Stick-slip and convergence of feedback-controlled systems with Coulomb friction

An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.Comment: 14 pages, 8 figure

An Observer-Based Design for Cogging Forces Cancellation in Permanent Magnet Linear Motors

International audienceThis paper adresses the high precision positioning issue of permanent magnet (PM) linear motors, in presence of spatially periodic forces, also known as cogging. Using an internal model representation of this perturbation, an observer- based controller only relying on position measurements is derived. The observation error is not autonomous, and the stability analysis of the resulting closed loop system is regarded as the stability of two interconnected systems. For the motor to quickly track a desired trajectory, while being robust to large magnitude cogging forces, a small-gain like theorem is derived and used to tune the gains of the control law in an explicit way. The experimental results obtained through this method are then showed and compared with those of a PID controller

Control of limit cycling in frictional mechanical systems

+116hlm.;24c

Control of Randomly Sampled Robotic Systems

This paper studies control problems of sampled data systems which are subject to random sample rate variations and delays. Due to the rapid growth of the use of computers more and more systems are controlled digitally. Complex systems such as space telerobotic systems require the integration of a number of sub-systems at different hierarchical levels. While many sub-systems may run on a single processor, some sub-systems require their own processor or processors. The sub-systems are integrated into functioning systems through communications. Communication between processes sharing a single processor are also subject to random delays due to memory management and interrupt latency. Communications between processors involve random delays due to network access and to data collisions. Furthermore, all control processes involve delays due to causal factors in measuring devices and to signal processing. Traditionally, sampling rates are chosen to meet the worst case communication delay. Such a strategy is wasteful as the processors are then idle a great proportion of the time; sample rates are not as high as possible resulting in poor performance or in the over specification of control processors; there is the possibility of missing data no matter how low the sample rate is picked. Randomly sampled systems have been studied since later 1950\u27s, however, results on this subject are very limited and they are not applicable to practical systems. This paper studies asymptotical stability with probability one for randomly sampled multi-dimensional linear systems. A sufficient condition for the stability is obtained. This condition is so simple that it can be applied to practical systems. A design procedure is also shown. These results are applied to robot control systems using PD controllers with a feedforward term, computed torque controllers or simple computed torque controllers. The effectiveness of the method is demonstrated by simulations

Friction Modeling, Identification and Compensation (PhD Thesis)

Abstract HIGH-PRECISION tracking requires excellent control of slow motion and positioning. Recent advances have provided dynamic friction models that represent almost all experimentally observed properties of friction. The state space formulation of these new mathematical descriptions has the property that the state derivatives are continuous functions. This enables the application of established theories for nonlinear systems. The existence of locally stable fixed points does not imply for nonlinear systems the absence of limit cycles (periodic orbits) or unstable solutions. Therefore, global properties of PI velocity and PID position control are analyzed using a passivity and Lyapunov based approach. These linear control laws are then extended by nonlinear components based on the friction model considered. The applications presented in this work are in the domains of mechatronics and machine-tools

Energy-Based Control for the Cart-Pole System in Implicit Port-Hamiltonian Representation

This master thesis is devoted to the design, analysis, and experimental validation of an energy-based control strategy for the well-known benchmark cart-pole system in implicit Port-Hamiltonian (PH) representation. The control scheme performs two tasks: swingup and (local) stabilization. The swing-up controller is carried out on the basis of a generalized energy function and consists of bringing the pendulum trajectories from the lower (stable) position to a limit cycle (homoclinic orbit), which passes by the upright (unstable) position, as well as the cart trajectories to the desired point. The (local) stabilizing controller is designed under a novel algebraic Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique and ensures the upright (asymptotic) stabilization of the pendulum as well as the cart at a desired position. To illustrate the effectiveness of the proposed control scheme, this work presents simulations and real-time experiments considering physical damping, i.e., viscous friction. The results are additionally contrasted with another energy-based control strategy for the cart-pole system in explicit Euler-Lagrange (EL) representation.Diese Masterarbeit widmet sich dem Entwurf, der Analyse und der experimentellen Validierung einer energiebasierten Regelstrategie für das bekannte Benchmarksystem des inversen Pendels auf einem Wagen in impliziter Port-Hamiltonscher (PH) Darstellung. Das Regelungssystem erfüllt zwei Aufgaben: das Aufschwingen und (lokale) Stabilisierung. Das Aufschwingen erfolgt auf Grundlage der generalisierten Energiefunktion und besteht darin, sowohl die Trajektorien des Pendels von der unteren (stabilen) Position in einen Grenzzyklus (homokliner Orbit) zu bringen, wobei die (instabile) aufrechte Lage passiert wird, als auch den Wagen in einer gewünschten Position einzustellen. Die (lokale) Regelung zur Stabilisierung ist nach einer neuartigen algebraischen Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) Methode konzipiert und gewährleistet die aufrechte (asymptotische) Stabilisierung des Pendels sowie die Positionierung des Wagens an einem gewünschten Referenzpunkt. Um die Funktionalität des entworfenen Regelungssystems zu veranschaulichen, werden in dieser Masterarbeit Simulationen und Echtzeit-Experimente unter Berücksichtigung der physikalischen Dämpfung, d.h. der viskosen Reibung, vorgestellt. Die Ergebnisse werden zusätzlich mit einem weiteren energiebasierten Regelungsansatz für das System des inversen Pendels auf einem Wagen in expliziter Euler-Lagrange (EL) Darstellung verglichen.Tesi