Rensselaer Mechatronics
Lab 2 Submission
In this lab, you experimentally determine the parameters in the DC motor transfer function in two ways:
• “Black Box model”: Calculate K and t directly from the step response
• “Physics-based model”: Calculate K and t using physical parameter values measured from the motor (e.g. resistance, back EMF, etc.)
Part 1: Black Box method
• Plot the step response data. Clearly label the plot as directed in the course syllabus. Use the step response data to calculate the steady state gain, K, and the time constant, t . Show your work, including calculations and how you extracted information from the plot.
Step response plot and calculations of K and t
Part 2: Physics-based method
• Estimating b: Recall that in class you already estimated R and kb. If a DC motor system has relatively small losses, we can assume conservation of energy, meaning that kt = kb. Assuming that is the case for your DC motor system:
• Write down the steady-state mechanical subsystem equation (review posted notes from In-Class Discussion). This equation indicates b can be obtained by plotting kt*I vs w.
• Create a properly labeled plot of kt*I vs. w using the data points of current and speed measurements in last experiment of the in-class assignment. Obtain b from this plot by estimating the slope of kt*I vs w.
Plot and calculation of b
• Why do you have to plot this data to obtain b? Why can’t you just use the equation directly to solve for b?
• Starting with the electrical and mechanical ODEs for a DC motor system, derive the equation for the Time Constant, (s) and the Steady State Gain, K (rad/V.s) in terms of the physical motor parameters. You did a similar calculation in the Prelab, but this time do not assume b = 0. Show your work:
• Calculate the system Time Constant, (s) and the Steady State Gain, K (rad/V.s) for the DC motor using the motor parameters that have obtained. (use ).
• Calculate the system Time Constant, (s) and the Steady State Gain, K (rad/V.s) again, but assuming b = 0. Is it reasonable to neglect b?
Part 3: Comparison and Conclusions
• Compare the values of K and computed using the “Black Box” approach and the “Physics based” approach (not neglecting b). Discuss and explain any differences. Which method was easier?
The physical based model enables the precision of calculation that derives directly from the control diagram, which also including b thought small value into its calculation; however, the calculation from the black box one assume the b = 0, while alleviating the difficulty of calculations.
• Using the sample code below, you can simulate a step response of a first order system with the K and t .
Plot the simulated responses using K and t from both the “Black Box” and the “Physics-based” approaches. Plot these simulated responses on top of the experimental data (Hints: don’t forget to account for the non-zero initial conditions; you will have to shift the data accordingly. The MATLAB command ‘hold on’ will be useful). Paste the plot with all three curves here, including appropriate labels and legend.
Plot of experimental data and simulated step response from Black Box model and the Physics Based model