In this video, we learn how to find some quantifiable measures of speed, stability, and accuracy from the time response of the rack and pinion. We measure rise time, peak time, settling time, overshoot, and steady-state error. We make these measurements for three values of Kp in our proportional control, and we note the trends in these values for increasing or decreasing values of Kp.
In this video, we find the proportional gain that gives a 'critically damped' response of the rack and pinion. We do this experimentally by trying a gain, calculating the characteristics of the step response, then increasing or decreasing the gain appropriately.
To complete this lab activity, make a video that includes the following in one video:
Undergraduates: (1) You saying your name (2) Your critically-damped step response plotted in Excel (3) Calculations for rise time, peak time, settling time, overshoot, and steady-state error for one of the responses you captured in Excel
Graduates: (1) You saying your name (2) Your work showing how you calculated the Kp gain for your system for critical damping using the method taught in the video (3) The step response of your system plotted in Excel for the Kp value you calculated as shown in (2)
In this video, we find the proportional gain that gives a 'critically damped' response of the rack and pinion, but this time we do so analytically instead of by trial-and-error. To do this, we use the step response we captured in previous videos to create a model of the system, then set the damping ratio (zeta) to whatever we want it to be, and back-calculate the value of Kp that will give that value of zeta.
Note: Graduate students did these 'blue' videos previously. They can skip the blue videos this time.