Closed Loop System Specifications Interpreted Using Bode' Plots
An Example

Consider a system with this transfer function.

G(s) = 1/[(s + 1)(s + 4)]

This is the Bode' plot for the system as it stands - with no compensator or controller. Now, let's examine this system with an eye to designing a system with good performance. Assume that we want the following.

SSE < 2%
Phase Margin > 50^o
An Estimate of the Rise Time

Examining the Bode' plot we can conclude the following:

The zero db crossing should occur at around f = 0.8 to get a phase margin of 50^o.
If the zero db crossing is set at f = 0.8, the db gain at that point is-30 db.

If the gain is -30 db, we can add 30 db gain to the system.
If we add 30 db of gain, the DC gain will move from -12 db to +18 db.
A DC gain of 18 db is a gain of 8.
A gain of 8 will produce a SSE of .11 or 11%.

If the SSE if 11%, then we cannot simultaneously achieve both specifications above.
Also note that since the zero db crossing is at f = 0.8, we expect the closed loop bandwidth to be near that frequency, and the rise time to be given by:

Rise time ~= .35/0.8 = .44 sec.

Here is the response for the gain we have just computed. This response shows the following:

11% SSE.
About 24% overshoot (up to 1.1 when it settles out to 0.89). That's the overshoot for a phase margin of 50^o. You may want to compare that with what happens in other systems.
A rise time (10-90%) that looks to be a little less than 0.5 sec, and about what we predicted.