Three-Interacting Tank Controlled with Decentralized PI Controller Tuned Using Grey Wolf Optimization

  • K. AnbumaniEmail author
  • R. Rani Hemamalini
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 637)


In most of the process industries, modelling and control is the common problem for a multi-input–multi-output nonlinear process. In this chapter, for benchmark system the three-tank system is considered. Three-tank system is majorly used for many industrial applications in various domains. The main objective is to model the system and design a controller with good transient and steady-state performance for a nonlinear MIMO process, which is a challenging task. Decentralized PI controller is applied to three-interacting cylindrical tank process. The process under study is a MIMO process with two manipulated variable and three process outputs, height of the tanks. Decentralized controller needs controller design between the most interacting pair. Mathematical modelling is obtained from the first principle theorem, state-space and transfer function methods. The interaction among all the inputs and outputs are computed by relative gain array (RGA). Condition number is computed to check whether the process is ill-conditioned or not. The PI controller applied between the most interacting loops is tuned using grey wolf optimizer and the performance studies done for servo and regulatory operation. Simulation results show the proposed controller can be implemented for a non-square matrix.


Three-interacting cylindrical tank Decentralized controller RGA analysis Condition number Grey wolf optimizer 


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Sathyabama Institute of Science and TechnologyChennaiIndia
  2. 2.Sri Sairam Engineering CollegeChennaiIndia
  3. 3.Department of Electrical and Electronics EngineeringSt. Peter’s Institute of Higher Education and ResearchChennaiIndia

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