Sensitivity-Informed Assessment of Two-Degree-of-Freedom PID Control for a Refrigeration Unit

Carbon dioxide (R-744) refrigeration systems combine low environmental impact with high operating pressures, nonlinear thermodynamic behaviour, and strong interactions among their components and control loops. These features make control-system design particularly challenging, since the closed-loop effects of controller-parameter variations cannot be fully characterized without accounting for the nonlinear and coupled plant dynamics. To investigate these relationships, this thesis presents a sensitivity-informed assessment of two decentralized ISA-PID 2DOF controllers regulating superheat and suction pressure in a nonlinear dynamic model of a CO2 refrigeration unit implemented in MATLAB/Simulink–Simscape. The assessment is carried out through a Global Sensitivity Analysis based on the Morris Elementary Effects method, applied to the ten controller parameters comprising the proportional, integral, and derivative gains and the two set-point weights of each loop. Three excitation scenarios are considered: superheat-reference tracking, suction-pressure-reference tracking, and rejection of an evaporator-inlet-temperature disturbance. The analysis combines normalized error-based performance criteria and integrated controller-output metrics, while signed elementary effects and rank correlation provide complementary information on the sign and monotonic direction of parameter effects. The principal campaigns are also repeated at a second thermodynamic operating condition to assess whether the dominant sensitivity relationships remain recognizable when the plant equilibrium changes. The results show that the two integral gains form the most recurrent feedback sensitivity core, whereas the proportional set-point weights become particularly relevant when their corresponding reference is directly excited. The functional distinction expected from classical 2DOF control therefore remains recognizable in the nonlinear coupled system. At the same time, controller-parameter effects propagate across the two decentralized loops through the thermodynamic plant, revealing recurrent and asymmetric cross-loop sensitivities. The dominant relationships remain recognizable at the second operating condition, although sensitivity magnitudes and secondary rankings vary. The resulting sensitivity map does not prescribe an optimal tuning. Instead, it identifies the controller parameters and cross-loop relationships that deserve priority in subsequent controller design and optimization, providing a structured basis for exploiting the available 2DOF degrees of freedom without treating the entire parameter space as uniformly relevant.