allugtopics_Linear Control

allugtopics_Linear Control - T OPICS IN U NDERGRADUATE C...

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Unformatted text preview: T OPICS IN U NDERGRADUATE C ONTROL S YSTEMS D ESIGN Jo˜ao P. Hespanha April 24, 2010 Disclaimer: This is an early draft and probably contains many typos. Comments and information about typos are welcome. Please contact the author at ( hespanha@ece.ucsb.edu ). c circlecopyrt Copyright to Jo˜ao Hespanha. Please do not distribute this document without the author’s consent. Contents I System Identification 1 System Identification 3 1 Computer-Controlled Systems 5 1.1 Computer control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Continuous-time systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Discrete-time systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Discrete vs. continuous-time transfer functions . . . . . . . . . . . . . . . . . . . 10 1.5 MATLAB R circlecopyrt hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 To probe further . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Parametric identification using least-squares 15 2.1 Parametric identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Least-squares line fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Vector least-squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 MATLAB R circlecopyrt hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 To probe further . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 MATLAB R circlecopyrt hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5 To probe further . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 Practical considerations in parametric identification 29 4.1 Choice of inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Signal scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.3 Choice of sampling frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.4 Choice of model order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.5 Combination of multiple experiments . . . . . . . . . . . . . . . . . . . . . . . . 39 4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....
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This note was uploaded on 08/17/2010 for the course EE 123 taught by Professor Abdi during the Spring '10 term at Aarhus Universitet, Aarhus.

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allugtopics_Linear Control - T OPICS IN U NDERGRADUATE C...

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