Full State Feedback Control with Observer for Multi Variable Temperature Regulation in Vapour Compression Refrigeration Systems

Achieving tight and reliable temperature regulation across all functional components of a vapour-compression refrigeration system remains a persistent challenge, primarily because classical control strategies struggle to account for the multi-dimensional, nonlinear, and coupled thermal dynamics inherent to such systems. This paper presents the design, analysis, and simulation-based validation of a full state feedback controller augmented with an observer for multi-variable temperature control of a single-stage vapour-compression refrigeration system. The plant model, derived by applying energy conservation principles to each of the four major components — evaporator, compressor, condenser, and expansion valve — is cast in state-space form, and its controllability and observability are analytically confirmed. A pole placement approach is employed to compute the state feedback gain matrix K, a forward path gain Kf is subsequently introduced to enforce zero steady-state tracking, and a Luenberger observer is designed to estimate unmeasured system states, thereby reducing reliance on physical sensors. MATLAB/Simulink simulations are conducted across five progressive design stages, and transient response metrics — rise time, settling time, peak overshoot, and steady-state error — are extracted and benchmarked. The proposed full state feedback controller with forward gain and observer achieves rise times of approximately 1.1 s for the evaporator and compressor and 0.732 s for the condenser and expansion valve, with settling times below 2.0 s, zero peak overshoot, and zero steady-state error. Practical validation with realistic operating temperatures confirms the controller's capacity to track and maintain desired temperatures for efficient cooling.