A model must survive another test
Estimating a plant from one response is the beginning of a model, not the end of validation.
Estimate the gain and time constant of a first-order model, then state what still needs validation.
Sampling can distort what we observe. Once measurement is trustworthy, we can estimate a model and test whether it predicts a different experiment.
Review the previous lesson: When samples tell a different storyFirst, picture it
A motor model might match a small speed step perfectly because you tuned its parameters to that trace. Will it also predict a different target or load pulse? That unseen trial is more revealing.
Build the idea step by step
System identification means estimating a model from known inputs and measured outputs. First choose a model shape, such as a gain and one time constant. Use one experiment to estimate its parameters. Then freeze those parameters and predict another experiment. A good fit to the first trace is not enough. A real motor has electrical and mechanical states, so one step response may hide faster behavior or fail to identify every parameter. Use a model only over the conditions that your tests support.
Read the equations
This stable first-order model has no delay and starts at equilibrium. Its step response reaches about 63.2% of its final change after one time constant.
What the symbols mean
- steady output change divided by input change
- time constant, seconds
- input and output changes from the initial equilibrium
- elapsed time and Laplace variable
The worked first-order fit is an illustrative calculation. The current lab changes simulated inertia and friction to expose model mismatch; it does not estimate parameters from uploaded hardware data. Use a separate target or load trial for validation.
Fit a model, then make a new prediction
A 2 volt input step changes final speed by 10 radians per second. Use changes from the initial equilibrium, not absolute readings.
The measured speed change reaches 6.32 radians per second after 0.4 seconds. Estimate the time constant as 0.4 seconds, provided a first-order, no-delay shape is plausible.
Predict a separate 1 volt step: final change 5 radians per second and change 3.16 after 0.4 seconds. Test this new input without refitting first. Saturation, delay, or operating-point changes may invalidate the fit.
More detail and model assumptions
Fit on one trial, judge on another
A step test can suggest motor gain and dominant time scale, but many different parameter sets may resemble one short noisy trace. Estimate parameters on one set of known inputs and outputs, then test the resulting model on a target, load or amplitude it did not see. The new trial probes prediction rather than memory.
Specify the measured output, sample rate, actuator limit and noise level. If voltage clipped during the fitting trial but the model assumed unlimited input, a fitted constant may compensate for a missing nonlinearity rather than represent the motor's physical inertia.
What this Lab does and does not identify
Here the nominal motor model is fixed. The model-mismatch lesson changes actual inertia or friction in the time simulator while the frequency design plot keeps nominal parameters. That is a robustness thought experiment, not an automatic parameter fit from hardware data. The mismatch is known because the simulation defines both models.
Hold one controller fixed while changing actual parameters. If you retune after each change, you have tested several designs rather than the robustness of one design. Report the parameter range that passed your stated settling, error and voltage requirements; do not extend that conclusion to all real motors.
Connect the example to the lab
Pin the nominal motor at a fixed controller and target. Double actual inertia; the nominal Bode and root locus do not move, but the time response does. Change target or load to probe whether the mismatch matters for your objective.
Challenge the nominal modelMake a prediction before moving a control.
- PREDICTDoes a model that matches one run deserve trust?
- CHANGE ONE THINGPin the nominal motor, double actual inertia without changing gains, then test a different target or load.
- OBSERVECompare time response and nominal frequency plots, noting which one changed.
- EXPLAINState what this exercise reveals about model mismatch and what real-data identification would still require.
A good fit on the experiment used to select parameters is not independent evidence of predictive accuracy; neither is a pretty nominal stability margin.
Check your understanding+
Why test a model on a load pulse that was not used to tune it?
It checks predictive behavior outside the fitting trial and exposes errors relevant to disturbance rejection.Put the course into practice
Return to one plant in the lab. State a target and input limit, build a model, choose a controller, predict a response, then test a different load. Explain any mismatch using the assumptions from this course.