Issues of algebra and optimality in Iterative Learning Control

Abstract In this thesis a set of new algorithms is introduced for Iterative Learning Control (ILC) and Repetitive Control (RC). Both areas of study are relatively new in control theory, and the common denominator for them is that they concentrate on controlling systems that include either reference signals or disturbances which are periodic. This provides opportunities for using past information or experience so that the control system learns the control action that results in good performance in terms of reference tracking or disturbance rejection. The first major contribution of the thesis is the algebraic analysis of ILC systems. This analysis shows that in the discrete-time case ILC algorithm design can be considered as designing a multivariable controller for a multivariable static plant and the reference signal that has to be tracked is a multivariable step function. Furthermore, the algebraic analysis reveals that time-varying algorithms should be used instead of time-invariant ones in order to guarantee monotonic convergence of the error in norm. However, from the algebraic analysis it is not clear how to select the free parameters of a given ILC algorithm. Hence in this thesis optimisation methods are used to automate this design phase. Special emphasis is placed on the so called Norm-Optimal Iterative Learning Control (NOILC) that was originally developed in (Amann:1996) as a new result it is shown that a convex modification of the existing predictive algorithm will result in a considerable improvement in convergence speed. Because the NOILC algorithm is computationally quite complex, a new set of Parameter-Optimal ILC algorithms are derived that converge under certain assumptions on the original plant. Three of these new algorithms will result in monotonic convergence to zero tracking error for an arbitrary discrete-time, linear, time-invariant plant. This a very strong property that has been earlier reported for only a small number of ILC algorithms. In the RC case it is shown that an existing RC algorithm that has been widely analysed and used in the research literature is in fact highly unrobust if the algorithm is implemented using sampled-data processing. Consequently, in this thesis a new optimality based discrete-time RC algorithm is derived, which converges to zero tracking error asymptotically for an arbitrary linear, time-invariant discrete-time plant under mild controllability and observability conditions