Variable speed refrigeration systems (VSRSs) are widely used in various industrial fields due to their excellent energy saving ability and high-precision temperature control capability. VSRSs, which are composed of a variable speed compressor, an electronic expansion valve (EEV), and heat exchangers, have inherent nonlinear characteristics. Consequently, it is challenging to perform linear approximation modeling for VSRS controller design. Even a sophisticated numerical model in the form of a high-dimensional linear state-space model encounters difficulties in the suitable design of a VSRS control system due to the model uncertainties and disturbances including noises. Moreover, accurate identification of the system parameters in high-dimensional models for VSRSs is extremely laborious and tedious. Therefore, a control method that is based on a low-dimensional practical model for VSRSs and is robust against model uncertainties and disturbances must be formulated. The target temperature in VSRSs is controlled by regulating the mass flow rate of the refrigerant according to the change in the compressor rotation speed. Moreover, the superheat is controlled by adjusting the EEV opening angle to prevent adverse effects such as a decrease in the coefficient of performance (COP) due to superheated vapor compression and liquid back phenomenon. Therefore, the control system for a VSRS can be considered a multiple input/output (MIMO) system.
Sliding mode control (SMC) has attracted considerable attention as a robust control method for VSRSs. The SMC is based on variable structure control: the structure of the control system is changed, and the sliding mode is realized on the designed sliding plane (or line). Because the discontinuous control input of the SMC is independent of the system parameters of the nominal model, this control method is robust against model uncertainties and disturbances.
This paper proposes an SMC with a two-dimensional phase plane for a VSRS that is based on a low-dimensional practical state-space model. Using this approach, the proposed controller can render the behavior of state variables intuitively understandable and enhance the control performance. Moreover, the number of parameters to be identified, that can increase the model uncertainty, is significantly reduced, and modeling is facilitated. The state observer is composed of a Kalman filter to ensure robustness against process and observation noise. To suppress chattering due to the switching function, which is a notable problem in SMC, a saturation function is used instead of a signum function. Moreover, a feedforward controller is designed to avoid the deterioration in the transient characteristics of the main controlled variable due to the use of this saturation function. Furthermore, the genetic algorithm (GA) is used to avoid the cumbersome trial and error process for determining the design parameters of the saturation function, which influence the control performance, and for selecting the optimal values. The validity of the proposed controller is verified through simulations and experiments with a VSRS-based oil cooler system (OCS) as the plant. In addition, the effectiveness of the suggested controller is demonstrated by comparing the control performance with that of a conventional proportional?integral (PI) controller.