A certain control system is required to follow sinusoids, which may be any frequency in the range 0 ≤ ωl ≤ 450 rad/sec and have amplitudes up to 5 units with (sinusoidal) steady-state error to be never more than 0.01. Sketch (or describe) the corresponding performance function W1(ω).

Question

A certain control system is required to follow sinusoids, which may be any frequency in the range [latex] 0 ≤ ω_{\ell} ≤ 450 ext{ rad/sec } [/latex] and have amplitudes up to [latex] 5 [/latex] units with (sinusoidal) steady-state error to be never more than [latex] 0.01. [/latex] Sketch (or describe) the corresponding performance function [latex] W_1(ω). [/latex]

Accepted Answer

The magnitude of [latex] W_1 [/latex] is given by the ratio [latex] |R| /e_b = 5/0.01 = 500. [/latex] The performance function would then have the value [latex] 500 [/latex] for frequencies up to [latex] 450 ext{ rad/sec }.[/latex] The Bode magnitude plot would be required to be above this curve for these frequencies.

Question 6.RQ.16: A certain control system is required to follow sinusoids, wh...

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