# Implementation of a digital temperature PID controller

**Introduction**

Regulators can be developed using analog and digital techniques.
Different mathematical methods are needed to analyze and design analog
and digital regulators. Though digital technology can replicate analog
system operation, its abilities go much further. For example, nonlinear
and self-adjusting systems, which are difficult to create using only an
analog system, can be designed. The main issue in digital control is
regulator structure and parameter definition.

After the parameters are determined, implementation of controller
algorithms is a simple task.

Regulator systems are widespread in industry applications. In many
cases, the process is passed with a preset temperature profile. These
applications need a corresponding regulator to satisfy process
requirements. The structure of the simplest regulator is presented in
Figure 1.

*Figure 1. Structure of the Simplest Regulator*

This structure presents an automatic control system with feedback. See the following definitions:

w(t): System function algorithm

u(t): Control effect

z(t): External disturbance impact, which must be minimized

y(t): Output variable

e(t) = w(t) - y(t): Output variable y(t) deviation from required value w(t)

Examples of output variables are: temperature in the stove, the engine shaft rotation speed, liquid level in the cistern, etc. The key to temperature control is to constantly adjust the output variable, y(t), so that it is near the value of w(t). Doing this, will minimize the control error, e(t).

Temperature adjustments can be made with an automatic Regulator, Gr (Figure 1), which is described by control law:

u(t) = Gr[e(t)].

To select the correct control law, the automatic regulator must know the mathematical model of the control object:

y(t) = Go[u(t)].

The mathematical model is usually a nonlinear, ordinary system of differential equations or differential equations in partial derivatives. Identifying the form and coefficients of these equations is done via the control object identification task. For conventional systems, mathematical models are commonly used and then the principal task is identification of equation coefficients. In many cases, these coefficients can be selected empirically during the system tuning process or by performing some special tests. Some features of control systems with feedback indicators are:

- Independent corrective action initialization when control variables deviate from reference values.
- Dynamic regulation of temperature variation with minimal detail.