Question

Given the following transfer function:

G(s)= (s+1) /(s+2+j2)(s+2−j2)
a) Find the poles and zeros of the system.

Answer 1

The given transfer function has a single zero at s = -1 and two poles at s = -2-j2 and s = -2+j2. These are found by setting the numerator and denominator of the function to zero.

Step-by-step explanation:

The question asks about finding the poles and zeros of a given transfer function in the field of control systems, which is a part of electrical engineering. The transfer function provided is G(s) = (s+1) / (s+2+j2)(s+2−j2). To find the poles and zeros, we look at the values of s that make the numerator equal to zero (the zeros) and the denominator equal to zero (the poles).

Finding Zeros

For the numerator (s+1) to be zero, s must be -1. Therefore, the system has a single zero at s = -1.

Finding Poles

To find the poles, we set the denominator to zero:

(s+2+j2) = 0 gives the pole s = -2-j2

(s+2−j2) = 0 gives the pole s = -2+j2

Thus, the system has two complex conjugate poles at s = -2-j2 and s = -2+j2.