Brief paper: Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties

  • Authors:

  • Meng-Bi Cheng;Verica Radisavljevic;Wu-Chung Su

  • Affiliations:

  • Department of Electrical Engineering, National Chung-Hsing University, Taichung 402, Taiwan, ROC;Department of Mechanical Engineering, California State University, Los Angeles, CA 90032-8153, USA and Department of Mechanical Engineering, American University of Sharjah, Sharjah, United Arab Em ...;Department of Electrical Engineering, National Chung-Hsing University, Taichung 402, Taiwan, ROC

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

This paper considers the stabilization problem of a one-dimensional unstable heat conduction system (rod) modeled by a parabolic partial differential equation (PDE), powered with a Dirichlet type actuator from one of the boundaries. By applying the Volterra integral transformation, a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties. The associated Lyapunov function is used for designing an infinite-dimensional sliding manifold, on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances. It is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero. A continuous control law satisfying the reaching condition is obtained by passing a discontinuous (signum) signal through an integrator.