I'm trying to determine the transfer function of a simple DC motor connected to a resistive load, the added difficulty is in measuring the temperature of the resistor as it heats up (with a thermistor).
The equation dealing with temperature changes are Q = m*c*(dT/dt), where the energy put into a material is equal to the mass of the material multiplied by the specific heat capacity of the material and the change in temperature of the material. In this case, it is a wire-wound resistor.
The motor's shaft is being rotated and this produces energy which will heat up the resistor. So basically the transfer function is of the form: Temperature/Speed (Output/Input). When I do the resulting working out (see pictures), I am left with Temperature/Speed^2 and this is confusing me, what have I done wrong?
Note: s = Laplace
J = moment of inertia
kT = torque constant of motor
w = speed of motor
I got i = (s*J*w)/kT by equating:
kT*i = Jdw/dt, solving for i, and converting to Laplace domain
The integral of Torque*w (Power) is the energy of rotational movement = 0.5*J*w^2, and the integral of the power dissipated by an inductor is 0.5*L*i^2
The equation dealing with temperature changes are Q = m*c*(dT/dt), where the energy put into a material is equal to the mass of the material multiplied by the specific heat capacity of the material and the change in temperature of the material. In this case, it is a wire-wound resistor.
The motor's shaft is being rotated and this produces energy which will heat up the resistor. So basically the transfer function is of the form: Temperature/Speed (Output/Input). When I do the resulting working out (see pictures), I am left with Temperature/Speed^2 and this is confusing me, what have I done wrong?
Note: s = Laplace
J = moment of inertia
kT = torque constant of motor
w = speed of motor
I got i = (s*J*w)/kT by equating:
kT*i = Jdw/dt, solving for i, and converting to Laplace domain
The integral of Torque*w (Power) is the energy of rotational movement = 0.5*J*w^2, and the integral of the power dissipated by an inductor is 0.5*L*i^2
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