Iterative learning control for nonlinear systems

If one cannot overcome the divergence problem by an adjustment of the operating point resp. the FRF, then one has to modify resp. extend the model class under consideration, i. e. one has to consider nonlinear models instead of linear ones. But in general, deriving adequate nonlinear physical models for the complex systems under consideration is likely to be too time consuming and too expensive, in particular for a commercially oriented company. Moreover, in general, the derived nonlinear model cannot describe the system exactly, and a model error is likely to remain. On the other hand, the majority of the existing research results for iterative learning control applied to nonlinear systems are restricted in the sense that the system resp. the model has to be of a specific structure, and the derived convergence conditions depend on the exact knowledge of the output equation resp. the partial derivatives related to the output equation. This is in particular a problem, if the model does not describe the system exactly and differences with respect to the partial derivatives between the system and the model occur. The approach chosen in the underlying thesis has the potential to overcome these difficulties. The class of nonlinear models considered in the underlying thesis is known as the class of operating regime based local model networks, or shorthand as the class of local model networks (LMN). In a local model network, local models of the system, which are valid only within some subset of the systems entire operating space, are combined to form a global nonlinear model in order to cover the entire operating space. We restrict ourselves to the typical case, i. e. the consideration of linear local models. This modelling approach can be viewed as a rather new topic in literature related to modelling of nonlinear systems, and main contributions to this field, which are important for the underlying thesis, are e. g. the PhD–thesis of Johansen and Angelis, which were published in 1994 resp. in 2001. Combining different local linear models to a global nonlinear model is likely to be acceptable from an industrial point of view, as the experienced engineer, as noted above, already gained some knowledge in the sense that linear models, derived in different operating points, may deliver satisfactory results. Moreover, besides the acceptable modelling procedure, the stability resp. convergence conditions, that will be derived in the underlying thesis, will not depend on any derivative related to the system’s output equation, and we will be able to develop robust synthesis procedures for the free parameters in the input update law.