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Suppression of high order disturbances and tracking for nonchaotic systems: a time-delayed state feedback approach

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Abstract

Time-delayed state feedback is an easy realizable control method that generates control force by differencing the current and the delayed versions of the system states. In this paper, a new form of the time-delayed state feedback structure is introduced. Based on the proposed time-delayed state feedback method, a new robust tracking system is designed. This tracking system improves the conventional state feedback with integral action disturbance rejection characteristics in the presence of the disturbance signals imposed on the system dynamics or on the sensors that measure the system states. Also, the proposed tracking system tracks the ramp-shaped reference input signal, which is not achievable through conventional state feedback. Moreover, since the proposed method adds delays to the closed-loop system dynamics, the ordinary differential equation of the system changes to a delay differential equation with an infinite number of characteristic roots. Thus, conventional pole placement techniques cannot be used to design the time-delayed state feedback controller parameters. In this paper, the simulated annealing algorithm is used to determine the proposed control system parameters and move the unstable roots of the delay differential equation to the left half-plane. Finally, the efficiency of the proposed reference input tracker is demonstrated by presenting two numerical examples.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Zahed Dastan & Mahsan Tavakoli-Kakhki

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  1. Zahed Dastan
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  2. Mahsan Tavakoli-Kakhki
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Correspondence to Mahsan Tavakoli-Kakhki.

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Dastan, Z., Tavakoli-Kakhki, M. Suppression of high order disturbances and tracking for nonchaotic systems: a time-delayed state feedback approach. Control Theory Technol. 20, 54–68 (2022). https://doi.org/10.1007/s11768-021-00073-9

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