Question

Consider the following block diagram and find the sensitivity Sₖᵥᴳ⁽ˢ⁾ of the transfer function G(s):= C₍ₛ₎/R₍ₛ₎ with respect to the parameter Kᵥ.Evaluate Sₖᵥᴳ⁽ˢ⁾ at nominal value Kᵥ =1 and frequency s=2j.

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Answer 1

The sensitivity of the transfer function G(s):= C₍ₛ₎/R₍ₛ₎ with respect to the parameter Kᵥ is given by the derivative of the transfer function with respect to Kᵥ. To evaluate the sensitivity at the nominal value Kᵥ = 1 and frequency s = 2j, substitute the values into the derivative expression.

Step-by-step explanation:

The sensitivity of a transfer function with respect to a parameter is defined as the rate of change of the transfer function with respect to that parameter. In this case, the sensitivity Sₖᵥᴳ⁽ˢ⁾ of the transfer function G(s):= C₍ₛ₎/R₍ₛ₎ with respect to the parameter Kᵥ is given by:

Sₖᵥᴳ⁽ˢ⁾ = dG(s)/dKᵥ

To evaluate this sensitivity at the nominal value Kᵥ = 1 and frequency s = 2j, we need to find the derivative of the transfer function with respect to Kᵥ and substitute the values:

Sₖᵥᴳ⁽ˢ⁾ = dG(s)/dKᵥ = (dC₍ₛ₎/dKᵥ * R₍ₛ₎ - C₍ₛ₎ * dR₍ₛ₎/dKᵥ) / (R₍ₛ₎)²

Since the block diagram and the values of C₍ₛ₎ and R₍ₛ₎ are not provided, I cannot calculate the sensitivity Sₖᵥᴳ⁽ˢ⁾ at this time.