Oct 9 – 13, 2022
FHNW Campus Brugg-Windisch
Europe/Zurich timezone

Iterative Learning –Deep Dive

Oct 12, 2022, 3:16 PM
1m
Lichthof (Building 1)

Lichthof

Building 1

Poster Low Level RF Workshop 2022 Poster Session

Speaker

SHANE KOSCIELNIAK (TRIUMF)

Description

The stability and convergence of an Iterative Learning Controller (ILC) may be assessed in time domain, by actually iterating the equations for a variety of inputs, or by finding the eigenvalues (lambda) of the iterated system (lambda-domain), or by forming the Z-transform and applying analogues of the Nyquist criteria. Two often-used criteria are (i) Asymptotic Convergence (AC) of the difference vectors, and (ii) monotonic convergence (MC) of the vector norm. Both criteria have lambda and Z domain counterparts. In this paper we apply all three methods and both convergence tests to a simple plant, namely an RF cavity oscillator with proportional and integral control, with an ILC wrapper to reject a periodic beam-loading disturbance. One, two and three-term (causal and acausal) learning function are used. Simplicity of the system means all convergence tests can be applied analytically. We can then ask the questions: do all the tests work, and do they agree on the stability? For this particular system, the Z-domain AC test agrees with the lambda-domain MC test. Moreover, soliton solutions appear in time domain for gain parameters constrained only by the AC test in lambda-domain.

Primary author

Presentation materials