**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).**is a little similar. It calculates the speed of

**Differentiating unit with inertia****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.

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