A dynamic model for a thermostat

A new mathematical model for the dynamic behavior of a thermostat situated in the cooling system of an engine is presented. The model is in the form o f a system of delay-differential equations with hysteresis. An algorithm fo r numerical solutions of the model is described and some representative sim ulations are presented. The model predicts steady oscillatory solutions for certain ranges of the system parameters which are depicted for some parame ter values. Also, it predicts initial overshooting of the engine coolant te mperature. A Design of Experiments approach is used to characterize the reg ions in the model parameter space where oscillations occur and the results for those parameters which most influence the oscillations of solutions are presented.