Pole location determines speed of response.  Here is the argument.

• How far into the left half plane the pole is defines how quickly the system will respond.
• There are two kinds of poles.
• Oscillatory poles have complex parts - real and imaginary - (only one of two poles shown)
• Exponentially descying poles are real poles.
• On the figure below there are hot spots around the pole locations - for a typical complex pole and a typical real pole.  Move the mouse over those hotspots for more information - and read the material after the figure.

What do we note?

• The real part of the two poles are the same.
• The settling times would be the same for a system with the real pole and for a system with the two complex poles - because the same time constant behavior is observed in both systems.
• A system with a real pole has a time constant that is the negative reciprocal of the pole.
• t = 1/(-p), where p = pole location (negative).
• A system with complex poles has a time constant for the decay of the sinusoid that is the negative reciprocal of the real part of the pole.
• t_decay= 1/(zw_n)
• The angle off the horizonal (shown as f in the diagram) determines the damping ratio for the two complex poles.  In particular, we have z = cos(f), where the damping ratio is z.
• The damping ratio determines how quickly the oscillations die out compared to the frequency of the oscillations.  The chart below is taken from this lesson, and shows percent overshoot in a step response as a function of damping ratio.  Note that overshoot is imperceptible for damping ratios larger than about 0.8.

What do we conclude?

• The speed of response of a system is determined by how far into the left half plane the poles of the system are.
• The distance into the left half plane is -1/t since the pole is located there.

• Speed of response is discussed here.  This is a general discussion of what we mean by speed of response, and then it relates speed of response so system parameters like pole position and system bandwidth.