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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    • "Time delays occur in many engineering systems and can lead to difficulties in controller design and performance . For example, delays can be a significant concern in networked control systems [9] [10], in engine control [11] [12], or in teleoperation of robots [13]. Such TDS are described by DDEs and have an infinite eigenspectrum, which makes their analysis and control challenging. "
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    ABSTRACT: While time delays typically lead to poor control performance, and even instability, previous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTI) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equations (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single-and two-degree of freedom (DOF) mechanical systems. The simulation results demonstrate excellent performance with improved stability margins.
    Journal of Dynamic Systems Measurement and Control 04/2015; 137(4):041014. DOI:10.1115/1.4028528 · 0.98 Impact Factor
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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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    ABSTRACT: This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in general there is no one to one correspondence between the branches of the matrix Lambert W function and the characteristic roots of the system. Furthermore, it is shown that under mild conditions only two branches suffice to find the complete spectrum of the system, and that the principal branch can be used to find several roots, and not the dominant root only, as stated in previous works. The results are first presented analytically, and then verified by numerical experiments.
    Automatica 03/2015; 53(3):339-345. DOI:10.1016/j.automatica.2015.01.016 · 3.02 Impact Factor
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    • "where A [l] (x, u, v, a) are determined recursively by A [1] (x, u, v, a) =f (x, u) A [2] (x, u, v, a) = ∂A [1] (x, u, v, a) ∂x A [1] (x, u, v, a)+ "
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    ABSTRACT: When calculating the sampled-date representation of nonlinear systems second-order hold (SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input. Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method. The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems. The comparison between SOH assumption with first-order hold (FOH) and zero-order hold (ZOH) assumptions is given to show the advantages of the proposed method.
    International Journal of Automation and Computing 06/2014; 11(3):320-327. DOI:10.1007/s11633-014-0795-4
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