MIT16_30F10_lec05_slides

MIT16_30F10_lec05_slides - 16.30 Estimation and Control of...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
16.30 Estimation and Control of Aerospace Systems Topic 5 addendum: Signals and Systems Aeronautics and Astronautics Massachusetts Institute of Technology Fall 2010 (MIT) Topic 5 addendum: Signals, Systems Fall 2010 1 / 27
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline 1 2 3 4 5 Continuous- and discrete-time signals and systems Causality Time Invariance State-space models Linear Systems (MIT) Topic 5 addendum: Signals, Systems Fall 2010 2 / 27
Background image of page 2
Continuous- and discrete-time signals Continuous-time signal A (scalar) continuous-time signal is a function that associates to each time t R a real number y ( t ), i.e., y : t y ( t ). Note: We will use the “standard” (round) parentheses to indicate continuous-time signals. Discrete-time signal A (scalar) discrete-time signal is a function that associates to each integer k Z a real number y [ k ], i.e., y : k y [ k ]. Note: We will use the square parentheses to indicate discrete-time signals. y ( t ) y [ k ] t k (MIT) Topic 5 addendum: Signals, Systems Fall 2010 3 / 27
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Signals are vectors Multiplication by a scalar Let α R . The signal α y can be obtained as: ( α y )( t ) = α y ( t ) , and ( α y )[ k ] = α y [ k ] . Notice 0 y is always the “zero” signal, where 0( t ) = 0 for all t R , and 0[ k ] = 0 for all k Z , and 1 y = y . Addition of two signals Let u and v be two signals of the same kind (i.e., both in continuous or discrete time). The signal u + v is deFned as: ( u + v )( t ) = u ( t ) + v ( t ) , and ( u + v )[ k ] = u [ k ] + v [ k ] . Notice that u u = u + ( 1) u = 0. (MIT) Topic 5 addendum: Signals, Systems Fall 2010 4 / 27
Background image of page 4
Systems Defnition (system) A system is an operator that transForms an input signal u into a unique output signal y . u ( t ) y ( t ) t t u ( t ) y ( t ) System u [ k ] y [ k ] u [ k ] y ( t ) t k (MIT) Topic 5 addendum: Signals, Systems Fall 2010 5 / 27
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A classifcation Continuous-Time System: CT CT This is the kind of systems you studied in 16.06. Discrete-Time System: DT DT We will study this kind of systems in this class. Sampler: CT DT This class includes sensors, and A/D (Analog Digital) converters. Let us call a sampler with sampling time T a system such that y [ k ] = u ( kT ) . Hold: DT CT This class includes actuators, and D/A (Digital Analog) converters. A Zero-Order Hold (ZOH) with holding time T is such that y ( t ) = u ± t T ²³ . (MIT) Topic 5 addendum: Signals, Systems Fall 2010 6 / 27
Background image of page 6
Outline 1 2 3 4 5 Continuous- and discrete-time signals and systems Causality Time Invariance State-space models Linear Systems (MIT) Topic 5 addendum: Signals, Systems Fall 2010 7 / 27
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Static/Memoryless systems Defnition (Memoryless system) A system is said to be memoryless (or static ) iF, For any t 0 R (resp.
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 28

MIT16_30F10_lec05_slides - 16.30 Estimation and Control of...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online