Direct digital and adaptive control by input-output state variable feedback pole assignment

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Abstract
The paper describes a general approach to state variable feedback pole assignment for linear discrete-time systems. This is based on the definition of a non-minimal state space (NMSS) whose state variables are defined only in terms of the present and past values of the system output and the past values of its input. In more conventional block-diagram terms, it can be interpreted as an extension to a proportional-integral (PI) control system in which linear feedback and forward path digital filters are introduced to ensure the required closed-loop pole assignment, For this reason, we refer to it as a proportional-integral-plus or PIP system. The paper discusses the conditions for pole assignability. Practical examples which illustrate the performance of the PIP system in fixed gain and self tuning/adaptive applications are also discussed.

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