System identification
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 seminar class Active In SP Posts: 5,361 Joined: Feb 2011 14-02-2011, 03:26 PM presented by: HOSSEIN NEJATBAKHSH   system identification.pptx (Size: 511.63 KB / Downloads: 60) What is identification?  System identification is the art and science of building mathematical models of dynamic systems from observed input-output data. it’s an interface between the real world of applications and the mathematical world of control theory.  in control engineering the field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data.  The core of estimating models is statistical theory. Other Definition Zadeh(1962) Identification is the determination on the basis of input and output, of a system within a class of systems, to which the system under test is equivalent. •Parameter estimation is the experimental determination of values of parameters that govern the dynamic and/or non-linear behaviour, assuming that the structure of the model is known. System identification and parameter estimation Model validation Identification: time-domain & frequency-domain Time domain • y(t) = ∫ h(t’)u(t-t’)*dt’ + n(t) • Unknown system: impulse response of h(t’) • Mostly: direct model parameterization Frequency domain • Y(ω) = H(ω)U(ω) + N(ω) • Unknown system: transfer function H(ω) for number of frequencies • Open loop identification Car shock absorber testing • Response loudspeaker • Knee jerk reflex • Etc, etc Ti[b]me-domain & Frequency-domain Cross-product function Auto-product function Covariance and correlation functions Special cases of auto-covariance Open loop identification(time domain)with cross-covariance Open loop identification(frequency dom[/b]ain) Identification in the closed loop • Time domain models for identification Least squares (LS) • ARX • ARMAX • Output Error (OE) • FIR Least squares model • equation system- • Least Squares (LS) Method (LUENBERGER, D. G. 1996) • minimization =⇒the best linear nondeviated estimation Identification of Dynamical Systems ARX model (Auto Regresive model with eXternal input)– prediction of mean value ˆy(t|t − 1) is linear function of measurable datalinear regression can be used for model parameters stimation • ARMAX model (Average model with eXternal input)enables us to model deterministic and stochastic parts of the system independentlylinear regression cannot be used for model parameters estimation→pseudolinear reg. OE model (Output Error model) Example - Model Identification Using ARX Model  FIR MODEL Finite impulse response(FIR) models are frequently used in model Predictive control (MPC) systems because they can fit arbitrarily Complex stable linear dynamics.  However , identification of FIR models from experimental data my result in data-over fitting and high modeling uncertainly.  To overcome this, FIR models may be determined by : (a) regularization – based least squares, and (b) indirectly after prior identification of other parametric models such as ARX.