Applied Nonlinear Control by Jean-Jacques Slotine, Weiping Li

By Jean-Jacques Slotine, Weiping Li

Covers in a innovative style a couple of research instruments and layout suggestions without delay acceptable to nonlinear keep watch over difficulties in excessive functionality platforms (in aerospace, robotics and car areas).

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Determine the stability of these limit cycles. 10 represents a satellite control system with rate feedback provided by a gyroscope. Draw the phase portrait of the system, and determine the system's stability. 10 : Satellite control system with rate feedback Chapter 3 Fundamentals of Lyapunov Theorj. Given a control system, the first and most important question about its various properties is whether it is stable, because an unstable control syster;] 1s typically useless and potentially dangerous.

The phase portrait of the undamped mass spring system belongs to this category. :ly determined by the nature of their singularity points. This, however, is not true for nonlinear systems. ;hould be kept in mind. Phase plane analysis of nonlinear systems is related to that of linear systems, because the local behavior of a nonlinear system can be approximated b y the behavior of a linear system. Yet, nonlinear systems can display much morl: complicated patterns in the phase plane, such as multiple equilibrium points and lil lit cycles.

In the first step. a field of directions of tangents to the trajectories is obtained. In the second step, phase plane trajectories are formed from the field of directions . 2). , a straight line. Along the line, we can draw a lot of short line segments with slope a. 7. To obtain trajectories from the field of directions, we assume that the the tangent slopes are locally constant. Therefore, a trajectory starting from any point in the plane can be found by connecting a sequence of line segments.

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