Sintonia de controladores PID usando planejamento experimental

Abstract

This work presents the application of experimental design methodology to the tuning of a PID controller for a first-order plus dead-time system, whose transfer function represents a tank level control process. The initial tuning, obtained using the Ziegler–Nichols method (P = 82.8 PWM/cm, I = 20.7 s, and D = 82.8 s), with saturation applied to the manipulated variable, showed unsatisfactory performance, characterized by an overshoot of 87.2%, rise time of 5.560 s, integral of squared error (ISE) of 8.621 cm² s, and integral of the absolute manipulated variable of 8332.0 PWM s. In order to achieve an optimized tuning, a 2³ factorial design with a central point was developed to evaluate the influence of the proportional (P), integral (I), and derivative (D) parameters on overshoot, rise time, and ISE. From the experiments, response surface models were fitted for each performance metric. The model associated with ISE was used to guide the path of steepest descent, resulting in the parameters P = 83.7500 PWM/cm, I = 0.0179 s, and D = 44.4038 s. This new tuning reduced the overshoot to 36.7%, rise time to 4.176 s, ISE to 4.577 cm² s, and the integral of the absolute manipulated variable to 6537.5 PWM s, indicating lower pump actuation effort throughout the simulation. Additionally, the Minitab response optimizer was applied, yielding an optimal point close to that obtained by the steepest descent method, with similar performance and high composite desirability. These results confirm the effectiveness of experimental design as a tool for PID controller tuning.