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Abstract
Bananas is a kind of fruit that has many benefits and economic value. However, because it is perishable, an unappropriate post-harvest handling will decreasing the economic value. Many factors affect the ripening of bananas, one of it is ethylene gas. The ethylene gas that contained in the banana flows from the higher concentration to the lower one. The flow should be controlled in order to make it decaying properly. Temperature is a parameter that affects the flow of ethylene. This research offers storage temperature regulation such that the life time of banana could be extended. A mathematical model that represents the ethylene flow among the subpopulations is discussed. The population are devided into sub-population of unripe bananas, normal ripe bananas, ripe bananas wounds, and rotten bananas. The Stability of the model is evaluated in the critical point by Jacobian matrix and the Routh Hurwitz Criteria. The control is design by minimizing the temperature parameters using the Pontryagin Minimum Principle. Simulation is ilustrated in four cases, the firts case is no bananas wound initially, second case is no bananas rot initially, third case is no ripened normal bananas initially, and the fourth case is the bananas ripe initially exiting. The simulations shows that before controling the temperature, in the amount of 120 bananas of firts case, the proces is condcuted in sixteen days, ten days for the second case, nine days for the third case, and eight days for the fourth case. After controling the temperature, for some amount of bananas of firts case, the proces is conduted in seventeen days, eleven days for the second case, ten days for the third case, and nine days for the fourth case.