Drawing Bode Phase Plots: Real Poles & Zeros in RHP

[FrogPad]

Well, it has been awhile... and I need to remember how to draw a Bode phase plot quickly. The problem I am having is, how do I deal with real poles and zeros in the right half plane?

I can quickly draw bode phase plots for transfer functions like:
$$H(s) = (s+1)(s+10)\frac{1}{(s+100}\frac{1}{(s+1000)}$$

but, how do I quickly deal with transfer functions like:
$$H(s) = (s+1)(s-10)\frac{1}{(s+100}\frac{1}{(s+1000)}$$


if anyone can explain it, or (even better) point me to a good resource for quickly drawing the asymptotic approximations, that would be awesome!

thanks

 

[Valkarie]

!One way to quickly draw a Bode phase plot for transfer functions with real poles and zeros in the right half plane is to consider the asymptotic approximations of the phase plot. This means that you can use the standard methods of drawing the phase plot, but with certain modifications. For example, when dealing with a pole in the right half plane, you will need to subtract 180 degrees from the phase plot at that point. Similarly, when dealing with a zero in the right half plane, you will need to add 180 degrees to the phase plot at that point. Additionally, you can use a phase lead/lag compensator to "shift" the phase plot in order to achieve the desired result. A good resource for quickly drawing Bode phase plots is the book Control System Design: An Introduction to State-Space Methods by Bernard Friedland.

 

[piercas]

for the help

Drawing Bode phase plots for transfer functions with real poles and zeros in the right half plane can be challenging, but with some practice and understanding of the concept, it can be done quickly and accurately. One approach is to use the asymptotic approximation method, which involves breaking down the transfer function into simpler components and then combining them to get an overall approximation of the phase plot.

First, identify the real poles and zeros in the right half plane. In the given example, there is one real zero at s=10 and two real poles at s=-1 and s=-1000.

Next, plot the individual contributions of each pole and zero on the phase plot. For a real zero, the phase will decrease by 90 degrees as we move from left to right on the plot. For a real pole, the phase will increase by 90 degrees as we move from left to right.

After plotting the individual contributions, combine them using the following rules:

1. If there is a single zero or pole, the phase plot will be a straight line with a slope of -90 or 90 degrees, respectively.

2. If there are multiple zeros or poles, the phase plot will have a curve with a slope of -180 or 180 degrees, respectively.

3. If there is a combination of zeros and poles, the phase plot will have a curve with a slope that is the difference between the slopes of the individual components.

Using these rules, we can quickly draw the asymptotic approximation of the phase plot for the given transfer function.

First, plot the individual contributions of the zero at s=10 and the pole at s=-1000. The slope will be -90 degrees for the zero and 90 degrees for the pole.

Next, combine these individual contributions to get an overall slope of -180 degrees. This will result in a curve on the phase plot.

Finally, add the contribution of the pole at s=-1, which will have a slope of 90 degrees. This will result in a curve with a slope of -90 degrees on the phase plot.

By following these steps, we can quickly draw the asymptotic approximation of the phase plot for transfer functions with real poles and zeros in the right half plane. As for resources, there are many online tutorials and videos that explain this concept in detail and provide practice problems for better understanding. It may also be helpful to consult a textbook or attend a workshop