On the Design of Robust Four Degree of Freedom Controllers for Linear Discrete-Time Systems

The aim of this paper is to consider an alternative robust design method of integrated controls and diagnostics by making use of the so-called four degree-of-freedom (4-DOF) controller. This controller has 2-inputs and 2-outputs whereby the additional controller output is viewed as a diagnostic output which detects sensor and actuator failures. The 4-DOF controller is a simple case of the standard regulator framework; therefore, the design of integrated controls and diagnostics can thus be done in the framework of
$\mathcal {H}^{2}$
and
$\mathcal {H}^{\infty }$
whereby the latter gives the advantage of synthesizing the 4-DOF controller in a single step approach. Unlike previous methods, explicit state-space formulae are derived (in discrete-time) for a 4-DOF controller. For the
$\mathcal {H}^{\infty }$
case it stabilizes an augmented plant with respect to unstructured additive coprime factor perturbations whilst simultaneously providing robust control and diagnostic performance when uncertain plants are used. Moreover, the 4-DOF
$\mathcal {H}^{\infty }$
controller derived (albeit, of adequate complexity that can be further reduced using model/controller reduction techniques) is applied to a distillation system example to illustrate the effectiveness of the proposed unified framework.