# Analyzing Non-Linearities in Control Systems using Simulink

#### What is a non-linearity?

By definition, non- linear systems are those that do not follow the principle of superposition and homogeneity. Simply speaking, change in input is not proportional to the change in output. In practice, all physical systems have some kind of non-linearity. Sometimes it may even be desirable to introduce a non-linearity deliberately in order to improve the performance of a system in order to remove existing non-linearities or to make its operation safer.

The non-linearities we will be studying are:

1.  Saturation Non-Linearity

This is perhaps the most common of all nonlinearities. All devices when driven by sufficiently large signals, exhibit the phenomenon of saturation due to limitations of their physical capabilities. Saturation in the output of electronic, rotating, and flow amplifiers are some of the well-known examples.

A dead-zone is a kind of nonlinearity in which the system doesn’t respond to the given input until the input reaches a particular level. Many devices do not respond to small signals, i.e., if the input of amplifiers is less than some small value, there will be no output. This is true for many sensors and amplifiers. These devices are said to have deadzone (no output for given values of input). The following figure shows linear-segmented approximation of deadzone nonlinearity.

2.  Open the Simulink Library Browser by clicking on the icon with four squares (encircled in the figure below).

3.  Make the following connection. All the required blocks can be found in the Source, Sink, and Discontinuities section.

4.  Simulate the file by clicking on the green play icon, then double click on the scope to view the output. The output is as follows:

5.  Replace the Ramp Signal with the Step Signal in the connection. The step signal can be found in the Sources section. The connection is as follows:

6.  Simulate the above connection and double click on scope. The output obtained is as follows:

7.  Replace the Ramp signal with the Sine wave which will also be found in the sources section in the Simulink Library Browser. The connection obtained will be as follows:

8.  Simulate the above connection and double click on the scope. The output obtained is as follows:

9.  Replace the saturation nonlinearity with the deadzone nonlinearity. The deadzone linearity can be found in the discontinuities section in the Simulink Library Browser. The connection obtained will be as follows:

10.  Simulate the above connection and double click on the scope. The output obtained will be as follows:

#### Conclusion

The saturation and deadzone nonlinearity were simulated in Simulink for different types of input signals.

##### Shivani Singh

A final year engineering student from Bharati Vidyapeeth's College of Engineering, New Delhi with great zeal and passion for writing and technology. I have great love for food, nature, reading and am a true Delhiite at heart !

### Recommended Posts

##### Counters using conditionally executed subsystems | Simulink Tutorial

16 Feb 2018 - Simulink, Tutorial

##### Regulating drum boiler pressure

16 Feb 2018 - Simulink, Tutorial