PID Regulatory Control Design for a Double Tank System Based on Time-Scale Separation

  • Marian BlachutaEmail author
  • Robert Bieda
  • Rafal Grygiel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11431)


An intuitive and simple yet efficient novel approach to the PID control system synthesis for load disturbance rejection in a cascaded tanks system is presented. It is assumed that the controller is fitted with a first order noise filter. The design method consists in choosing appropriate values of filter and controller parameters such that a time-scale separation takes place between control signal and output dynamics while keeping the noise amplification gain at a reasonable value. As a result, low measurement noise results in very high performance of load disturbance rejection. Moreover, the solution shows high degree of robustness against changes of the working point. Simple formulas providing analytical solutions for extrema of time responses are derived that allow to design control system with predefined characteristics.



The research has been supported by the Department of Automatic Control Grant No. 02/010/BK18/0102.


  1. 1.
    Apkarian, J.: Coupled Water Tank Experiments Manual. Quanser Consulting Inc., Markham (1999)Google Scholar
  2. 2.
    Åström, K.J., Österberg, A.-B.: A teaching laboratory for process control. Control Syst. Mag. 6(5), 37–42 (1986)CrossRefGoogle Scholar
  3. 3.
    Åström, K.J., Hägglund, T.: PID Controllers: Theory, Design and Tuning. Instruments Society of America, Pittsburgh (1995)Google Scholar
  4. 4.
    Bieda, R., Blachuta, M., Grygiel, R.: A new look at water tanks systems as control teaching tools. IFAC World Congr. 13480–13485 (2017a). Toulouse, FranceCrossRefGoogle Scholar
  5. 5.
    Bieda R., Blachuta, M., Grygiel, R.: High performance PID control of a coupled tanks system as an example for control teaching. In: 22nd International Conference on Methods and Models in Automation and Robotics, MMAR 2017, Miedzyzdroje, Poland, pp. 803–808 (2017).
  6. 6.
    Blachuta M., Bieda, R., Grygiel, R.: High performance single tank level control as an example for control teaching. In: 25th Mediterranean Conference on Control and Automation, MED 2017, Valletta, Malta, pp. 1053–1058 (2017).
  7. 7.
    Lund University: Reglerteknik AK, Laboration 2. Modellbygge och beräkning av PID-regulatorn, Assistenthandledning, Lund tekniska högskola (2013)Google Scholar
  8. 8.
    Visioli, A.: Practical PID Control. Springer, London (2006). Scholar
  9. 9.
    Segovia, V.R., Hägglund, T., Åström, K.J.: Measurement noise filtering for common PID tuning rules. Control Eng. Pract. 32, 43–63 (2014)CrossRefGoogle Scholar
  10. 10.
    Soltesz, K., Grimholt, Ch., Skogestad, S.: Simultaneous design of proportional-integral-derivative controller and measurement filter by optimisation. IET Control Theory Appl. 11(3), 341–348 (2017). Scholar
  11. 11.
    Yurkevich, V.D.: Design of Nonlinear Control Systems with the Highest Derivative in Feedback. World Scientific, Singapore (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Silesian University of TechnologyGliwicePoland

Personalised recommendations