matlab-identify-linear-system

Use tfest with the number of poles, zeros, and an estimated delay on an iddata object. Estimate the delay first with delayest, try delay values nk-1 through nk+1, and validate the model by simulation on held-out data using compare.

ssest uses n4sid subspace estimation as initialization, then refines the model via iterative optimization, outperforming standalone n4sid in most cases. Use n4sid mainly for order selection diagnostics and ssest for the final model.

Use state-space models (ssest) for MIMO systems, high-order dynamics, or when you need a quick default model requiring only an order number. Transfer functions (tfest) suit SISO continuous-time systems with moderate complexity up to about 10 poles.

This indicates overfitting from excessive model order or validating with prediction fit instead of simulation fit. Reduce the order, add regularization via arxRegul, and always validate by simulation on a held-out dataset.

Yes, but ARX and OE give biased plant estimates in closed loop. Use the indirect method, iv4 instrumental variables, or BJ/ARMAX with a correct noise model, and validate by simulation since prediction fit is misleadingly good in closed loop.

Avoid it when the system is strongly nonlinear, data quality is poor, or excitation is insufficient. Check nonlinearity with amplitude-dependence tests or isnlarx, and consider Hammerstein-Wiener, NLARX, or neural state-space models instead.