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34                                     Introduction to Control Theory















































            Figure 2.3.2: Van der Pol Oscillator Time Trajectories: (a) Time history, (b) phase
            plane.



            In this example, we will concentrate on writing the n coupled differential
            equations into a state-space form. In fact, let a state vector x be






            and the input vector be u=τ and suppose the output vector is y= q. Due to
            some special properties of rigid robots (see Chapter 2), the matrix M(q) is


            Copyright © 2004 by Marcel Dekker, Inc.
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