Springs 12/23

On Thursday we combined two circuits to create an electrical spring. This is the abstraction of what we did:

The voltage went into the motor  proportional to torque, came out proportional to speed, went into the integrator, and came out of the integrator proportional to the angular position of the motor.  My last post about motors was pretty short. But I feel like I have a much better grasp of the concepts now, so I will go back and cover some of that information. Here is the diagram of the circuit we built with the motor in it:

The voltage going into the motor was proportional to to the torque. Motors turn electrical energy into mechanical energy,  and torque is the the twisty force of the motor. Since we had created a virtual ground using negative feedback we could control the current going into the motor by controlling the resistance with our potentiometers. The resistor to the right of the motor on the diagram made it so we could measure the speed coming out of the motor. On Thursday, we turned the motor into an electrical spring. To do this we added this integrator to our circuit:

It makes the voltage coming out of the motor proportional to position instead of speed, since position is the integral of speed. This works because of the capacitor: Vc = (1/C) ∫ i dt, so, since i=V/R, Vc = (1/RC) ∫ V dt and the output voltage of the whole circuit is Vout =  V+ + (1/RC) ∫ V+ dt.  Both parts of the circuit put together look like this:

As you can see, Vout on the current driver connects to V+ on the integrator, so the speed is converted into the position. Then, the position goes back into the motor as the torque. In a mechanical spring, the spring measure the distance that it has been compressed or stretched, computes the resulting torque, and applies the torque. Our circuit does that electrically. At the end we attached  a pendulum to the motor, and the pendulum always tried to stand straight up no matter which way the motor was positioned.