# DC motor modelling with Bond Graph

I am trying to construct an equation that describes the output torque as a function of lambda and omega I have obtained the following bond graph but I am unsure of how to proceed.

It might help to organize the equations a little in steps. I think you have all this above:

Output torque of system:

$$\tau_F$$

Output torque at motor:

$$\tau_0 = \tau_F/N$$

Motor output speed:

$$\omega_a = N\omega_M$$

Motor torque speed relationship$$^{*}$$:

$$\displaystyle{\frac{K_m}{R}}V_{in} = \frac{L}{R}\displaystyle{\frac{d\tau_0}{dt}} + \displaystyle{\frac{K_m^2}{R}}\omega_a$$

I think it is also correct to state that:

$$\lambda = LI_a$$

This doesn't quite answer your question, but maybe gives you some new ideas.

$$^{*}$$ See, e.g., Harry Asada, Introduction to Robotics, Chapter 2