By Felix L. Chernous'ko, I. M. Ananievski, S. A. Reshmin
This ebook is dedicated to new tools of regulate for complicated dynamical structures and offers with nonlinear keep watch over structures having a number of levels of freedom, subjected to unknown disturbances, and containing doubtful parameters. a number of constraints are imposed on keep an eye on inputs and nation variables or their mixtures. The publication comprises an creation to the idea of optimum regulate and the idea of balance of movement, and likewise an outline of a few identified equipment in keeping with those theories.
Major recognition is given to new equipment of keep watch over constructed by way of the authors over the past 15 years. Mechanical and electromechanical structures defined through nonlinear Lagrange’s equations are thought of. basic tools are proposed for a good building of the mandatory keep an eye on, usually in an specific shape. The e-book comprises a variety of suggestions together with the decomposition of nonlinear keep an eye on structures with many levels of freedom, piece-wise linear suggestions keep watch over according to Lyapunov’s services, equipment which intricate and expand the methods of the traditional keep an eye on concept, optimum keep watch over, differential video games, and the speculation of balance. The virtue of the equipment built within the ebook is that the controls received fulfill the imposed constraints and steer the dynamical approach to a prescribed terminal country in finite time. specific top estimates in the time of the method are given. In all situations, the keep watch over algorithms and the estimates bought are strictly confirmed.
The tools are illustrated by means of a few keep an eye on difficulties for numerous engineering platforms: robot manipulators, pendular platforms, electromechanical platforms, electrical automobiles, multibody structures with dry friction, and so forth. The potency of the proposed ways is proven through laptop simulations. The authors desire that the monograph may be an invaluable contribution to the clinical literature at the thought and strategies of keep watch over for dynamical structures. The publication may be of curiosity for scientists and engineers within the box of utilized arithmetic, mechanics, concept of keep an eye on and its purposes, and likewise for college kids and postgraduates.
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Additional resources for Control of Nonlinear Dynamical Systems: Methods and Applications
34) B1 = B2 . 2 Control of the subsystem and feedback control design 47 The points (ξ , η ) and (ξ ∗ , η ∗ ) belong to two branches of the switching curve ψ0 = 0; also, η > 0 and η ∗ < 0. 36) 1 1 ξ = − η 2 , ξ ∗ = (η ∗ )2 for λ = 0. 36) expressing ξ and ξ ∗ in terms of η and η ∗ . 37) λ = 0, where η > 0 and η ∗ < 0. 37) connect the values of η ∗ and η . Let us ﬁrst consider the case λ = 0. 38) 0 ≤ ρ < 1. One can easily see that κ increases monotonically from 0 to ∞ as ρ increases from 0 to 1. 618.
8), this asymptote is itself also a phase trajectory for u = 1. Dependence x1 (x2 ) is shown for u = 1 and B = 0 in Fig. 1, where the arrows indicate the direction of increasing t. 6) are obtained from the curve described above by a translation along the x1 axis. x2 O x1 Fig. 8), the resulting relationships remain valid. Consequently, the phase trajectories corresponding to u = −1 are obtained by means of the central symmetry from the trajectories described above and corresponding to u = 1. 7) with B = 0 and u = ±1.
1), that is, along the trajectories of Fig. 2 for λi > 0 or Fig. 2 for λ = 0. 43). 45), as is usually the case, then the phase trajectories for each ith degree of freedom in the plane (x1 , x2 ) deviate from the optimal ones. Here, the motion along the switching curves takes place in a sliding regime. 1)]. 46) i = 1, . . , n. 37) for ξ and η . 14) for those i for which λi > 0. We summarize the results in the form of a theorem. 2. 12) are satisﬁed, and that all the trajec˙ that solves tories considered lie in domain Ω .