2. Consider the system of 1 + KG(s) = 0 for G(s) = (s + 2) /...

2. Consider the system of 1 + KG(s) = 0 for G(s) = (s + 2) / (s^2(s + 5)) (a) Plot the root locus using the Matlab command rlocus(). (You don't have to draw a manual sketch) (b) What is the complex conjugate poles that give the maximum damping ratio. Consider the complex poles as two dominant poles. What is the approximate value of the damping ratio? (c) Using the vector method, find the value of K for the complex conjugate poles determined in part (b). (d) Find the location of the third closed-loop pole in addition to the complex conjugate poles for K determined in part (c). Notice that the third pole is on the real axis.

Transcript

00:01 Hello students, today we will discuss about this question.

00:03 In this question, we need to consider the system of 1 plus kg of s is equal to 0 for g of s is equals to s plus 2 divided by s square s plus 5.

00:17 Now in part b, we need to find the pair of complex conjugate poles that give a maximum damping ratio and consider the complex poles as a complex poles as complex.

00:35 Two dominant poles then we need to find the approximate value of the damping ratio.

00:42 So here we need to find the approximate value of the damping ratio that is we need to find r that is equals to question mark.

01:01 So here first of all let's take g of s is equal to s plus 2 divided by s squared plus multiplied by s plus 5 so t of s is equals to g divided by 1 plus g that is equal to s plus 2 divided by s plus 2 s plus 5 plus s plus 2 so that is equals to s plus 2 divided by s q plus 5 s square plus s plus so therefore here poles that are minus 488 comma minus 0 .605 plus plus or minus j 0 .6374.

01:45 They are the pair of poles and here 0s that is equals to minus 2.

01:52 Now the entering the given data and explain the option a in program and drawing the graph then we have to consider the dominant that always being complex dominant so therefore t of s that is equals to s plus 2 divided by s plus 4 .88, s plus 0 .0605 plus j 0 .63474, multiplied by 5 plus 6 .0605 minus j .066374.

02:32 So that is equals to s plus 2 divided by s plus 0 .0605 plus j 0 .605 plus j 0 .74.

02:45 6374 s plus 0 .0605 minus j 0 .6374.

02:52 So that is equals to s plus 2...

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