Controller reduction via stable factorization and balancing

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Abstract
A controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper. For a certain right coprime factorization of an LQG designed controller K(s) = N(s)D-1(s), we approximate using a balancing technique the pair [D(s), N(s)]T by a low-order pair [D1(s), N1(s)]T defining a factorization of the reduced-order controller K 1(s) = N1(s)D1 -1(s). We show that reducing the controller order in this way is motivated in a natural way, which leads to the expectation of both good stability properties and good accuracy of approximation of closed-loop behaviour. This is also demonstrated in some examples.

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