Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

The authors present an integrated approach for designing low‐order multi‐objective controllers for linear time‐delay systems (TDSs), combining recently developed methods for reduction of delay systems and fixed‐order control design, respectively. As a benchmark problem for process control applications, a model of an experimental heat transfer setup is used, which serves to motivate the adopted combination of model reduction and control technique. The former corresponds to a Krylov based reduction procedure, which is generalised to multiple‐input‐multiple‐output systems with state, input and output delays, and allows the adaptive construction of an accurate low‐order linear time‐invariant approximation of the original linear TDS. Concerning the latter, a fixed‐order controller is synthesised for the delay‐free approximation, exploiting a recently proposed linear matrix inequality based framework for fixed‐order controller design, and validated on the original model. In this way, the systematic overall design procedure, which is grounded in convex optimisation, complements approaches based on directly optimising stability and performance measures as a function of the controller parameters, which may lead to highly nonconvex, even non‐smooth optimisation problems. The successful design of a fixed‐order multi‐H 2 controller is validated on the benchmark problem, confirming the potential of the adopted approach for realistic industrial applications.