In this paper we propose a new dynamic model for friction. The model captures most of the friction behavior that has been observed experimentally. This includes the Stribeck effect, hysteresis, spring-like characteristics for stiction, and varying break-away force. Properties of the model that are relevant to control design are investigated by analysis and simulation. New control strategies, including a friction observer, are explored, and stability results are presented. >

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A new model for control of systems with friction

A survey of models, analysis tools and compensation methods for the control of machines with friction

During the past several years, an analytical theory of manual control of vehicles has been in development and has emerged as a useful engineering tool for the explanation of past test results and prediction of new phenomena. An essential feature of this theory is the use of quasi-linear analytical models for the human pilot wherein the models' form and parameters are adapted to the task variables involved in the particular pilot-vehicle situation.

A Review of Quasi-Linear Pilot Models

''Model-free control'' and the corresponding ''intelligent'' PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.

https://hal-polytechnique.archives-ouvertes.fr/hal-00828135/document

Model-free control

Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q < 0, these systems are shown to approach the equilibrium point in finite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2,...,2)T. The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.

Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems

The possibility of hunting in closed-cycle control systems is often contributed to by: (a) backlash in gearing which is part of the main sequence of the control. (b) friction that falls with increase in speed over some range of low speeds. It is shown how, to an approximation sufficiently close for practical purposes, the effect of each of these features may be introduced into the usual treatment of stability by the loop response-vector locus or Nyquist diagram. For this purpose, vector loci are provided that give the additional phase-shift and amplitude ratio due to backlash and speed-dependent friction respectively, for sinusoidal inputs of any frequency or amplitude. The effects of the harmonics that are also produced because of the essentially non-linear nature of these phenomena are disregarded. The general method is based on unpublished work of the late Professor P.J. Daniell, who provided an analytical treatment of the effect of backlash of which the present paper is essentially an interpretation in geometrical terms.

A. Tustin

Papers

The effects of backlash and of speed-dependent friction on the stability of closed-cycle control systems