Optimality and iterative learning control: duality and input prediction

摘要

This thesis considers the use of optimal techniques within iterative learning control (ILC) applied to linear systems. Two different aspects are addressed: the first is the duality relationship existing between iterative learning control and repetitive control which allows the synthesis of controllers developed in one domain to be applied in the other. Significant extensions to existing duality framework are made by eliminating an explicit current-error feedback loop and providing the facility of both current error feedback, and previous error feedforward within the control structure. This, in turn, with the case when either state-feedback or output-feedback is used to solve the ILC control paradigm extends the range of underlying plants to which the framework can be applied. In this context optimal control is used to solve the stabilisation problem which yields solutions for both RC and ILC cases in terms of state-feedback, and for ILC in terms of output-injection. These significantly extend the range of underlying plants to which the framework can be applied. The second aspect addressed is the selection of a suitable first input. Whilst ILC algorithms have been shown to over a high level of performance both theoretically and in practical applications, resulting error convergence is generally highly dependent on the initial choice of input applied. Optimal techniques are therefore applied to generate the most appropriate initial input to speed up the learning process over subsequent trials. Two approaches are developed to tackle the problem, both involving optimal solutions. The first is frequency domain bases, and involves a description of system uncertainty. An input is constructed which maximises convergence in the presence of uncertainty and noise, making use of the Fast Fourier Transform (FFT). The second approach is time domain based and an initial input is constructed using a library of previous references and their associated converged inputs. The assumption of system linearity is used to find the choice of previous inputs which maximises robust convergence. It is then shown how the frequency and time domain schemes may be combined. Both the duality and initial input techniques developed in this thesis have been evaluated experimentally on a gantry robot testbed, and the results obtained confirm the success of these additions to the ILC/RC framework