Question

Let α be a positive number. The numerical value of α is not given. All calculations should be in terms of α. Let

G(s)= 10α²/(s+α)²
You will sketch the Nyquist plot following these steps:
a) Write the frequency response G(jω).

Answer 1

The Nyquist plot of G(s) = 10α² / (s+α)² is constructed by substituting s with jω to get G(jω) and then graphing this frequency response over a range of frequencies.

Step-by-step explanation:

To sketch the Nyquist plot of the transfer function G(s) = 10α² / (s+α)², we first need to find the frequency response G(jω). The frequency response is found by substituting s with jω, which represents a complex frequency where j is the imaginary unit and ω is the radial frequency.

So, G(jω) = 10α² / (jω+α)². To simplify this, we need to compute the response for various values of ω, ranging from ω = 0 to ω = ∞, noting how the plot behaves as it encircles the origin of the complex plane (a requirement for Nyquist plots).

Remember, the Nyquist plot is a graphical representation of the complex frequency response of a system, and it is used to predict stability and performance of control systems.