Design of observer-based feedback control for time-delay systems with application to automotive powertrain control

Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109, USA
Journal of the Franklin Institute (Impact Factor: 2.4). 02/2010; 347(1):358-376. DOI: 10.1016/j.jfranklin.2009.09.001


A new approach for observer-based feedback control of time-delay systems is developed. Time-delays in systems lead to characteristic equations of infinite dimension, making the systems difficult to control with classical control methods. In this paper, a recently developed approach, based on the Lambert W function, is used to address this difficulty by designing an observer-based state feedback controller via assignment of eigenvalues. The designed observer provides estimation of the state, which converges asymptotically to the actual state, and is then used for state feedback control. The feedback controller and the observer take simple linear forms and, thus, are easy to implement when compared to nonlinear methods. This new approach is applied, for illustration, to the control of a diesel engine to achieve improvement in fuel efficiency and reduction in emissions. The simulation results show excellent closed-loop performance.

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    • "The design of memory-less (delay-free) analog/digital observers for time-delay systems can be found in the literature[1,6,17,18,31], whether as the point-wise delayed (integer delayed) analog observer for a class of CIDDE can be found in[32]and the digital observer for a class of DIDDE can be found in[17,19] Fig. 2. Observer-based digital control. From (50), we construct an extended state-space model[6,17] "
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    • "the rank of B in (1) is at least n − 1, i.e., B does not have a repeated zero eigenvalue, the characteristic roots with largest real part correspond to the S 0 matrix, found using the principal branch of the matrix Lambert W function in Algorithm 1. This conjecture is formally stated in [23] and it is the basis for several derivative works [7] [20] [24] [26] [27] [29] [32]. "
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