Chapter 4

# 4.3 Step response specifications – Definitions

**4.3.1 Percent Overshoot**

Maximum Overshoot is defined as:

[latex]MO = y_{max} - y_{ss}[/latex] | Equation 4‑1 |

Percent Overshoot is defined as:

[latex]PO = \frac{y_{max} - y_{ss}}{y_{ss}} \cdot 100[/latex]% | Equation 4‑2 |

Note that while the constant reference signal (which can be referred to as [latex]r_{ss}[/latex]) in Figure 4‑2 is shown as unit (1), in fact, it does not have to be that, and can be any value.

**4.3.2 Settling Time**

The Settling Time [latex]T_{settle}[/latex] is defined, as shown in Figure 4‑3, as either [latex]T_{settle(\pm 5 \%)}[/latex] – within 5% of the steady state value, or [latex]T_{settle(\pm 2\%)}[/latex] – within 2% of the steady state value.

**4.3.3 Rise Time**

The Rise Time [latex]T_{rise}[/latex] is defined, as shown in Figure 4‑4, as either calculated as time from 10% to 90% of the steady state value of the output, [latex]y_{ss}[/latex], or from 0 to 100% of the steady state value of the output, [latex]y_{ss}[/latex].

**4.3.4 Steady State Error**

The Steady State Error [latex]e_{ss}[/latex] is defined, as shown in Figure 4‑5 and Equation 4‑3:

[latex]e_{ss} = r_{ss} - y_{ss}\%[/latex]

[latex]e_{ss\%} = \frac{r_{ss} - y_{ss}}{r_{ss}} \cdot 100\%[/latex]