**Chapter 11.1 Introduction**

**Fig. 11-1
Oscillation **and

**Double inertial units**are

**G(s)**examples where numerator is a constant number

**d**and denumerator is a

**binomial**with the parameters

**a, b, c**–>

**Fig. 11-1a**.

These parameters

**a,b,c,d**are for example

**8,2,2,4**–>

**Fig. 11-1b**.

You need to transform

**G(s)**–>

**Rys. 11-1a**to its standardized form. It’s this same

**G(s)**of course but it’s possible to read some useful parameters.

**Fig. 11-2**

Oscillation unit- standardized form

**k**– steady state

**gain**

**q**– attenuation

**rate**

**T**– oscillation

**rate**.I emphasize. It isn’t oscillation period (as suggest the symbol

**T**) but only any

**rate**. The real oscillation period is

**Tosc=2*Π*T**. It’s estimated period furthermore.

Standardized

**G(s)**form is slightly bizarre , but all be clear at the moment. Let’s transform the Fig. 11-1b

**G(s)**to the standardized

**G(s)**as

**Fig. 11-2**.

**Fig. 11-3**

How to do it?

**1 **Divide numerator and denumerator by **2**–>the free factor (without **s) **is **1 **now.

**2** … etc

**Right=Left** check it

Standarized form tell us that **k=2**, **T=2 sec** (i.e. **Tosc=2*Π*T=12.56 sek**) and **q=0.25**

We will test the standarized **G(s) **with different **q **rates.

Let’s go to laboratory!

**Chapter 11.2 k=2 T=2 sec q=0.25 with the potentiometer and bargraf**

Call Desktop/PID/01_podstawowe_człony_dynamiczne/06_człon_oscylacyjny/01_oscylacyjny_bargraf.zcos.

**Fig****. 11-4**

Click “Start”

**Fig****. 11-5
**Play a little with this “weight and spring”. You observe the oscillations. Please count the gain

**k**in steady state. You have to use digital meters here. It should be

**k=2**.

**Chapter 11.3 k=2 T=2 sec q=0.25 x(t) step type and oscillocope
**What will be the real oscillation period

**Tosc**beside theoretical period

**Tosc=12.56**as in

**Fig**

**. 11-3**?

Call desktop/PID/01_podstawowe_człony_dynamiczne/06_człon_oscylacyjny/02_oscylacyjny_skok_oscyloskop.zcos

**Fig. 11-6**

Click “Start”

**Fig. 11-7**

Gain

**k=2**is acc. to the theory. The real

**Tosc=13 sec**is a little more than

**Tosc=12.56 sec**. And what about the attenuation rate

**q.**It isn’t so easy read it from the

**Fig. 11-7**but it’s possible. Let’s poop out about it in this course.

**Chapter 11.4 k=2 T=2 sec q=0.125 x(t) step type and oscillocope**

Call Desktop/PID/01_podstawowe_człony_dynamiczne/06_człon_oscylacyjny/03_oscylacyjny_skok_oscyloskop.zco

**Fig. 11-8**

Click “Start”

**Fig. 11-9
**Attenuation rate

**q**is minimised–>oscillations lasts longer. The first amplitude is bigger.

And what about

**q=0**, no attenuation.

**Chapter 11.5 k=2 T=2 sec q=0 x(t) step type and oscillocope**

Call desktop/PID/01_podstawowe_człony_dynamiczne/06_człon_oscylacyjny/04_oscylacyjny_skok_oscyloskop.zcos

**Fig. 11-10**

Click “Start”

**RFig. 11-11
**What is this? There is no steady state

**y(t)=2**, but the constant component of the sinusoid

**y(t)**.

Note that real

**Tosc=12.56 sek**is as theoretical! Let’s increase the attenuation rate up to

**q=0.5**.

**Chapter 11.6 k=2 T=2 sec q=0.5 x(t) step type and oscillocope**

Call desktop/PID/01_podstawowe_człony_dynamiczne/06_człon_oscylacyjny/05_oscylacyjny_skok_oscyloskop.zcos

**Fig. 11-12**

Click “Start”

**Fig. 11-13
**Draw conclusions

**please. First amplitude minimized and**

**Tosc=14.8 sec**increased.

Let’s Make a Deal and

**q>1**for example

**q=1.5**.

**Chapter 11.7 “Oscillation unit” k=2 T=2 sec q=1.5 x(t) step type and oscillocope
**Quotation marks suggest something.

Call Desktop/PID/01_podstawowe_człony_dynamiczne/06_dwuinercyjny_skok_oscyloskop.zcos

**Fig****. 11-14**

Click”Start”

**Rys. 11-15**

Typical double inertial response! When **q>1** –>**oscillation** unit transforms to** double inertal **unit!

**Chapter 11.8 k=2 T=2 sec q=0.25 x(t) Dirac type and oscilloscope**

Call Desktop/PID/01_podstawowe_człony_dynamiczne/07_oscylacyjny_dirac_oscyloskop.zcos

**Fig. 11-16**

Click “Start”

**Rys. 11-17**

**Dirac** shows the most interesting attribute of the **oscillation** unit–>variable component.

**Chapter 11.9 4 diracs simultaneously and oscilloscope
**All the units are

**T=0.5 sec**and

**k=1.**You can observe the attenuation rate influence for the transient response.

Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_4_na_raz _z_dirakiem_oscyloskop.zcos

**Fig. 11-18**

Click “Start”

**Fig**

**. 11-19**

The

**oscillation**unit changes to

**double inertial**unit when

**q=1.2**

**>1**

**.**

The lower is attenuation parameter

**q**–> the the bigger are oscillations.

**q=0**–> infinity oscillations.

**q=>1**–>no oscillations. It’s double inertial unit, not a oscillation unit!

**Chapter 11.9** **Conclusions
**

**1. Oscillation**unit when

**0 <q<1**–>

**Fig**

**. 11-2**

2. Idealunit when

2. Ideal

**Oscillation****q=0**

3. Attenuationrate

3. Attenuation

**increases**–>oscillations decreases and

**Tosc**increases

**4. When**–>

**q>=1****oscillation**unit changes to

**double inertia unit**

The other look for** oscillation** and double** inertia** unit.

**Fig. 11-20**

The same but with so-called **complex numbers**

**Fig****. 11-21
**We will discuss

**complex numbers**later.

Good day I am so glad I found your web site, I really found you by error, while I was searching on Google for something else, Anyhow I am here now and would just like to say thanks a lot for a fantastic post and a all round exciting blog (I also love the theme/design), I don’t have time to browse it all at the minute but I have book-marked it and also added your RSS feeds, so when I have time I will be back to read much more, Please do keep up the awesome jo.|

Howdy! I know this is kinda off topic but I was wondering which blog platform are you using for this site? I’m getting fed up of WordPress because I’ve had problems with hackers and I’m looking at options for another platform. I would be great if you could point me in the direction of a good platform.

Can you tell us more about this? I’d like to find out some additional information.

My brother suggested I would possibly like this website. He was once totally right. This publish actually made my day. You can not consider simply how a lot time I had spent for this info! Thank you!

There is definately a lot to learn about this subject. I like all of the points you made.

Wonderful blog you have here but I was curious about if you knew of any discussion boards that cover the same topics discussed here? I’d really like to be a part of group where I can get opinions from other experienced individuals that share the same interest. If you have any suggestions, please let me know. Cheers!

online education http://www.educationhints.eu

Hi! I know this is kinda off topic however I’d figured I’d ask. Would you be interested in exchanging links or maybe guest authoring a blog post or vice-versa? My blog discusses a lot of the same subjects as yours and I believe we could greatly benefit from each other. If you are interested feel free to send me an e-mail. I look forward to hearing from you! Excellent blog by the way!

marketing plan

http://www.dealhint.eu

Hmm is anyone else having problems with the images on this blog loading? I’m trying to determine if its a problem on my end or if it’s the blog. Any feedback would be greatly appreciated.

This problem is first time! Please try from another computer.

Maybe you are thinking about “block diagrams files loading” chapter 3?

Its not my first time to pay a quick visit this web page, i am visiting this web page dailly and obtain fastidious data from here daily.

This design is wicked! You most certainly know how to keep a reader entertained. Between your wit and your videos, I was almost moved to start my own blog (well, almost…HaHa!) Great job. I really loved what you had to say, and more than that, how you presented it. Too cool!

An impressive share, I just given this onto a colleague who was doing a little analysis on this. And he in fact bought me breakfast because I found it for him.. smile. So let me reword that: Thnx for the treat! But yeah Thnkx for spending the time to discuss this, I feel strongly about it and love reading more on this topic. If possible, as you become expertise, would you mind updating your blog with more details? It is highly helpful for me. Big thumb up for this blog post!

Great post, my name is ron spinabella and i run a great blog and twitter account. I’m going to repost it for my followers.

magnificent issues altogether, you just gained a emblem new reader. What may you recommend about your publish that you made some days ago? Any certain?

I have been examinating out some of your posts and i can state pretty good stuff. I will definitely bookmark your website.

Hello! I just wish to give an enormous thumbs up for the good information you might have right here on this post. I can be coming again to your blog for more soon.