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On global properties of passivity‐based control of an inverted pendulum
Author(s) -
Shiriaev A.,
Pogromsky A.,
Ludvigsen H.,
Egeland O.
Publication year - 2000
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(20000415)10:4<283::aid-rnc473>3.0.co;2-i
Subject(s) - passivity , inverted pendulum , control theory (sociology) , double inverted pendulum , control (management) , pendulum , computer science , mathematics , physics , engineering , nonlinear system , artificial intelligence , mechanical engineering , quantum mechanics , electrical engineering
The paper adresses the problem of stabilization of a specific target position of underactuated Lagrangian or Hamiltonian systems. We propose to solve the problem in two steps: first to stabilize a set with the target position being a limit point for all trajectories originating in this set and then to switch to a locally stabilizing controller. We illustrate this approach by the well‐known example of inverted pendulum on a cart. Particularly, we design a controller which makes the upright position of the pendulum and zero displacement of the cart a limit point for almost all trajectories. We derive a family of static feedbacks such that any solution of the closed loop system except for those originating on some two‐dimensional manifold approaches an arbitrarily small neighbourhood of the target position. The proposed technique is based on the passivity properties of the inverted pendulum. A possible extension to a more general class of underactuated mechanical systems is discussed. Copyright © 2000 John Wiley & Sons, Ltd.