Download Applied Nonlinear Control by Jean-Jacques Slotine, Weiping Li PDF

By Jean-Jacques Slotine, Weiping Li

ISBN-10: 0130408905

ISBN-13: 9780130408907

Covers in a revolutionary type a few research instruments and layout thoughts at once acceptable to nonlinear keep watch over difficulties in excessive functionality structures (in aerospace, robotics and car areas).

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Extra info for Applied Nonlinear Control

Sample text

1) does not expl~citlycontain the control input as a variable, it is directly applicable to feedback conlrcl systems. 1) can represent the closed-loop dynamics ~f feedback control system, with the control input being a function of state x and time t, and therefore disappearing in the closed-loop dynamics. 1). 1) can ;:scl represent dynamic systems where no control signals are involved, such as a fre::ily swinging pendulum. A special class of nonlinear systems are linear systems. The dynar;~icsof linear systems are of the form where A(t) is an nxn matrix.

One simple inference from this theoren is that a limit cycle must enclose at least one equilibrium point. The theorem's I-ezultcan be Sect. 10. The second theorem is concerned with the asymptotic properties of the trajectories of second-order systems. 2 (Poincare-Bendixson) If a rrajectory of the second-order autonomous system remains in a finite region a,then one of the following is true: ( a ) the tl-ajecrol-ygoes to an equilibrium point ( b ) the 11-ajecrol-ytends to an asymptotically stable limit cycle ( c ) the 11-ajectol-yis itselfa limit cycle While the proof of this theorem is also omitted here, its intuitive basis is easy to see, and can be verified on the previous phase portraits.

It is important to notice, however, that they have no equivalent in higher-order systems, where exotic asymptotic behaviors other than equilibrium points and limit cycles can cc:c,lr. 7 Summary Phase plane analysis is a graphical method used to study second-order dynamic systems. The major advantage of the method is that it allows visual exarrl nat~onof the global behavior of systems. te n achieved with the aid of computer graphics). m points and ll of limit cycles are clearly seen in phase plane analysis.

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