What is system identification and what methods are commonly used?

System identification determines mathematical models from input-output data. Methods include: step response (measure delay, time constant, gain from step test), frequency response (sweep frequency, measure gain and phase), correlation methods (use random input, compute impulse response), and parametric methods (fit model parameters to minimize prediction error - ARX, ARMAX). Modern tools use least squares, maximum likelihood, and subspace methods. Model validation compares model output to measured data for fresh input sequence.