Singular perturbation methods in the design of tracking systems incorprating inner-loop compensators and fast-sampling error-actuated controllers

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Abstract
Singular perturbation methods are used to exhibit the asymptotic structure of the transfer function matrices of discrete-time tracking systems incorporating linear multivariate plants which are amenable to fast-sampling error-actuated digital control only if extra plant output measurements are generated by the introduction of appropriate transducers and processed by inner-loop compensators. It is shown that these results greatly facilitate the determination of controller and transducer matrices which ensure that the closed-loop behaviour of such discrete-time tracking systems becomes increasingly non-interacting as the sampling frequency is increased. These general results are illustrated by designing a fast-sampling error-actuated digital controller for an aircraft.