[Feb 16] Motor Model and Building a Circuit with Motor

We started today’s class with a review of the motor model. Basically, there is a resistance within the motor, which adds Rm * Im to the electromotive voltage generated by the rotational speed of the motor, for a total motor voltage Vm = Rm * Im + Vemf. 

We want to separate the Vemf from the voltage across Rm.


As shown below, if we control the voltage of the motor, we do not control the torque. 

From T=K*Im, Vemf  = K * w (angular speed of the motor), we have T = K * Im = K (Vin – Vemf)/ Rm = (K/ Rm) * Vin – (K^2/Rm) w.

This equation shows that the torque in this circuit depends on both the input voltage Vin and the rotational speed omega (w).

Therefore, we need to control Im directly, so that we control the motor torque directly.

If we want to design a circuit to control Im, we can use negative feedback.

The secret of this circuit is the voltage divider.

We can work it out that the Voltage going out of this small part of the system (Vout) is (-R/ (Rm+ R) * Kw – dependent only on R.

Then we started to build the circuit. Today was the first time that I really enjoyed building my own circuit, even though it was not that original since Oscar drew the graph for us beforehand. I thought that knowing where to plug in and connect different places was really fun. Although we learned a hard lesson: CUT THE WIRES SHORT AND MAKE A PRETTY CIRCUIT! I didn't think that it was all that important until our circuit didn't work when we use the oscilloscope to test it out and Oscar came and said he had trouble tracing our circuit because it was too messy. We look at his instead and all the wires were cut nicely and fit right between the two connect points. Ours was full of "bridges" and sometimes that could cause connection problems and we would not know where to start.

Anyway, after Oscar helped us figure out the connection problem, our motor was able to spin with different speed and reverse direction when we change the voltage.

Then Essie and I spent the rest of our time fixing our circuit and cutting everything to scale. That took a little while but I do believe that it would be worth the time going through debugging every little connection.