Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2753

Full Length Research Paper

Internal model control - proportional integral derivative controller tuning for first order plus time delayed unstable systems using bacterial foraging algorithm

V. Rajinikanth1* and K. Latha2
1Department of Electronics and Instrumentation Engineering, St. Joseph’s College of Engineering, Chennai - 600 119, India. 2Department of Aerospace Engineering, Division of Avionics, MIT Campus, Anna University, Chennai - 600 044, India.
Email: [email protected]

  •  Accepted: 21 May 2012
  •  Published: 23 October 2012


This paper proposes a bacterial foraging optimization (BFO) algorithm based approach to tune the parameters of IMC-PID controller for a class of first order plus time delayed (FOPTD) unstable systems with various ‘θ/τ’ ratios. Initially, the proportional controller based system identification procedure is attempted to convert the higher order unstable process model into an equivalent FOPTD unstable model. Similarly the identification procedure is also carried out for a class of FOPTD unstable models. The converted FOPTD unstable model which shows a nominal model mismatch is then considered for the controller tuning manoeuvre. In this work, BFO algorithm is employed to search the best possible controller parameters such as Kp, Ki, Kd by minimizing the performance index, assigned to supervise the algorithm convergence. The relative efficiency of the BFO basedinternal model control - proportional integral derivative (IMC - PID) controller tuning has been confirmed through a comparative study with the existing nature inspired algorithms such as particle swarm optimization (PSO) and Ant colony optimization (ACO) algorithms. The robustness of the proposed controller tuning method is validated on an unstable continuous stirred tank reactor (CSTR) model. During this test, the CSTR process model with an introduced model uncertainty in the process gain ‘K’, process time constant ‘τ’ ‘and the delay time ‘θ’ are analysed. The result also testifies that the BFO tuned IMC-PID provides a robust performance in reference tracking for the CSTR process model with perturbed model parameters.


Key words: Unstable system, model order reduction, internal model control -proportional integral derivative (IMC - PID) controller, bacterial foraging algorithm, performance index, model uncertainty, robustness.