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Robust State Feedback-Based Design of PID Controllers for High-Order Systems with Time-Delay and Parametric Uncertainties

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Abstract

This paper presents a general framework for designing robust Proportional-Integral and Proportional-Integral-Derivative controllers for time-delay systems. The proposed approach considers systems of any order, with parametric uncertainties, unknown time-delay, and possibly unstable. The main appeal is to get a polytopic state-space realization of the uncertain transfer function where the control design is rewritten as a convex state feedback problem that can be solved by new linear matrix inequalities based on a parameter-dependent Lyapunov–Krasovskii type functional. For performance criteria, we consider robust pole placement for minimum decay rate and \(\mathcal {H}_{\infty }~\)guaranteed cost. We also include in the design a first-order filter in the derivative action. Numerical examples illustrate the effectiveness of the proposed approach for uncertain and unstable systems.

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Notes

  1. The coefficients \(a_{n}\) and \(b_{m+1}\) are only inserted to clarify the structure of the matrices.

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Acknowledgements

The work was supported by Brazilian agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Apoio a Pesquisa do Distrito Federal (FAPDF).

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  1. Department of Electrical Engineering, University of Brasilia – UnB, Brasília, DF, 70910-900, Brazil

    Eduardo S. Tognetti & Guilherme A. de Oliveira

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  1. Eduardo S. Tognetti
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  2. Guilherme A. de Oliveira
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Correspondence to Eduardo S. Tognetti.

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Tognetti, E.S., de Oliveira, G.A. Robust State Feedback-Based Design of PID Controllers for High-Order Systems with Time-Delay and Parametric Uncertainties. J Control Autom Electr Syst 33, 382–392 (2022). https://doi.org/10.1007/s40313-021-00846-2

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