Brief A phase-plane approach to time-optimal control of single-DOF mechanical systems with friction

  • Authors:

  • Dong-Soo Choi;Seung-Jean Kim;In-Joong Ha

  • Affiliations:

  • ASRI/ACRC, School of Electrical Engineering, Seoul National University, San 56-1 Shinlim-Dong, Kwanak-Ku, Seoul 151-742, South Korea;ASRI/ACRC, School of Electrical Engineering, Seoul National University, San 56-1 Shinlim-Dong, Kwanak-Ku, Seoul 151-742, South Korea;ASRI/ACRC, School of Electrical Engineering, Seoul National University, San 56-1 Shinlim-Dong, Kwanak-Ku, Seoul 151-742, South Korea

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

In this paper, we attempt to solve the time-optimal control problem for single-degree-of-freedom (DOF) mechanical systems with friction, while taking into account not only the velocity-dependent control input constraint but also the state constraint. Direct application of the Pontryagin's maximum principle (PMP) leads to a sixth-order nonlinear two-point boundary-value problem (TPBVP) which is very difficult to solve numerically. In this context, we take a phase-plane analysis without resorting to the PMP. Thereby, the exact time-optimal solution can be obtained simply by solving a set of first-order differential equations with continuous right-hand sides. We also present some simulation results to demonstrate the practical use of the time-optimal solution.