Problem 1: Draw the straight-line approximation of the Bode...

Problem 1: Draw the straight-line approximation of the Bode plot for the following transfer function. Verify the straight-line approximation of the Bode plot with the bode plot in Matlab. a) $L(s) = \frac{10(s+4)}{s(s+1)(s+200)}$ b) $L(s) = \frac{100}{s(0.1s+1)(0.5s+1)}$ c) $L(s) = \frac{1}{s(s+1)(s+5)(s+10)}$

Transcript

00:01 Hello students in this question we are given a transfer function g of s is equal to 18 times s plus 10 divided by s square plus 0 .9 x plus 9 times s plus 2.

00:20 Okay, so this is the transfer function which is given now.

00:24 We need to determine the first determine the normalized proper form of the transfer function, right? so we can we can expand the terms in the numerator.

00:34 So you'll get this is the a part.

00:37 So you'll get 18 times s plus 180 divided by s cube plus 0 .9 s plus 9 s plus 2 s square plus 0 .9 times 2.

00:55 So that is 1 1 .8 1 .8.

01:00 This is s right s 1 .8 s 0 .9 s square.

01:15 Okay, 1 .8 8s plus 18 so we can simplify that and we can say 18 s plus 180 divided by s cube plus 2 .9 s square plus 1 .8 s times 9 s.

01:39 So that is 10 .8 s plus plus 18.

01:52 Okay, so this is the this is the expanded form.

01:56 Now, we need to reorder this.

01:58 We don't need to reorder that this will be the normalized proper form of the transfer function a proper form of the transfer function.

02:10 So this is that now coming to the second part b part using semi -log charts.

02:17 We need to sketch the magnitude and phase of the responses of each term and then frequency.

02:22 To sketch that we can use this function right and then we can consider the transfer function of as a sum of individual terms.

02:35 So you can say that it is 18 s divided by this whole term...

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