The method of optimal constrained tuning of pi-controllers

Authors

  • Yu. Romasevych National University of Life and Environmental Sciences of Ukraine image/svg+xml
  • V. Loveikin National University of Life and Environmental Sciences of Ukraine image/svg+xml
  • A. Lyashko National University of Life and Environmental Sciences of Ukraine image/svg+xml
  • V. Makarets National University of Life and Environmental Sciences of Ukraine image/svg+xml

DOI:

https://doi.org/10.31548/energiya2019.03.129

Abstract

Abstract. In the work, a method is developed for optimal tuning of PI-controllers with constraints. The method is based on reducing the tuning problem to the unconstrained optimization problem. In order to reduce the problem, a special complex criterion has been proposed. It is characterized by the desired topological properties. The latter have been obtained using weight coefficients that take into account the requirements for system stability, constraints and a set of criteria that reflect undesirable controlling indicators. The predetermined topological properties of the criterion made it possible to find its global minimum. In the work, a modification of the ME-PSO particle swarm method has been used. It is characterized by reinitialization of the swarm in the stage of stagnation.

In order to show the effectiveness of applying the method, the coefficients of the PI controller with the constraint on overshoot (it is assumed that it should be zero) have been calculated. The optimization criterion was the settling time. As a result, it was found that for four test transfer functions (second and third orders, one transfer function corresponds to an object of regulation with a time delay), the settling time is significantly decreased while ensuring overshoot constraint.

The obtained results were compared with those that correspond to the controllers that are tuned using other (known in engineering practice) PI-controller tuning methods (compared methods allow to obtain zero overshoot). In addition, the analysis of the quality of controlling was carried out using indicators: mean integral error and mean integral control.

The developed approach is quite universal. It might be used for the synthesis of optimal control systems, including non-linear ones.

Keywords: controller, optimization, criterion, constraints, tuning, particle swarm optimization

References

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Published

2019-10-17

Issue

No. 3 (2019)

Section

Статті

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