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FREQUENCY-RESPONSE ANALYSIS

ECE4510/5510: Feedback Control 1 FREQUENCY-RESPONSE : Motivation to study FREQUENCY-RESPONSE methods Advantages and disadvantages to root-locus design approach:ADVANTAGES: Good indicator of transient response. Explicitly shows location of closed-loop poles. Tradeoffs : Requires transfer function of plant be known. Difficult to infer all performance values. Hard to extract steady-state response (sinusoidal inputs). FREQUENCY-RESPONSE methods can be used tosupplementroot locus: Can infer performance and stability from same plot. Can use measured data when no model is available. Design process is independent of system order (# poles). Time delays handled correctly (e s ). Graphical techniques ( ANALYSIS /synthesis) are quite simple. What is a frequency response? We want to know how a linear system responds to sinusoidal input, insteady notes prepared by and copyrightc 1998 2017, Gregory L. Plett and M.

Plot method #1: Polar plot in complex plane Evaluate G(jω) at each frequency for 0 ≤ ω<∞. Result will be a complex number at each frequency:a + jbor Aejφ. Lecture notes prepared by and copyright ⃝c 1998–2017, Gregory L. Plett and M. Scott Trimboli

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