topic3 - Topic#3 16.31 Feedback Control Frequency response...

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Unformatted text preview: Topic #3 16.31 Feedback Control Frequency response methods • Analysis • Synthesis • Performance • Stability Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Fall 2007 16.31 3–1 FR: Introduction • Root locus methods have: – Advantages: Good indicator 0f transient response; Explicitly shows location of all closed-loop poles; Trade-offs in the design are fairly clear. – Disadvantages: Requires a transfer function model (poles and zeros); Difficult to infer all performance metrics; Hard to determine response to steady-state (sinusoids) Hard to infer stability margins • Frequency response methods are a good complement to the root locus techniques: – Can infer performance and stability from the same plot – Can use measured data rather than a transfer function model – Design process can be independent of the system order – Time delays are handled correctly – Graphical techniques (analysis and synthesis) are quite simple. September 2, 2007 Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Fall 2007 16.31 3–2 Frequency Response Function • Given a system with a transfer function G ( s ) , we call the G (j ω ) , ω ∈ [0 , ∞ ) the frequency response function (FRF) G (j ω ) = | G (j ω ) | G (j ω ) – The FRF can be used to find the steady-state response of a system to a sinusoidal input since, if e ( t ) → G(s) → y ( t ) and e ( t ) = sin 2 t , | G (2j) | = 0 . 3 , G (2j) = 80 ◦ , then the steady-state output is y ( t ) = 0 . 3 sin(2 t − 80 ◦ ) ⇒ The FRF clearly shows the magnitude (and phase) of the response of a system to sinusoidal input • A variety of ways to display this:...
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This note was uploaded on 11/07/2011 for the course AERO 16.31 taught by Professor Jonathanhow during the Fall '07 term at MIT.

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topic3 - Topic#3 16.31 Feedback Control Frequency response...

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