Control of Nonlinear Dynamical Systems: Methods and by Felix L. Chernous'ko, I. M. Ananievski, S. A. Reshmin
By Felix L. Chernous'ko, I. M. Ananievski, S. A. Reshmin
This publication is dedicated to new equipment of keep watch over for complicated dynamical structures and bargains with nonlinear keep an eye on platforms having numerous levels of freedom, subjected to unknown disturbances, and containing doubtful parameters. a variety of constraints are imposed on keep watch over inputs and kingdom variables or their mixtures. The publication includes an creation to the idea of optimum regulate and the speculation of balance of movement, and likewise an outline of a few recognized equipment in line with those theories.
Major cognizance is given to new tools of regulate built through the authors over the past 15 years. Mechanical and electromechanical platforms defined by means of nonlinear Lagrange’s equations are thought of. normal tools are proposed for an efficient building of the necessary regulate, frequently in an specific shape. The booklet comprises a variety of strategies together with the decomposition of nonlinear regulate platforms with many levels of freedom, piece-wise linear suggestions regulate in response to Lyapunov’s features, equipment which problematic and expand the methods of the traditional regulate conception, optimum keep watch over, differential video games, and the idea of balance. The virtue of the tools constructed within the booklet is that the controls acquired fulfill the imposed constraints and steer the dynamical process to a prescribed terminal country in finite time. specific top estimates in the course of the method are given. In all circumstances, the keep an eye on algorithms and the estimates bought are strictly confirmed.
The tools are illustrated by way of a couple of keep watch over difficulties for varied engineering structures: robot manipulators, pendular platforms, electromechanical structures, electrical cars, multibody structures with dry friction, and so forth. The potency of the proposed methods is proven through desktop simulations. The authors wish that the monograph might be an invaluable contribution to the medical literature at the idea and strategies of regulate for dynamical platforms. The ebook can be of curiosity for scientists and engineers within the box of utilized arithmetic, mechanics, conception of keep an eye on and its purposes, and likewise for college students and postgraduates.
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Extra resources for Control of Nonlinear Dynamical Systems: Methods and Applications
11). 11). Hence, the ﬁrst part of the trajectory should belong to the other family of parabolas. 3) and intersects the parabola of the other family reaching the zero point. Thus, we obtain the ﬁeld of optimal phase trajectories shown in Fig. 2 by thin lines. The locus of states where the bang-bang control changes its sign is called the switching curve. In our example, the switching curve consists of two semi-parabolas of different families that reach the zero point. These semi-parabolas are optimal phase trajectories themselves.
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. 5) with B1 = B2 = 0 and u = ±1. 5) for λ = 0] constitute the switching curve of the optimal control: the only possible change of sign of the control u along each trajectory takes place on this curve. As a result, we arrive at the ﬁeld of optimal phase trajectories that is shown in Fig.
Here and in what follows, all the relationships are given separately for the cases λ > 0 and λ = 0. We note that the case λ = 0 can be obtained by taking the limit as λ → +0. 2) hold for t = τ . 5), we obtain the equations for the phase trajectories x1 = B − λ −1 x2 − λ −2 w log |1 − λ w−1 x2 | x1 = B + (2w)−1 x22 for for λ = 0. 7) Here, B is a new constant expressed in terms of B1 and B2 . 6), we assume that λ B2 = w. 8) x2 = λ −1 w. 7) for λ = 0 are parabolas that are symmetric about the x1 -axis.