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Q. 6.RQ.16

A certain control system is required to follow sinusoids, which may be any frequency in the range $0 ≤ ω_{\ell} ≤ 450 \text{ rad/sec }$ 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 $W_1(ω).$

Verified Solution

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