Model Order Reduction and Control Design for a Time Delay System

Time-delay systems in power and industrial control applications pose significant challenges due to their infinite-dimensional nature. This paper proposes a Hybrid Model Control Design (HMCD) integrating Model Order Reduction (MOR) with Enhanced Differential Evolution (EDE). The method employs Padé approximation, Mihailov stability criterion and moment matching to construct a reduced-order model (ROM), optimized via EDE to minimize Integral Square Error (ISE) while ensuring stability and energy preservation. An Internal Model Control (IMC) structure is converted to Proportional–Integral–Derivative (PID) form for practical implementation. Validation on load-frequency control (LFC) and continuous stirred tank reactor (CSTR) systems achieves Integral Absolute Error (IAE) [Formula: see text] 2.30, ISE [Formula: see text] 0.998, Integral Time Absolute Error (ITAE) [Formula: see text] 9.03 and Integral Time Squared Error (ITSE) [Formula: see text] 1.23 — drastically outperforming conventional IMC (IAE [Formula: see text] 72.54, ISE [Formula: see text] 13.99) and metaheuristic methods (errors [Formula: see text]). The framework enables efficient real-time control of high-order time-delay systems.