Linear and non Linear Control Systems:

Linear Control Systems:

 In order to understand the linear control system, we should first understand the principle of superposition. The principle of superposition theorem includes two important properties and they are explained below:

Homogeneity: A system is said to be homogeneous, if we multiply input with some constant A then the output will also be multiplied by the same value of constant (i.e. A).

Additivity: Consider we have a system S and we are giving the input to this system as a1 for the first time and we are getting the output as b1 corresponding to input a1. On the second time we are giving input a2 and correspond to this we are getting the output as b2.

Now consider this time we are giving input as a summation of the previous inputs (i.e. a1 + a2) and corresponding to this input consider we are getting the output as (b1 + b2) then we can say that system S is following the property of additivity. Now we are able to define the linear control systems as those types of control systems which follow the principle of homogeneity and additivity.

Examples of Linear Control System:

Consider a purely resistive network with a constant DC source. This circuit follows the principle of homogeneity and additivity. All the undesired effects are neglected and assuming ideal behavior of each element in the network, we say that we will get linear voltage and current characteristic. This is the example of a linear control system.

Non-linear Control Systems:

We can simply define a nonlinear control system as a control system which does not follow the principle of homogeneity. In real life, all control systems are non-linear systems (linear control systems only exist in theory). The describing function is an approximate procedure for analyzing certain nonlinear control problems.

Examples of Non-linear System

A well-known example of a non-linear system is a magnetization curve or no load curve of a DC machine. We will discuss briefly no-load curve of DC machines here: No load curve gives us the relationship between the air gap flux and the field winding mmf. It is very clear from the curve given below that in the beginning, there is a linear relationship between winding mmf and the air gap flux but after this, saturation has come which shows the nonlinear behavior of the curve or characteristics of the nonlinear control system.