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By Marcio S. de Queiroz, Darren M. Dawson, Siddharth P. Nagarkatti, Fumin Zhang

The layout of nonlinear controllers for mechanical structures has been an ex­ tremely energetic sector of study within the final 20 years. From a theoretical viewpoint, this realization may be attributed to their fascinating dynamic habit, which makes them appropriate benchmarks for nonlinear keep watch over the­ oreticians. nevertheless, contemporary technological advances have produced many real-world engineering purposes that require the automated con­ trol of mechanical platforms. the mechanism for de­ usually, Lyapunov-based ideas are applied as veloping varied nonlinear keep an eye on buildings for mechanical structures. The attract of the Lyapunov-based framework for mechanical process keep an eye on de­ signal can probably be assigned to the truth that Lyapunov functionality candi­ dates can frequently be made from actual perception into the mechanics of the approach. that's, regardless of the nonlinearities, couplings, and/or the versatile results linked to the method, Lyapunov-based ideas can usually be used to investigate the soundness of the closed-loop method by utilizing an strength­ like functionality because the Lyapunov functionality candidate. In perform, the layout technique frequently has a tendency to be an iterative approach that ends up in the demise of many timber. that's, the controller and energy-like functionality are frequently developed in live performance to foster an useful balance estate and/or robustness estate. thankfully, during the last 15 years, many method the­ ory and keep an eye on researchers have worked during this zone to provide a variety of layout instruments that may be utilized in various situations.

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88). Assumption 1: The load function TL(q, q) E Loo if q(t), q(t) E Loo. Assumption 2: The Stribeck function g(q) is constructed such that (i) it ensures that f(q) E Loo if q(t), q(t) E Loo and (ii) 0 < g(q) < DO where Do is some positive constant [9J. , z(t) E Loo). 5 /30, /31, and /32 are positive constant parameters. 4. The PSFB condition stems from the fact that the controllers will only require direct measurement of q (t) and q (t), while a filter and/or observer will generate an estimate for the unmeasurable friction state z (t).

The amount of friction could be varied by adjusting a vice arrangement. An integrally mounted resolver provided rotor position measurement. The resolver signal was converted to quadrature format by a resolver-to-digital converter mounted inside the driver unit. 00234 deg. The rotor velocity signal was obtained by applying a standard backwards difference algorithm to the position signal with the resulting signal being filtered by a second-order digital filter. A Pentium 266 MHz PC running Qmotor provided the environment to write the control algorithm in the C programming language.

Lischinsky, A New Model for Control of Systems with Friction, IEEE Transactions on Automatic Control, Vol. 3, pp. 419-425, Mar. 1995. [10] C. Canudas de Wit and P. Lischinsky, Adaptive Friction Compensation with Dynamic Friction Model, IFAC World Congress, pp. 197-202, San Francisco, CA, June 1996. [11] L. da Vinci, The Notebooks, New York, NY: Dover. [12] P. R. Dahl, A Solid Friction Model,TOR-158(3107-18), The Aerospace Corporation, El Sugundo, CA. [13] P. E. Dupont and E. P. Dunlap, Friction Modeling and Control in Boundary Lubrication, Proceedings of the American Control Conference, pp.

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