[Feb 23] Abstraction

Today in class we learned about the idea of abstraction - getting the big picture of a complex circuit. Here is the abstraction of the circuit that we are eventually building. The specific equation will be explained later.

This is a circuit that creates a virtual spring. The box on top generates a voltage proportional to the speed of the motor. The integrator at the bottom integrates the speed to position. The box on top then generates a torque proportional to position, which is a spring. This makes the motor spins in alternating directions, as if it was attached to a real spring.

This is the circuit of the box on top:

We did this circuit last class and we knew that it generates a speed: Vout = -nKw. If T = -bw (torque and speed are in the opposite directions), then I * α = - bw (T = I * α, α is the angular acceleration). Torque proportional to w is friction, so the object will slow down (in this case, the motor will slow down). The circuit could be abstracted to this diagram: 

Torque proportional to w is a "damper" - it has friction and is slowing down at every second. 

To review how a motor works:

Since there is a voltage difference across R, we know that there is current coming down through R. This Im generates a torque, which is proportional to w, making it a damper.


If we want to make a virtual spring, we need an integration box. The integration box looks like this:

This circuit integrates w to position; therefore, it creates a "spring."
We can calculate Vout as following:

This circuit can also be abstracted to this diagram:

Then we connect the two boxes together and have the first diagram in this post.


The second half of the class, we started building the circuit. There was something wrong with our power source again (the connection of the board was bad), so we had to change the position of the power source to finally make it work. Oscar also encouraged us to put the pendulum on. And the pendulum was "confused" on where it should go... I didn't take a picture because we will keep on building it next class.