Three Two-Dimensional Fuzzy Regulators for PID Controller Parameter Tuning (Kp, Ki, Kd)

The system employs three two-dimensional fuzzy regulators to adjust the parameters Kp, Ki, and Kd of a PID controller. The control mechanism operates by processing two input variables - error (e) and error change (ec) - through three fuzzy controllers (FC1, FC2, FC3). Each controller performs three sequential operations: fuzzification (converting crisp inputs to fuzzy sets using membership functions), fuzzy logic inference (applying if-then rules from a predefined rule base), and defuzzification (converting fuzzy outputs to precise adjustment values). In practical implementations, designers typically create triangular or Gaussian membership functions for input variables (e, ec) and output variables (ΔKp, ΔKi, ΔKd). The rule base might contain statements like "IF e is Large AND ec is Small THEN ΔKp is Medium". The centroid method is commonly used for defuzzification to compute final parameter adjustments. Additional factors such as system stability and response speed can be incorporated during the fuzzy inference process. For code implementation, one would structure fuzzy associative matrices for each parameter and use interpolation methods for smooth transitions between rules. Fine-tuning the fuzzy controllers through rule optimization and membership function adjustment can further enhance system control performance by improving rise time, reducing overshoot, and minimizing steady-state error.