Smooth Sliding Control of Van der Pol Oscillators With a Single Input: Application to Micro-Thermal-Fluid Cooling Systems

In this letter, a smooth sliding control for robustly regulating a set of identical oscillatory systems, interconnected in parallel and with only one common input for all, is discussed. Our focus is primarily on oscillators resembling the Van der Pol type. To achieve this goal, a control strategy for synchronizing the oscillators is evaluated, using their phase response curve (PRC), thereby aligning them under identical conditions. The proposed control law, the combined synchronization plus regulation control actions, is applied to a flow micro-thermal-fluid cooling system in the two-phase regime, which has similarities to Van der Pol oscillators. In this application, the idea is to control the mass flow rate of the refrigerant fluid circulating in the microchannels and, consequently, the temperature at the walls of these channels, achieving better performance in heat transfer. Simulation results are presented to validate the proposed control strategy.