Consider that a battery in an electric vehicle is installed in a rectangular package such that...

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Consider that a battery in an electric vehicle is installed in a rectangular package such that all but two sides of the package are well insulated. It is given that the battery package has some thermal capacity C. Also, the process of the heat escaping through the two uninsulated walls is described by a thermal resistance R that is a function of the wall materials and their geometry. Therefore, the equation describing the temperature of the battery TB is as follows, where To is the ambient temperature outside of the package. Ств B = (1/1₁ + 12/2) Rewriting the given differential equation in terms of the difference between the battery's temperature and the ambient temperature, d = T3 - To, where the ambient temperature is assumed constant, the above equation becomes: cả + (T (To-TB) (1/2 + 1/12) 1- ) d=0 ₁ R₁ R2 If we additionally consider that the battery itself generates heat at a rate q, our final thermal battery model is the following: cắt l (a) Find the transfer function D(s)/Q(s). (b) Is this system BIBO stable? Does your answer make physical sense to you? Explain. (+1²) ² R₁ 12/₂) d = q Consider that a battery in an electric vehicle is installed in a rectangular package such that all but two sides of the package are well insulated. It is given that the battery package has some thermal capacity C. Also, the process of the heat escaping through the two uninsulated walls is described by a thermal resistance R that is a function of the wall materials and their geometry. Therefore, the equation describing the temperature of the battery TB is as follows, where To is the ambient temperature outside of the package. Ств B = (1/1₁ + 12/2) Rewriting the given differential equation in terms of the difference between the battery's temperature and the ambient temperature, d = T3 - To, where the ambient temperature is assumed constant, the above equation becomes: cả + (T (To-TB) (1/2 + 1/12) 1- ) d=0 ₁ R₁ R2 If we additionally consider that the battery itself generates heat at a rate q, our final thermal battery model is the following: cắt l (a) Find the transfer function D(s)/Q(s). (b) Is this system BIBO stable? Does your answer make physical sense to you? Explain. (+1²) ² R₁ 12/₂) d = q

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SOLUTION a To find the transfer function Ds Qs we can take the Laplace transform of the differential ... View the full answer