The synthesis of an optimal on-off controller with minimum number of switchings
DOI:
https://doi.org/10.31548/energiya2020.02.023Abstract
Abstract. A method of synthesis of optimal on-off controllers with a minimum number of switchings is developed in the work. The essence of the method is in reducing the original problem to the problem of minimizing the function of the generalized criterion in the parameter domain of the controller. The topology of the latter makes it possible to sequentially find sets of controller parameters that ensure the fulfillment of ranked problem conditions.
An on-off-PI-controller has been proposed in the paper. Its parameters (gains of proportional and integral components of the controller, as well as the threshold at which switching of the control function is carried-out) have been found in the article.
In order to prove the effectiveness of the developed method, calculations were performed for four second- and third-order plants (one plant has a time delay). The quality of controlled processes was compared in terms of: average normal error, module of average control, overshoot, settling time and number of switchings. The results of the comparative analysis on these indicators showed that ceteris paribus the synthesized PI-controller has the least number of control switchings. This result extends the duration of use of the automatic control system actuators.
The calculations showed that the method of minimizing the number of switchings can be successfully applied within the methodology of synthesis of optimal regulators, which had been developed in the previous author’s researches.
Key words: on-off controller, synthesis, criterion, optimization, switching
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