PID controllers are used in many applications and are considered an example of a fixed structure controller. For each specific system, the controller's PID parameters must be adjusted accordingly. Therefore, database-driven control, which automatically adjusts PID controller parameters using a large amount of experimental data, is attracting attention. Database-driven control is one of the methods that does not require model information. Therefore, in database-driven PID (DD-PID), the Jacobian of the system used for the steepest descent is unknown. In this paper, we propose an optimization method using gradient descent based on a local model of the system and confirm its effectiveness through simulation using the polystyrene reactor model as an example.