# Classical Control Theory Toolbox

I just finished my mock qualifying exam this morning and one of the pieces of advice I got from some of the more senior students was to know when to use Bode plots, Nyquist plots and root locus plots. I am going to start a list of when to use each kind of plot, and I may come back to update this post occasionally based on what I learn as I do more problems.

### Bode Plots

Bode plots give information about the **frequency domain** behavior of a system. They should be used if you are concerned about:

**(1)** Gain/phase margin

**(2)** Gain crossover frequency

**(3)** System bandwidth

**(4)** DC gain

### Root Locus

Root locus plots give information about the **time domain** behavior of a system. They should be used if you are concerned about:

**(1)** Rise time

**(2)** Settling time

**(3)** Damping ratio

**(4)** Overshoot

### Nyquist Plots

Nyquist plots can give you a view into system stability, especially when you don’t have the root locus plot. They should be used if you are concerned about:

**(1)** Gain/phase margin

**(2)** System stability

### Notes

There are some other tools that you have available which can answer questions that the 3 plots above cannot address. Some of these other tools include:

#### Final Value Theorem

This helps you calculate the steady state error of a system **if you know the system is stable.** This Theorem should NOT be used if you have not confirmed that your system is stable.

#### Routh-Hurwitz Criterion

This helps you to check for stability and find gains for which a system is stable, especially if you cannot factor out the characteristic equation for drawing a root locus plot.