I was asked to sketch the magnitude and phase bode plots for the open loop transfer function Gs=(4s^2+40s)/(4s^3+409s^2+540s+400) Where do I start? Thanks
Find the poles and the zeroes and the DC gain of the transfer function. For the magnitude plot, start from the DC gain level (in dBs) and go horizontally. For every pole, your gain will fall 20dB/decade. For every zero, your gain will rise 20dB/decade. For the phase plot, start from 0deg level. For every pole, subtract 45deg in the decade before a pole and another 45deg in the next decade. For every zero, add 45deg in the decade before a pole and another 45deg in the next decade. Check here for more info: http://en.wikipedia.org/wiki/Bode_plot Is that clear?
So for the zeros i got -10 and 0 and for the poles i got -100.922, -.6639+.74166j, and -.6639-.74166j so what is my starting point to subtract the 20db's
The DC gain can be found if you replace s with 0. In the dB scale that you will plot your bode plot, however, that will be -infinite, and that's not very useful. Usually, when we draw a dB frequency scale we start from a relatively small frequency, like 1Hz or 0.1Hz, not 0. So pick a start point and use that frequency on s to start with. We are going in all that trouble because you have a zero at 0, which will immediately from the start make your plot incline. As for the negative frequencies on the poles and zeroes, just use their absolute value.
Here's an example that might help you out a little. I think the complex numbers might be tripping you up a little. That's okay...there are ways to work around that. That's why you are an engineer...
In his pdf, staticd chose to start the frequency scale from 1. Thus, the pole in 0 will start inclining from 0dB in his scale. Notice how you can first find the responses from different poles, zeroes and the DC gain in separate graphs and then sum them up. Same goes for the phase. And a side note: you don't have to find the magnitude (absolute quantity) of the transfer function in order to perform the above method.