热力学系统建模

热力学系统由一个理想绝热空间、一个电热丝、一个传感器组成。

Thermal power is proportional to the control voltage

\[ P_C=K_C u_C, \quad K_C \text { is power amplification } \]

Temperature sensor output voltage is proportional to temperature

\[ u_T=K_T T \]

Power loss is proportional to the temperature difference between the cabinet and the environment

\[ P_D=K_D\left(T-T_0\right) \]

Temperature change in cabinet is proportional to the net heat power

\[ m C \frac{d T}{d t}=P_C-P_D \]