What is control theory and how does it apply to non-linear systems?

What is control theory and how does it apply to non-linear systems?

Control theory is a field of engineering and mathematics that deals with the behavior of dynamical systems. It focuses on how to manipulate the inputs to a system to achieve desired outputs. Non-linear systems are those where the output is not directly proportional to the input, making them more complex to analyze and control.

Can you give me an example of a non-linear system?

Sure! A common example of a non-linear system is a pendulum. The motion of a pendulum is governed by non-linear equations, especially when the angle is large. This non-linearity affects how we control its motion.

What are some methods used to control non-linear systems?

Some methods include feedback linearization, sliding mode control, and adaptive control. Each method has its own advantages and is chosen based on the specific characteristics of the system.

How does feedback linearization work?

Feedback linearization works by transforming a non-linear system into an equivalent linear system through a change of variables. This allows us to apply linear control techniques to manage the system effectively.