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2.3 Nonlinear State-Variable Systems 33

Figure 2.3.1: Damped pendulum trajectory.

2. A classical nonlinear system is the Van der Pol oscillator which is described
by

or in state-space with

The time history of y(t) and the phase-plane plot (i.e. x 2 versus x 1) is shown
in Figure 2.3.2.

EXAMPLE 2.3–2: Rigid Robot Dynamics
A rigid robot is described by the following equations

where M(q) is an n×n Inertia matrix, q and its derivatives are n×1 vectors of
generalized coordinates, V(q, q), G(q) and τ are n×1 vectors containing
velocity-dependent torques, gravity torques, and input torques respectively.

Copyright © 2004 by Marcel Dekker, Inc.