Determination Of Static Velocity Error Constants

Determination of static velocity error constants

Consider the unity-feedback control system shown in Figure 8-15. Figure 8-17 shows an example of the log-magnitude plot of a type 1 system. The intersection of the initial - 20 dB/decade segment (or its extension) with the line ω = 1 has the magnitude 20 log Kv. This may be seen as follows:

In a type 1 system

The intersection of the initial -20-dB/decade segment (or its extension) with the O-dB line has a frequency numerically equal to Kv. To see this, define the frequency at this intersection to be ω1; then

As an example, consider the type 1 system with unity feedback whose open-loop transfer function is


If we define the comer frequency to be ω2 and the frequency at the intersection of the -40-dB/decade segment (or its extension) with 0-dB line to be ω3, then


On the Bode diagram,



Thus, the ω3 point is just midway between the ω2 and ω1 points. The damping ratio of the system is then