## Preliminary Automatics Course

Chapter 13. Differentiating unit with inertia
Chapter 13.1 Introduction Fig. 13-1
Differentiating unit with inertia
transfer function
Do you remember ideal  differentiating unit? The ramp type input x(t) caused step type output y(t). Differentiating unit with inertia is a little similar. It calculates the speed of x(t) (i.e. x'(t))but does it with some inertia. Not immediately as an ideal Differentiating unit.

Chapter 13.2 Differentiating unit with inertia – Td=2sec, T=0.5 sec , ramp with the oscilloscope
Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_różniczkujacy_z_inercja/01-różniczkujący_oscyloskop_narastanie.zcos Fig. 13-2
Differentiating unit with inertia Td=2 sec T=0.5 sec
Click “Start”. Fig. 13-3
The input x(t) ramp type signal is best to test Differentiating unit with inertia. Ideal Differentiating unit too. Output y(t)=x'(t) is teady after 5T=5*2.5sec. So treat Differentiating unit with inertia as non ideal Differentiating unit-speed meter. The better is this speed meter (more expensive ) the lower is inertia T.
And what is Td parameter? It’s the scale of this speed meter.
See for yourself! Change the Td=4 sec. (Fig. 7-5 chapter 7) and click “start”. The red y(t) will jump up to y(t)=4 in steady state.

Chapter 13.3 Differentiating unit with inertia – Td=2, T=0.5 sec , rectangular pulse with the oscilloscope
Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_różniczkujacy_z_inercja/02-rozniczkujacy_oscyloskop_1_impuls.zcos Fig. 13-4
x(t) rectangular pulse instead of the ramp
Click “Start” Fig. 13-5
Please connote it with the numbers in the block Fig. 13-4.
1–> x(t)=1 in the Fig. 13-5
4=(2/0.5)/1 =  4/1sec–> y(t=3sec) in the Fig. 13-5
2–>block in the Fig. 13-5
0.5–>block in the Fig. 13-5
Conclusion-rectangular pulse has more difficult interpretation than a ramp.