I have a system that is modeled by the following differential equation:
db/dt = j(t)ha + k(Ta-b(t))
where db/dt is the rate of temperature change, j(t) is an input, ha, k, Ta are all constants, and b(t) is an output. Note that this is newtonian cooling with a heating input, j(t)*ha.
I want to find the transfer function is the laplace domain, B(s)/J(s). Taking the laplacian of the equation of interest, assuming all IC's are 0, yields: s*B(s)+k*B(s)-(k*Ta)/s = ha*J(s)
What I can't figure out is the term k*Ta/s is not a function of J(s) or B(s) so I can not get a transfer function of purely B(s)/J(s). Does anyone know how to solve this equation or a better way to find the transfer function relating the input to the output?