Chapter 4

# 4.3 Step response specifications – Definitions

4.3.1 Percent Overshoot

Maximum Overshoot is defined as:

 $MO = y_{max} - y_{ss}$ Equation 4‑1

Percent Overshoot is defined as:

 $PO = \frac{y_{max} - y_{ss}}{y_{ss}} \cdot 100$% Equation 4‑2

Note that while the constant reference signal (which can be referred to as $r_{ss}$) 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 $T_{settle}$ is defined, as shown in Figure 4‑3, as either $T_{settle(\pm 5 \%)}$ – within 5% of the steady state value, or $T_{settle(\pm 2\%)}$ – within 2% of the steady state value.

### 4.3.3 Rise Time

The Rise Time $T_{rise}$ 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, $y_{ss}$, or from 0 to 100% of the steady state value of the output, $y_{ss}$.

The Steady State Error $e_{ss}$ is defined, as shown in Figure 4‑5 and Equation 4‑3:
$e_{ss} = r_{ss} - y_{ss}\%$
$e_{ss\%} = \frac{r_{ss} - y_{ss}}{r_{ss}} \cdot 100\%$