Francisco Gordillo

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.

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.

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.

Stabilization of oscillations in the inverted pendulum

Abstract This paper addresses the problem of obtaining robust and stable oscillations in an electromechanical system. These oscillations are associated to a limit cycle that is born through a supercritical Hopf bifurcation. The method proposed in the paper works well for fully actuated systems, and even for certain underactuated ones. In order to illustrate the method, we have chosen an underactuated system that is well known in the literature and in control systems laboratories: the inverted pendulum. Actual stable and robust oscillations have been obtained experimentally in a rotating Furuta pendulum.

Partial-Energy-Shaping Control for Orbital Stabilization of High-Frequency Oscillations of the Furuta Pendulum

We consider the problem of creating oscillations of the Furata pendulum around the open-loop unstable equilibrium. Following a proposed technique, we start with shaping the energy of the unactuated link. An dissipativity-based controller is designed to create oscillations, neglecting possibility of unbounded motion of the directly actuated link. After that, an auxiliary linear feedback action is added to the control law, stabilizing a desired level of the reshaped energy. Parameters of the controller are tuned to approximately keep the originally created oscillations but ensuring bounded motion of both links. The analysis is valid only for oscillations of sufficiently high frequency and is based on higher order averaging technique. Performance of the designed controller is verified using numerical simulations and experiments.

A new family of smooth strategies for swinging up a pendulum

The paper presents a new family of strategies for swinging up a pendulum. They are 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. A two-parameter family of simple strategies without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set will 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.

Control and stability analysis for the Vdd-hopping mechanism

In low-power electronics, achieving a high energy efficiency has great relevance. Nowadays, Global Asynchronous Local Synchronous Systems en- ables to use a Local Dynamic Voltage Scaling archi- tecture. This technique allows to reach a high energy efficiency. Moreover, Local Dynamic Voltage Scaling can be implemented using different approaches. One of them is the Vdd-Hopping technique. In this paper, we propose an innovative control approach which aims for minimizing the energy dissipated during the Vdd-Hopping transients. In addition, our control also includes the ability to limit the current peaks during such transients. Stability of the closed-loop system is analyzed. A discrete version of this controller is obtained, which coincides with ENergy-AwaRe Control (ENARC) that is patent pending. And a comparison of this last one with another published is done.