In the early development, an analog system, not containing a digital device like computer,in which some of the signals were sampled was referred to as a sampled data system. With the advent of digital computer, the term discrete-time system denoted a system in which all its signals are in a digital coded form. Most practical systems today are of hybrid nature, i.e., contains both analog and digital components.

Before proceeding to any depth of the subject we should first understand the reason behind going for a digital control system. Using computers to implement controllers has a number of advantages. Many of the difficulties involved in analog implementation can be avoided. Few of them are enumerated below.

1. Probability of accuracy or drift can be removed.

2. Easy to implement sophisticated algorithms.

3. Easy to include logic and nonlinear functions.

4. Reconfigurability of the controllers.

1.1 A Naive Approach to Digital Control

One may expect that a digital control system behaves like a continuous time system if the sampling period is sufficiently small. This is true under reasonable assumptions. A crude way to obtain digital control algorithms is by writing the continuous time control law as a differential equation and approximating the derivatives by differences and integrations by summations. This will work when the sampling period is very small. However various parameters, like overshoot, settling time will be slightly higher than those of the continuous time control.

Example: PD controller
A continuous time PD controller can be discretized as follows:

where represents the discrete time instants and is the discrete time step or the sampling period. We will see later the control strategies with different behaviors, for example deadbeat control, can be obtained with computer control which are not possible with a continuous time control.