IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4229-d1256557.html
   My bibliography  Save this article

Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models

Author

Listed:
  • Mikulas Huba

    (Institute of Automotive Mechatronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, SK-812 19 Bratislava, Slovakia)

  • Pavol Bistak

    (Institute of Automotive Mechatronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, SK-812 19 Bratislava, Slovakia)

  • Damir Vrancic

    (Department of Systems and Control, J. Stefan Institute, SI-1000 Ljubljana, Slovenia)

Abstract

The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model.

Suggested Citation

  • Mikulas Huba & Pavol Bistak & Damir Vrancic, 2023. "Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models," Mathematics, MDPI, vol. 11(20), pages 1-32, October.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4229-:d:1256557
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4229/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/20/4229/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Runzhi Wang & Xuemin Li & Jiguang Zhang & Jian Zhang & Wenhui Li & Yufei Liu & Wenjie Fu & Xiuzhen Ma, 2018. "Speed Control for a Marine Diesel Engine Based on the Combined Linear-Nonlinear Active Disturbance Rejection Control," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-18, December.
    2. Dina A. Zaki & Hany M. Hasanien & Mohammed Alharbi & Zia Ullah & Mariam A. Sameh, 2023. "Hybrid Driving Training and Particle Swarm Optimization Algorithm-Based Optimal Control for Performance Improvement of Microgrids," Energies, MDPI, vol. 16(11), pages 1-18, May.
    3. Mikulas Huba & Damir Vrancic, 2021. "Delay Equivalences in Tuning PID Control for the Double Integrator Plus Dead-Time," Mathematics, MDPI, vol. 9(4), pages 1-14, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mikulas Huba & Pavol Bistak & Damir Vrancic, 2022. "Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes," Mathematics, MDPI, vol. 11(1), pages 1-24, December.
    2. Zhong Guan & Hui Wang & Zhi Li & Xiaohu Luo & Xi Yang & Jugang Fang & Qiang Zhao, 2024. "Multi-Objective Optimal Scheduling of Microgrids Based on Improved Particle Swarm Algorithm," Energies, MDPI, vol. 17(7), pages 1-20, April.
    3. Mikulas Huba & Damir Vrancic, 2022. "Tuning of PID Control for the Double Integrator Plus Dead Time Model by Modified Real Dominant Pole and Performance Portrait Methods," Mathematics, MDPI, vol. 10(6), pages 1-25, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4229-:d:1256557. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.