# Milestone II Demo Feedback

## Overview

Everything is generally good. Motor team has average of 82; controller team has an average of 84. Motor’s team has been scaled to have an average of 84.

## Motor Model

In the equivalent circuit, there are three powers: Conservation of power: Notice that the back EMF constant and the torque constant is the same given that they’re in the same units.

To model a motor, we need 6 parameters:

Parameter | Description |
---|---|

\(R\) | Resistance |

\(L\) | Inductance |

\(K_V\) | Back EMF constant |

\(K_\tau\) | Torque constant |

\(B\) | |

\(J\) |

### Test

Here’s our test:

- apply V
_{S}of 9V - measure current drawn, in this example, say I
_{A}=1A - measure speed, say it is 2 rad/s

Now let’s compute some parameters:

- \(V_A=V_S-I_A R_A=9-1(1)=8\)V
- \(K_b=\frac{V_A}{\omega}=\frac{8}{2}=4 \frac{\text{Vs}}{\text{rad}}\)
- \(K_\tau=4 \text{Nm/A}\)
- \(B=\frac{\tau}{\omega}=\frac{K_\tau I_A}{\omega}=\frac{4}{2}=2\text{Nms/rad}\)

For moment of inertia, calculate the moment of inertia for each component individually, then add them up.

For a cylinder with a hollow shaft with inner radius \(r_1\) and outer radius of \(r_2\), and mass of \(m_1\), the moment of inertia is given by:

## Impulse Response

Something like keep the motor turning and suddenly turn the motor off after some time.

- Give some non 0 input and let it run for a while for the transient behavior to go away
- Turn power off and measure the response
- Disregard data before we turned off the power

Note that the theoretical response and the real response are different possibly due to **stiction**.