**1. Introduction**

Many industrial applications have digital closed loop control systems and the main algorithm used at these applications is the Proportional Integral Derivative structure (PID). This chapter presents some useful MATLAB commands that might be used as an instrument to analyze the closed loop and also to help the control system design. The first part presents the general standard structure of this controller, whereas MATLAB/SIMULINK programs are used to illustrate some design aspects. Script codes are used to describe the dynamic systems through the Laplace Transform and time response analysis of the system with time delays. Block diagram descriptions employed to represent the distillation process are used to analyses the Proportional Integral controller (PI) applied to the system. Performance analysis is conducted to implement an exhaustive searching algorithm applied in tuning PI parameters. At the second part a Smith Predictor structure is designed and presented to enhance the system performance. Some common feedback structures are presented and the classical literature will be referenced to present the main topics.

Along the chapter the tuning algorithms and the system analyses tools are presented through a specific application. This example is related to the tuning of PI control system applied to the temperature and pressure control in a distillation process designed to obtain the anhydrous ethanol and the hydrated ethanol from the sugarcane fermentation and distillation.
