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# System model for motor controlled inverted pendulum with rotating motor body (used in camera stabilizer application)

2017-09-25 20:23:30

I'm planning to build a head-mounted camera stabilizer for pro GoPro camera. The idea is that when I tilt my head the camera would stay at a user-set angle.

I'm using an accelerometer and a gyro to measure camera angle $\theta$ and angular velocity $\dot{\theta}$, and some motor to control the camera angle. I derived the following differential equation for the system (which is basically an inverted pendulum) where $l$ is length of the rod, $\theta$ is the angle of the camera due to gravity, $m$ is the mass, $g$ is the gravitational acceleration, $b$ is damping coefficient (due to friction) and $\tau$ is torque. $\tau_{motor}$ will be the input of the system.

$\tau_{total} = \tau_{motor} - \tau_{gravity} - \tau_{friction}$

$I\ddot{\theta} = \tau_{motor} - mgl\sin\theta - b\dot{\theta}$

$ml^2\ddot{\theta} = \tau_{motor} - mgl\sin\theta - b\dot{\theta}$

$\ddot{\theta} = \frac{1}{ml^2}\tau_{motor} - \frac{g}{l}\sin\theta - \frac{b}{ml^2}\dot{\theta}$

From here I'll co

• There's a couple questions you can ask:

Can you control the signal? If not, then it's either a noise or disturbance input.

Is it affecting your system (plant), or is it affecting your measurements? If it's affecting the system, it's a disturbance input; if it's affecting the measurements, it's noise. Note that noise can be colored, biased, periodic, etc. That is, pretty much any signal can be noise or a disturbance.

Does the disturbance have enough power that is effectively a position regulator?

Regarding point 3, if the power output of the human neck is comparable with the power output of your stabilization system, then its position will vary with reaction forces applied by your stabilization system. If the power output of the neck is significantly higher, then it becomes effectively rigid and is better modeled as a position regulator.

Based on these questions, I would guess that the power of your stabilizer is much less than the power of the neck, so I would treat the neck a

2017-09-25 21:17:48
• how did you choose the motor? As in, how do you know the maximum torque of the system that the motor will have to handle?

2017-09-25 21:40:34