Exercise 13: 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(q) and Q(q) and consequences

The exercise can be found in the exercise compendium.

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(q). (Use Q(q) = 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.