Design and implementation of filters and PID controllers for dynamic system stabilization

In this work, the design and implementation of digital filters and discrete PID controllers to stabilize a given transfer function is addressed. Using Matlab's c2d tool, the original transfer function is discretized, and it is observed that the plant does not reach the desired value of 1. A digital filter is implemented by multiplying by a scale factor. Subsequently, the root locus method is used to analyze the behavior of the refed plant, revealing a slow response to stepping. Then, the Ziegler-Nichols method is applied to tune a PID controller. The resulting parameters generate a response with a slight overshoot. The PID Tuner tool is used to adjust the PID parameters, achieving a smoother response and faster stabilization. The paper addresses each phase of the design, from initial discretization to PID controller tuning and validation.