HW8.2.4.9
An electromechanical system has three electrical and one mechanical ports. The $\lambda$ - $i$ relations are:
$\begin{bmatrix} \lambda_{as} \\ \lambda_{bs} \\ \lambda_{r} \end{bmatrix} = \begin{bmatrix} 7 + \cos(2\theta) & 0 & 0.32\cos(\theta) \\ 0 & 7 - \cos(2\theta) & 0.32\sin(\theta) \\ 0.32\cos(\theta) & 0.32\sin(\theta) & 7\cos(4\theta) \end{bmatrix} \begin{bmatrix} i_{as} \\ i_{bs} \\ i_{r} \end{bmatrix}$
What is the co-energy at $i_{as} = 7 A$, $i_{bs} = 6 A$, $i_{r} = 6 A$ and $\theta = 24^\circ$?
$W_m'[J] = 1$
What is the torque of electric origin at $i_{as} = 7 A$, $i_{bs} = 6 A$, $i_{r} = 6 A$ and $\theta = 24^\circ$?
$T^e[Nm] = 1$
Correct answer
$W_m'[J] = 305.642419649$ $T^e[Nm] = -505.842414808$
