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An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain

Author

Listed:
  • Alejandro Rincón

    (Grupo de Investigación en Desarrollos Tecnológicos y Ambientales—GIDTA, Facultad de Ingeniería y Arquitectura, Universidad Católica de Manizales, Carrera 23 No. 60-63, Manizales 170002, Colombia
    Grupo de Investigación en Microbiología y Biotecnología Agroindustrial—GIMIBAG, Instituto de Investigación en Microbiología y Biotecnología Agroindustrial, Universidad Católica de Manizales, Carrera 23 No. 60-63, Manizales 170002, Colombia)

  • Fredy E. Hoyos

    (Departamento de Energía Eléctrica y Automática, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, Colombia)

  • John E. Candelo-Becerra

    (Departamento de Energía Eléctrica y Automática, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, Colombia)

Abstract

In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-defined and bounded: it takes on large but finite and user-defined values for tracking error values equal to or higher than the constraint boundary, and it comprises a previously known user-defined function for tracking error values far from the constraint boundary. This is a significant contribution that remedies two important limitations of common output constraint control designs: the infinite control effort for tracking error equal to or higher than the constraint boundary, and the impossibility of using previously known user-defined functions in the output feedback function for tracking error values far from the constraint boundary. As another contribution, the control design is based on the dead-zone Lyapunov function, which facilitates the achievement of convergence to a compact set with user-defined size, avoidance of discontinuous signals in the controller, and robustness to model uncertainty or disturbances. The proposed output feedback term consists of the product between two functions of the tracking error, an increasing function and a sigmoid function, whose exact expressions are user-defined. Finally, the effectiveness of the developed controller is illustrated by the simulation of substrate concentration tracking in a continuous flow stirred bioreactor.

Suggested Citation

  • Alejandro Rincón & Fredy E. Hoyos & John E. Candelo-Becerra, 2022. "An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain," Mathematics, MDPI, vol. 10(11), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1855-:d:826590
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    References listed on IDEAS

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    1. Mei, Keqi & Ding, Shihong, 2022. "Output-feedback finite-time stabilization of a class of constrained planar systems," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Wang, Shuzhan & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Ding, Chen & Ma, Li & Ding, Shihong, 2021. "Second-order sliding mode controller design with mismatched term and time-varying output constraint," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    4. Liu, Lu & Ding, Shihong, 2021. "A unified control approach to finite-time stabilization of SOSM dynamics subject to an output constraint," Applied Mathematics and Computation, Elsevier, vol. 394(C).
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