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Design of a Backstepping Tracking Controller for a Class of Linear Systems with Actuator Delay

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  • Yonglong Liao
  • Fucheng Liao

Abstract

This paper presents a method for designing a backstepping tracking controller for a class of continuous-time linear systems with actuator delay subject to a reference signal. The actuator delay can be modeled by a first-order hyperbolic PDE, and then a PDE-ODE coupled system is obtained. By applying the backstepping transformation to the coupled system, a feedback controller that includes the state of the system, the integral of the input control, and the integral of the tracking error is derived. We show that the closed-loop system is asymptotically stable at the equilibrium point and achieves complete regulation under the stabilizability assumption. The designs in this paper are illustrated with numerical simulations.

Suggested Citation

  • Yonglong Liao & Fucheng Liao, 2015. "Design of a Backstepping Tracking Controller for a Class of Linear Systems with Actuator Delay," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, October.
    • Handle: RePEc:hin:jnlmpe:160542
    DOI: 10.1155/2015/160542
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