Electrical components play a crucial role in filtering noise in analog PID controllers, while digital PID controllers achieve similar results through software-based approximations of these components. Noise can originate from long electrical lines and environmental factors, necessitating careful design to identify and mitigate significant sources of interference. Digital systems utilize Z-transforms for analysis, contrasting with the Laplace transforms used in analog systems, and can also incorporate non-linear techniques. The PID controller operates on an error signal, calculating proportional, integral, and derivative functions to adjust outputs effectively. Understanding the design process and specific controller manuals is essential for effective implementation and tuning of temperature controllers.