Pi-type fuzzy controller tuning by membership functions parameters determination using geometric series

Introduction. In the issue we consider the possibility of geometric series application for fuzzy logic controller tuning. Triangular and trapezoidal membership functions are often used for fuzzy controller parameters description, and determination of those functions bases is a common way to tune the controller. Our related publications review revealed that there is no universal fuzzy controllers tuning method, and that approaches to the problem are usually quite difficult and not sufficiently described to understand and reiterate. Aim. So for the purpose of our research we assumed that bases of fuzzy controller input and output parameters membership functions could be described with a numerical sequence. In that case the entire tuning procedure may be reduced to mere selection of such numerical sequence parameters. Materials and methods. Geometric series with unit as a first member were chosen to avoid ambiguity, different ratios from 1.5 to 3.5 with an increment of 0.2 were chosen for second and third series members calculations. Calculated values were used as membership functions term bases for eleven subsidiary linguistic variables. Then we obtained ranges of control, control error and its time integral values variations for a specific control object using automatically tuned PI-controller. Using MATLAB FIS-editor we constructed PI-type fuzzy controller assuming that both of its input and an output parameters has five terms. By projecting the subsidiary linguistic variables gained earlier on each parameter range we obtain eleven different types of PI-type fuzzy controller tunings. They then were applied for time delay technological object controlling, seven of which proved to be functioning. Results. Comparison of functioning fuzzy controllers’ transient processes with corresponding ordinary PI-controller transient process allowed us to determine that all seven PI-type fuzzy controllers’ quality criteria values are much better that those of ordinary PI-controller. Conclusion. Our research showed that usage of geometric series can be an effective and easy way to obtain fuzzy controllers tunings of satisfactory quality.