Nonlinear Control Systems by Zoran Vukic

By Zoran Vukic

Annotation content material: homes of nonlinear platforms; balance; linearization tools; working modes and dynamic research tools; part trajectories in dynamic research of nonlinear platforms; harmonic linearization in dynamic research of nonlinear keep an eye on structures working in stabilization mode; harmonic linearization in dynamic research of nonlinear regulate platforms in monitoring mode of operation; functionality estimation of nonlinear regulate procedure temporary responses; describing functionality strategy in fuzzy keep an eye on structures. Appendices: harmonic linearization; Popov diagrams. summary: Emphasizes classical equipment and offers analytical instruments for the development and improvement of layout tools in nonlinear keep watch over. This e-book bargains engineering strategies for the frequency area, and solved examples for realizing of regulate functions within the business, electric, strategy, production, and automobile industries. learn more...

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Copyright © 2003 by Marcel Dekker, Inc. 9 (REGIONOF ATTRACTION) ! 35) Every attractive equilibrium state has its own region of attraction. Such a region in state space means that trajectories which start from any initial condition inside the region of attraction are attracted by the attractive equilibrium state. The attractive equilibrium states are called attractors. The equilibrium states with repellent properties have the name repellers, while the equilibrium states which attract on one side and repel on the other side are saddles.

Then stability can be referred to as the stability in the Lyapunov sense, as he studied the stability in the vicinity of equilibrium states. “Stability is in itself such a clear concept that it speaks for itself’ wrote La Salle and Lefschetz (196 1). Nevertheless, mathematical analysis of stability requires a quantitative characteristic. Although the concept of stability is associated with the system, this is not the complete contents of the idea. Stability is a property required for a system in order to function for a long period of time.

The concept of stability is so important since every control system must be primarily stable, and only then other properties can be studied. The theory of stability was the preoccupation of scientists from the beginning of the theory of differential equations. The key problem is to obtain information on the system’s behavior (state trajectory) without solving the differential equation. e. as t + . L. Lagrange - his observation was that the equilibrium state of an unforced system is stable if it has a minimum of potential energy.

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