NiiL

Week 11 · Step Response Performance Metrics

English translation

Before practice

01 Criteria for a good response

Which is better: reaching the target quickly with large oscillations, or moving slightly slower and settling sooner? What should determine the choice?

Description
  • Rise time, settling time, and overshoot measure different characteristics
  • Specify metrics and tolerances suited to the design goal

02 Express performance numerically

How would expressing response speed and oscillation numerically help compare designs, rather than simply describing a graph as fast or highly oscillatory?

Description
  • Rise time, settling time, and overshoot measure different response characteristics.
  • Comparisons require consistent measurement criteria. Check the input, final value, and settling band together.

Practice

1. Measure the response numerically

State the units of rise time, settling time, and overshoot, and indicate which part of the plot each measures.

2. Correct a measurement using the wrong final value

  1. Record the rise time, settling time, and overshoot from correct and wrong in the “2. Correct a measurement using the wrong final value” code in the practice Live Script side by side. Explain that only the final-value argument differs between the two calls.
  2. Keep denominator [1 2 4] and change the numerator to 1 so that the DC gain of T becomes 0.25. Recalculate y on the same time vector.
  3. For the same y,t, call stepinfo with final values 1 and dcgain(T) separately, and record both results in the same format.
  4. Instead of changing the model to hide the error, correct only the final-value argument of stepinfo to the actual DC gain. State which reference value caused the metrics to differ.

3. Change pole and zero conditions

  1. Find dcgain and stepinfo for each of base, withZero, and slowPole.
  2. Use one row per model to record DC gain, rise time, settling time, and overshoot. Use the same stepinfo settings.
  3. Use (s+2)/2*base when changing the additional zero to −2-2, and 10/(s+10)*base when changing the additional pole to −10-10. Keep the baseline model base unchanged.
  4. Append the results for the two modified models to the same table. First check that their DC gains equal base. Then compare the changed zero with the original withZero and the changed pole with the original slowPole.
  5. For each change, state whether rise time, settling time, and overshoot increase or decrease. Use these results to explain whether the transient response changes even with the same final value.

Submission and saving

Include code, actual outputs and plots, and your own interpretation. Submit through KLAS; check the semester schedule and latest announcements for the deadline.

Filename: Name_StudentID_Week11.mlx.

Restart the runtime, run all code from the top, then save.

Optional practice

Example: specifying 20% when calculating the 2% settling time

  1. Using the same T in the “1. Measure the response numerically” code in the practice Live Script, calculate stepinfo(T,'SettlingTimeThreshold',.02) and stepinfo(T,'SettlingTimeThreshold',.2).
  2. Record the two settling times and the tolerance percentages used side by side. Change only the second call's argument to .02 for the 2% criterion, keeping the model unchanged.