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Unformatted text preview: Undergraduate Lecture Notes on System Identification Jo ao P. Hespanha April 1, 2007 Disclaimer: This is a draft and probably contains several typos. Comments and information about typos are welcome. Please contact the author at ( hespanha@ ece.ucsb.edu ). c Copyright to Jo ao Hespanha. Please do not distribute this document without the authors consent. Contents 1 Computer-Controlled Systems 3 1.1 Computer control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Continuous-time systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Steady-state response to sine waves . . . . . . . . . . . . . . . . . . . . 5 1.3 Discrete-time systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Steady-state response to sine waves . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Step and impulse responses . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Discrete vs. continuous-time transfer functions . . . . . . . . . . . . . . . . . 8 1.5 MATLAB hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 To probe further . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Parametric identification using least-squares 13 2.1 Parametric identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Least-squares line fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Vector least-squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 MATLAB hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 To probe further . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Parametric identification of an ARX model 23 3.1 ARX Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Identification of an ARX model . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3 Known parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 MATLAB hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4 Practical considerations in parametric identification 29 4.1 Signal scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Choice of inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Choice of model order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.4 Choice of sampling frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 i ii Jo ao P. Hespanha 5 Nonparametric identification 37 5.1 Nonparametric methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.2 Time-domain identification . . . . . . . . . . . . . . . . . . . . . . . . . . . .....
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