### 4.5. WHAT IS THE BEST DAMPING RATIO TO USE?

A very important question to answer before leaving this chapter is the best value of damping *ζ* to choose for a control system. Section 4.2 had indicated that most practical systems are usually designed to be somewhat underdamped. This will be discussed further in Section 5.6 from the viewpoint of various performance criteria. This section will present general guidelines for the selection of damping for three specific cases:

#### A. Design of a Control System for General Applications

Suppose it is desired to design a linear control system for general applications. It is assumed that the designer does not know the final application of the control system. The selection of the damping ratio for such a general application requires a tradeoff between maximum percent overshoot and the time where the peak overshoot occurs, *t*_{p}. A smaller damping ratio decreases *t*_{p} (which is desirable), but it increases the maximum percent overshoot (which is undesirable). Final choice of the damping ratio is subjective. It has been my experience that the damping ratio range is usually selected between 0.4 and 0.7 for this general case. It is important to note that Chapter 5, Section 5.8 on “The ITAE Performance Criterion for Optimizing the Transient Response” shows that the damping needed to minimize the integral of time times the absolute value of the error (ITAE) performance criterion is 0.7 for second-order systems.

The selection of the best damping ratio should ...