Desenvolvimento de módulo didático para ensino de controle PID baseado no problema barra-bola

Abstract

This work addresses the development, tuning, and validation of a didactic module based on the ball-and-beam problem, designed to assist in the learning of PID control theory in practical process control classes. The system consists of two aluminum bars, where carts move along the rails. The position of one of the carts represents the setpoint, which is defined by the user. The position of the second cart is adjusted by the device, which changes the inclination of the bar using a servo motor to reach the defined setpoint. Ultrasonic sensors are employed to measure the position of the carts based on the distance from the carts to the sensor. To correct the defined position, the system uses a PID controller, where the control parameters can be adjusted by the user in manual mode, while in automatic mode, the parameters are predefined, resulting from the system's tuning. Two tuning methods were applied: the Ziegler-Nichols method and the Astrom and Hagglund method. The application of the methods resulted in different parameter sets, and validation metrics were used to identify the most efficient parameter set for control. The Integral of Absolute Error (IAE) metric was applied to the parameter sets from the tuning procedures, and the lowest value found was for the Astrom and Hagglund method, indicating that it provides better control performance. The prototype demonstrated the ability to perform control quickly and visually. These characteristics, combined with the possibility of changing the control parameters during the use of the module, are fundamental for the educational purpose of this module.