solved applying Fradkovs speed-gradient (SG) method to a dimension 4 model of the system. The new law is compared with the conventional Åström-Furuta strategy, based on a dimension 2 model. A comparative analysis, including simulations and experiments, whereby the advantages and effectiveness of the new law for swinging the pendulum up are shown, is included.

Brief paper: A family of smooth controllers for swinging up a pendulum

The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach.

Periodicity and chaos in an autonomous electronic system

In this paper, a simple electronic circuit is analyzed from a qualitative viewpoint. The circuit shows a great variety of dynamical behaviors (equilibrium points, periodic oscillations, chaotic motions... ) and the analysis proceeds to catalog all of them through a bifurcation study (pitchfork and Hopf bifurcations, flip bifurcations... ). This study points out the relevance of qualitative analysis in systems of simple structure but with very complex behavior. The paper includes theoretical study, numerical simulations, and actual circuit experimentation.

Stabilization of a class of underactuated mechanical systems via total energy shaping

In this paper a system of ODEs and a method for its solution are proposed for passivity-based stabilization of a class of underactuated mechanical systems. This method simplifies the PDEs imposed by the passivity-based control via interconnection and damping assignment (IDA-PBC) technique. For a class of mechanical systems satisfying some mathematical properties the PDEs are reduced to a simple set of nonlinear ODEs. A general solution for these equations in the 2-DOF case is presented, through a new parametrization of the closed loop inertia matrix. Two examples illustrate the method, achieving kinetic and potential energy shaping in a straightforward manner. The simulation analysis in comparison with recent studies highlight the advantages of these techniques.

Describing function method for stability analysis of PD and PI fuzzy controllers

A fuzzy logic controller saturates outside the universe of discourse region. This saturation gives rise to a universal nonlinearity for this type of controller. In this paper, the effects of this nonlinearity are analyzed for the most usual fuzzy controllers: PD and PI fuzzy controllers. It is shown that due to this saturation some pathological behaviors such as oscillations or unstable limit cycles can occur. The methodology employed in the analysis is based on the describing function, which is determined for PD and PI fuzzy controllers. One example illustrates the relevance of the proposed methodology.

Brief Hopf bifurcation in indirect field-oriented control of induction motors

The appearance of self-sustained oscillations in high performance AC drives, and in particular, in induction motors whose speed is regulated with the industry standard field-oriented control, is a well-documented but little understood phenomenon. It is well known that the oscillations may be quenched by returning the outer-loop PI speed control, but no precise rules to carry out this task, which may be time consuming, are known. In this paper, we show that these oscillations may arise due to the existence of Hopf bifurcations. Some simple rules for selecting the gains of the PI controller are obtained as a result of our analysis.

Chaotic motion in an adaptive control system

An elementary non-linear control system with an adaptive mechanism that shows a strange attractor is analysed in this paper. The chaotic behaviour is due to a reinjection phenomenon associated with the folded characteristic of the non-linear element. Power spectra of the system confirm the existence of chaotic motion.

Stabilization of oscillations through backstepping in high-dimensional systems

This note introduces a method for obtaining stable and robust self-sustained oscillations in a class of single input nonlinear systems of dimension n/spl ges/2. The oscillations are associated to a limit cycle that is produced in a second-order subsystem by means of an appropriate feedback law. Then, the controller is extended to the full system by a backstepping procedure. It is shown that the closed-loop system turns out to be generalized Hamiltonian and that the limit cycle can be thought as born in a Hopf bifurcation after moving a parameter.

AN INTERACTIVE TOOL FOR INTRODUCTORY NONLINEAR CONTROL SYSTEMS EDUCATION

Abstract In this paper a new interactive tool for control education is presented. With this tool, developed in SysQuake (Piguet, 2000), the student can easily assimilate some concepts of introductory courses in nonlinear control such as the behaviour of piecewise linear systems, stable and unstable limit cycles and the describing function method. Furthermore, the basis of more sophisticated fields such as bifurcation theory applied to control systems can also be acquired. Three application examples are included in order to show the possibilities of the tool.