Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Abstract

Repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature. This paper discusses repetitive and iterative learning control from an internal model principle point of view. This allows the formulation of existence conditions for multivariable implementations of repetitive and learning control. It is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic disturbances. The design of such controllers is discussed. Next it is shown that iterative learning control can be implemented in the format of a disturbance observer/compensator. It is shown that the resulting control stucture is dual to the repetitive controller, and that both constitute an implementation of the internal model principle. Consequently, the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design procedure of the internal model framework, allowing to trade-off the convergence speed for periodic-disturbance cancellation versus other control objectives, such as stochastic disturbance suppression.

A common setting for the design of iterative learning and repetitive controllers with experimental verification

“…This conclusion holds for all choices of ILC algorithm, and means thatˆ.´/ always operates in the input space of the plant P .´/. This conclusion is also supported by results in [5,6].…”

“…Clearly in this caseˆ.´/ operates in the output space, and has the structureˆ.´/ WD .´N I m I m / 1 . Further details relating the structure of ILC and RC to the forms shown in Figure 1 and Figure 2 respectively are given in [5,6]. Although ILC assumes a fixed initial condition at the start of each new trial, RC has no such resetting and merely assumes that the initial condition at the start of each new period is the final condition at the end of the previous period.…”

“…The first case implements RC and the second ILC, in either current-error feedback or previous-error feedforward terms, and this property is termed duality in [6].…”

Stabilization of Discrete Linear Repetitive Processes with Switched Dynamics

“…As noted previously, this approach has been used in iterative learning control, see, for example, (De Roover et al, 2000;Moore, 2000;Norrlof & Gunnarsson, 2002;Rotariu et al, 2004) but most often the end point in analysis is to produce an equivalent 1D model for stability analysis over the finite trial length, i.e., asymptotic stability. In the analysis here it is the stronger property of stability along the pass which is considered and we aim to design the control law using the basic (i.e., non-lifted) model.…”

“…(De Roover, Bosgra & Steinbuch, 2000;Moore, 2000;Norrlof & Gunnarsson, 2002;Rotariu, Dijkstra & Steinbuch, 2004). This enables the analysis of parameter variant models to be replaced by that of parameter invariant models (but, obviously, of higher dimensions).…”