This report formulates a minimal model based on a control theoretic framework to best describe the dynamics of perfect adaptation shown by the hyper osmotic shock response system in yeast. Using principles from adaptive control and stability theory, we step by step apply system identification methods to build a simple second order linear system with only a few parameters, that can concisely model the High Osmolarity Glycerol (HOG) Mitogen Activated Protein Kinase (MAPK) signaling dynamics. Validation with experimental data demonstrate that the model is sufficient to predict response of yeast to an arbitrary external osmotic shock stimulus.