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).
Chapter 6
Q. 6.RQ.16
Step-by-Step
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.