In the previous post I explained the ILC controllers and compared them to the conventional feedback controllers. In this post I show a simple example that employs an ILC.

Check the following simple, linear plant:

In this system, is the input at time , and is the output of the system at time . The initial condition of the system also is represented with two simple equations.

We want to force the system to follow a square wave such as:

The ILC algorithm works as follows:

- consider and the initial input (first iteration, )
- run the system with this input and keep the result ()
- compute the error as $latex
- compute the next input using the previous result as:
- use and jump to 2.

By implementing this simple algorithm we can get the following result. For this result I have chosen .