To better understand the meaning behind poles and zeros, generate a mesh plot in

Question

To better understand the meaning behind poles and zeros, generate a mesh plot in Matlab of the transfer function G(s) defined below using the skeleton code provided. Note that s is complex number and is given by s=s+w. You need to take the absolute value of the result because Matlab can't plot complex numbers. S 10 (s +15) (s2+ 100) s) = [Sigma Omega] = meshgrid(-20:0.5:20); N = % numerator of transfer function in terms of sigma, omega and j D = %denominator of transfer function in terms of sigma, omega and j G = abs (N./D); , mesh (sigma, omega, G) a. Calculate the pole and zero locations of the transfer function G. b. Provide the mesh output (label axes). c. Identify the pole and zero locations on the plot. Does this make sense?

Explanation / Answer

the pole of the transfer function occurs when the numerator becomes zero, so

s+10=0

s= -10

the zeroes of the transfer function occur when denominatior becomes zero, so

(s+15)*(s^2+100) = 0

s= -15 or s=10i or s= -10i

where 'i' is the imaginary number

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