# Lab 5a Tips: DC Motor

## Pre-lab

- Equation (1)-(3) in state space form will look like the system below. The vector
**u** represents inputs to the system (*v*_{a} and *T*_{L}).

- For steady state use capital letters for variables (capital
*ω* is *Ω* ).
- Steps for finding the transfer functions.
- Start from equations (1)-(3).
- Neglect
*L*_{AA}.
- Combine equations (1)-(3) to eliminate
*i*_{a}.
- Convert the resulting equation to the frequency domain through application of Laplace transforms using the identities below. Note that the capital form
*ω* is *Ω*, the symbol we choose for *ω* in the frequency domain, and that it is safe to assume *ω*_{r}(0) = 0.

- Linearity:
- Differentiation:

- Solve the resulting equation for
*Ω* (*s*). Your result should be of the form given below where the parentheses represent constant terms.

- Solve the above equation for the transfer functions

.

- To Find
*ω*_{r}(*t*), use the first transfer function above and solve for *ω*_{r}(*t*) given
*v*_{a}(*t*) = *V*_{a}*u*(*t*). In other words, solve the following

.

## In-lab

- You can complete the entire lab with this one model.

- To convert from torque transducer voltage (as read on ocilliscope) to actual torque use the relations: 1 V = 15 oz-in and 1 N-m = 141.6 oz-in
- To find
*k*_{t}, *k*_{v}, and *B*_{m}, use Matlab's built in data fitting features.

- Select 'linear', 'show equations', and at least three significant digits.

### Check your work.

*r*_{a} ≈ *2* *Ω*
*L*_{AA} ≈ *4* mH
*k*_{T}, *k*_{v}, and *B*_{m}

## Post-lab

- For questions 3 and 4, show the relevant equations.