Variable speed refrigeration system (VSRS) with a variable speed drive is widely used in industry because of its quick reaction capability over a wide range of heat load variations, energy-saving performance, and high precision temperature control ability. The VSRS consists of a variable speed compressor, an electronic expansion valve (EEV), and heat exchangers. Specifically, it is interconnected by long pipes, resulting in dead times and frequent heat access through exposed pipes. Therefore, it has strong inherent nonlinear characteristics, such as time delay in the operational ranges. Thus, it is difficult to perform linear approximation modeling for VSRS and accurate control.
The dynamic model mainly uses a low-dimensional transfer function model obtained through experiments, to design a controller for VSRS. Low-dimensional transfer function model is easily obtained by experiments near the operating point. However, in practical operation, perturbation occurs due to changes in ambient temperature and operating point that are different from those during modeling. Therefore, a robust controller against the model uncertainty and disturbance is essential for accurate temperature control because VSRS is affected by heat load, i.e., disturbance.
Applying a model-based robust control with robustness to disturbance and model uncertainty for VSRS control is desirable. H-inf control is widely known as a model-based representative robust control method. H-inf control treats various uncertainties in the form of unstructured perturbation to a nominal model. However, the H-inf theory becomes somewhat conservative when the model uncertainty becomes highly structured. On the other hand, The μ-synthesis control (μ-controller) has been applied to improve the aforementioned problems of the . The μ-controller can be made less conservative than by considering the structure of the model uncertainty. The μ-synthesis controller treats model uncertainty as structured perturbation; it is designed using structured singular value. The μ-control simultaneously solves the robust stability and robust control performance (robust performance) problem by designing an optimal controller for structured uncertainty. Therefore, μ-controller is a control technique that allows the direct inclusion of modeling errors or uncertainties, measurement noises, disturbances, and performance requirements into a common formulation. Despite its advantages, there are only a few research papers on μ-synthesis controller that apply μ-controller to VSRS control. However, those studies did not optimize the weighting functions, which are crucial design parameters; moreover, some of those have not been experimentally verified. Furthermore, it is difficult to find servo control of μ-synthesis for accurate temperature control.
This paper introduces simulated annealing (SA) algorithm?a metaheuristic approach?to solve this problem. SA is an optimization technique that simulates an annealing process in which molecules of a high temperature substance are gradually cooled down to reach the lowest energy state. Parameters were selected to ensure robust stability and robust performance against the model uncertainty and disturbance by simultaneously optimizing the weighting functions using SA.
The μ-controller that satisfies robust stability and robust performance for VSRS was formulated as a mixed sensitivity problem using frequency weighting functions, where the weighting functions were optimized via SA. The validity of the designed μ-controller was confirmed through simulations and experiments for a VSRS-based oil cooler system. Moreover, its effectiveness was verified through performance comparison with the PI controller.