Skip to main content
SpringerLink
Log in

Estimation of Second-Order plus Time Delay Processes using Optimization Procedures

  • Published:
Journal of Control, Automation and Electrical Systems Aims and scope Submit manuscript

Abstract

In this paper, a nonparametric identification technique to estimate second-order plus time delay (SOPTD) processes from step response is proposed, named NMIE. It is based on optimization procedures by using the Nelder-Mead algorithm. Two cases are presented to perform the identification procedure. First, the SOPTD models are estimated using simulated data of a generic transfer function and then of a shell and tube heat exchanger. Second, the variables temperature, pH and level are estimated, using real data of a pH neutralization plant. The Integral Equation method (IE) is used to compare its results with the NMIE method. The results show that the NMIE algorithm estimated better SOPTD parameters with greater fidelity than the IE method when different SNRs and sampling times are used.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. We use the NMIE model and real data to compute the SNR of the temperature.

  2. We use the NMIE model and real data to compute the SNR of the pH.

  3. We use the NMIE model and real data to compute the SNR of the level.

References

  • Ahmed, S., Huang, B., & Shah, S. L. (2008). Identification from step responses with transient initial conditions. Journal of Process Control, 18(2), 121–130.

    Article  Google Scholar 

  • Bajarangbali, R., Majhi, S., & Pandey, S. (2014). Identification of FOPDT and SOPDT process dynamics using closed loop test. ISA Transaction, 53(4), 1223–1231.

    Article  Google Scholar 

  • Bobal, V., Kubalcik, M., Dostal, P., & Matejicek, J. (2013). Adaptive predictive control of time-delay systems. Computers and Mathematics with Applications, 66(2), 165–176.

    Article  MathSciNet  Google Scholar 

  • Cox, C., Tindle, J., & Burn, K. (2016). A comparison of software-based approaches to identifying FOPDT and SOPDT model parameters from process step response data. Applied Mathematical Modelling, 40, 100–114.

    Article  MathSciNet  Google Scholar 

  • Esakkiappan, C., Thyagarajan, T., & BlessyHepsiba, P. (2012). Identification of over damped second order plus dead time process using relay feedback test. In IEEE- International Conference on Advances in Engineering, Science And Management.

  • Fedele, G. (2009). A new method to estimate a first-order plus time-delay mode from step response. Journal of the Franklin Institute, 346, 1–9.

    Article  MathSciNet  Google Scholar 

  • Garcia, C. (2005). Modeling and Simulation of Industrial Process and Electromechanical Systems (In Portuguese). EDUSP, 2nd edition.

  • Kat, C. J., & Els, P. S. (2012). Validation metric based on relative error. Mathematical and Computer Modelling of Dynamical Systems, 18, 487–520.

    Article  MathSciNet  Google Scholar 

  • Kurokawa, R., Sato, T., Vilanova, R., & Konishi, Y. (2020). Design of optimal PID control with a sensitivity function for resonance phenomenon-involved second-order plus dead-time system. Journal of the Franklin Institute, 357(7), 4187–4211.

    Article  MathSciNet  Google Scholar 

  • Lagarias, J. C., Poonen, B., & Wright, M. H. (2012). Convergence of the restricted Nelder-Mead algorithm in two dimensions, SIAM. J. Optimization, 22, 501–532.

    MathSciNet  MATH  Google Scholar 

  • Ljung, L. (1999). System identification: Theory for the user (2nd ed.). Prentice Hall.

    MATH  Google Scholar 

  • Messikh, L., El-Guechi, H., & Benloucif, M. L. (2017). Critically damped stabilization of inverted-pendulum systems using continuous-time cascade linear model predictive control. Journal of the Franklin Institute, 354(16), 7241–7265.

    Article  MathSciNet  Google Scholar 

  • Narasimha, R. S., & Chidambaram, M. (2019). Model identification of critically damped second order plus time delay systems. Indian Chemical Engineer, 1, 67–77.

    Google Scholar 

  • Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. Computer Journal, 7, 308–313.

    Article  MathSciNet  Google Scholar 

  • Panda, R. C., Yu, C. C., & Huang, H. (2004). PID tuning rules for SOPDT systems: Review and some new results. ISA Transaction, 43, 283–295.

    Article  Google Scholar 

  • Rajapandiyan, C., & Chidambaram, M. (2012). Closed-loop identification of second-order plus time delay (SOPTD) model of multivariable systems by optimization method. Industrial & Engineering Chemistry Research, 51(28), 9620–9633.

    Article  Google Scholar 

  • Ramakrishnan, V., & Chidambaram, M. (2003). Estimation of a SOPTD transfer function model using a single asymmetrical relay feedback test. Computer and Chemical Engineering, 27, 1779–1784.

    Article  Google Scholar 

  • Şenol, B., Demiroğlu, U., & Matušů, R. (2020). Fractional order proportional derivative control for time delay plant of the second order: The frequency frame. Journal of the Franklin Institute, 357(12), 7944–7961.

    Article  MathSciNet  Google Scholar 

  • Silva, K. G., Aloise, D., Souza, S. X., & Mladenović, N. (2018). Less is more: Simplified Nelder-Mead method for large unconstrained optimization. Yugoslav Journal of Operations Research, 28(2), 153–169.

    Article  MathSciNet  Google Scholar 

  • Skogestad, S. (2003). Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control, 13(4), 291–309.

    Article  MathSciNet  Google Scholar 

  • Srivastava, S., Misra, A., Thakur, S., & Pandit, V. (2016). An optimal PID controller via LQR for standard second order plus time delay systems. ISA Transaction, 60, 244–253.

    Article  Google Scholar 

  • Yoo, C. K., Kwak, H. J., & Lee, I. B. (2001). Direct identification method of second order plus time delay model parameters. Chemical Engineering Research and Design, 79(7), 754–764.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Andritz Automation, Porto Alegre, Brazil

    Christiam Segundo Morales Alvarado

  2. Laboratory of Automation and Control, Department of Telecommunications and Control Engineering, Escola Politécnica of the University of São Paulo, São Paulo, Brazil

    Claudio Garcia

Authors
  1. Christiam Segundo Morales Alvarado
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claudio Garcia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christiam Segundo Morales Alvarado.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Morales Alvarado, C.S., Garcia, C. Estimation of Second-Order plus Time Delay Processes using Optimization Procedures. J Control Autom Electr Syst 32, 1563–1577 (2021). https://doi.org/10.1007/s40313-021-00788-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40313-021-00788-9

Keywords

Search

Navigation