Exercise 12: Iterative Learning Control

Paper Exercises

This week's exercise is focused on Iterative Learning Control (presented in Lecture 12). It will take a look at:

• Stability and causality of discrete systems
• Convergence of the ILC algorithm
• Choice of filters L(z) and Q(z) and consequences

The exercises can be found in the exercise compendium Download exercise compendium.

The preparatory exercise Download preparatory exercise for lab 3 must be completed in advance in order to take the lab. If you have any trouble, feel free to ask at the exercise and we will help you.

Computer Exercises

Download the files ILC.m and simul.m

a) In the file ILC.m  a simple system is described that does not follow the reference signal very well. Complete the code by implementing the ILC algorithm using the given filter L(z). (Use Q(z) = 1) 

(Hint: use the given function "simul" to evaluate the output of a filter or system.)

b) Look at the definition of the filter L. Explain why it is implemented like this.

c) Is the ILC algorithm stable for all values of k_L? What values give convergence? What values give the quickest convergence?

Solution for the implementation of the algorithm can be found here.