Smith predictor

The Smith predictor (invented by O. J. M. Smith in 1957) is a type of predictive controller for systems with pure time delay. The idea can be illustrated as follows.

Suppose the plant consists of ${\displaystyle G(z)}$ followed by a pure time delay ${\displaystyle z^{-k}}$.

As a first step, suppose we only consider ${\displaystyle G(z)}$ (the plant without a delay) and design a controller ${\displaystyle C(z)}$ with a closed-loop transfer function ${\displaystyle H(z)={\frac {C(z)G(z)}{1+C(z)G(z)}}}$ that we consider satisfactory.

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