Pareto Front Investigation of Multivariable Control Systems

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 151)


A multivariable thermal system with two inputs and two outputs is investigated. Its inputs are a pair of heaters controlled by a computer while its outputs are temperatures measured by two sensors. The system is fully interactive so two different controller structures can be used to ensure that the temperatures track their respective set-points. Both are multivariable controllers though one has a diagonal structure while the other has a triangular structure. Multi-objective optimization with a posteriori decision-making based on Pareto efficiency, level diagrams, hyper volumes and other performance indices is used to compare quantitatively the two controller structures when applied to a highly interactive multivariable system based on this plant.


  1. 1.
    Hamme H, Matuki K, Hiroki F, Miyazaki K (2010) Thermal MIMO controller for setpoint regulation and load disturbance rejection. Control Eng Pract 18:198–208Google Scholar
  2. 2.
    Rosenbrock HH (1974) Computer-aided control system design. Academic Press, New YorkGoogle Scholar
  3. 3.
    Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Parallel problem solving from nature—lecture notes in computer science, vol 1498/1998. pp 292–301Google Scholar
  4. 4.
    Rapson M (2007) Pareto analysis of controller design methodologies for integrator plus dead time process. IEEE Student Paper Contest, EuroCon 2007, pp 2607–2612Google Scholar
  5. 5.
    Braae M (2009) Multivariable control system. Course notes, Department of Electrical Engineering, 2009Google Scholar
  6. 6.
    Braae M (2009) Control theory for electrical engineers. UCT Press, Cape TownGoogle Scholar
  7. 7.
    Gambier A (2008) MPC and PID control based on multi-objective optimization. In: American control conference, 2008, pp 4727–4732Google Scholar
  8. 8.
    Graebe S (1994) Robust and adaptive control of an unknown plant: a benchmark of new format. Automatica 30(4):567–575MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Moore D (2010) Optimal controller comparison using pareto fronts. Technological developments in networking, education and automation. pp 209–214Google Scholar
  10. 10.
    Blasco X, Herrero JM, Sanchis J, Martínez M (2008) A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Inf Sci 178(2008):3908–3924Google Scholar
  11. 11.
    Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology, ZurichGoogle Scholar
  12. 12.
    Zitzler E, Thiele L, Laumanns M, Fonseca C, da Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7:117–132Google Scholar
  13. 13.
    Purshouse RC, Fleming PJ (2007) On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput 11(6):770–784Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of Cape TownCape TownSouth Africa

Personalised recommendations