I have a term project which is controlling a two-link manipulator with harmonic drive installed at each joint.
To control, i used Computed control method to determine the torque needed for each joints based on the formula:
$$\tau_i =M(\theta)(\ddot{\theta_i}+K_d\dot{e}+K_pe)+V+G $$
To calculate the torque that each motor needs to produce through harmonic drive, i use:
$$\tau_{motor} =(J_m+J_g)\rho\ddot{\theta_i}+\frac{\tau_i}{\rho\eta_g}$$
where:
$\rho$ and $\eta_g$ are gear ratio and efficiency of the harmonic drive. $J_m$ and $J_g$ are the motor and gear inertia, respectively.
after these calculation, i can see the effect of harmonic drive in the system by comparing input torque from motor in the model with harmonic drive ($\tau_{motor}$) to that torque in the model without harmonic drive ($\tau_i$)
But my professor doesn't agree the formula $\tau_{motor}$ i used. He want me to include the stiffness $k$ of the harmonic drive.
This is what i have done
P/S: This model which consists of two-link manipulator+harmonic drive at each joint is built in MATLAB.
Can anyone suggest me the formula about it?
Thank you so much.