Brief Paper: A Quasi-Tracking Approach for Finite-Time Control of a Mass-Beam System

  • Authors:

  • G. Zhu;S. S. Ge

  • Affiliations:

  • Centre for Intelligent Control, Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260;Centre for Intelligent Control, Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1998

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Abstract

This paper presents an approach for finite-time control of a distributed-parameter system: a flexible beam connected to a translational mass. A quasi-tracking variable is introduced, and a terminal sliding mode controller is developed to achieve finite-time convergence of the quasi-tracking variable to a properly pre-defined trajectory. This subsequently provides a set of boundary conditions to explicitly solve the corresponding boundary-value problem and prove finite-time regulation. End-point tracking control is also investigated. It is shown that the error between the end point of the beam and the pre-defined trajectory, though does not decay to zero, is always bounded by a small time-varying bound. A method to reduce the error bound is also given. The approach does not invoke any model truncation procedure, hence the problem of observation/control spillovers, which exists in the conventional truncated-model-based controller design methods, is essentially avoided. Satisfactory simulation results are provided to demonstrate the effectiveness of the presented approach.