## Preliminary Automatics Course

Chapter 6. Proportional unit
Chapter. 6.1 Introduction
The simplest dynamical unit proportional unit will be tested.
Try to remeber the steps:
2.-the block diagram testing
You will repeat these steps all the time in this course.
The proportional unit is very simple and treate rather this chapter as a chapter 5. About XCOS shortly continuation .

Fig. 6-1
Click Scilab shortcut and wait a moment. “Wait a moment” concerns all the course. Don’ t click many times to avoid many opened Scilabs!

Fig. 6-2
Main Scilab window directly after the call. Touch by mouse the Scilab icon to see all the opened windows. The Scilab 5.5.2. console window should be opened only. Close all other windows if are opened.
Click Xcos button.

Fig. 6-3
The naked untitled main Xcos window is opened. Why naked? Because it’s without block diagram
This Xcos window enables:
1. New block diagram editing.
2. Block diagrams loading from the PID folder. This function will be used in the course only.
The block diagram editing is that you paste single basic blocks from the special Xcos magazine – palette explorer and connect them. Palette explorer contains basic blocks: Go(s) objects, signal generators, oscilloscopes, PID controller, e.t.c. Connecting is a lines drawing between blocks. It’s similar to Windows Paint program. More about editing–>click show movie.
You will load ready, made by me block diagrams from the PID folder only. So the editing knowlege isn’t necessary.

Every further lesson is similar:
1.You call Scilab and Xcos then
3. You test it.
The input generator x(t) is mostly:
step signal
linear signal (ramp)
dirac signal–> “short hammer hit” otherwise
virtual potentiometer–>hand operated
3. You observe the output signal y(t) with:
bargraf–>analog meter
digital meter
oscilloscope–>mostly
The other signals will be observed of course. –> control error e(t), control signal s(t) e.t.c…
The experiments wiil be repeated with different x(t) input signals, object and controller parameters. You will “feel” the transfer function Go(s) concept without differential and operational calculus!

Fig. 6-4
You glance through similar G1(s) and G2(s) only and you will see the dynamics and static differences.

Chapter. 6.2 The first block diagram call- Proportional Unit Go(s)=1 with virtual potentiometer and bargraf
Bargraf–>analog meter with the vertical line
Call Pulpit/PID/01_podstawowe_człony_dynamiczne/01_człon_proporcjonalny/01_proporcjonalny_bargraf.zcos.
I would be a sadist if I order You to write the path to every block diagram and thus click the PID folder and then…

Fig. 6-5
The first block diagram will occure when clicked

Fig. 6-6
Proportional Unit G(s)=1–>Our first block diagram-Victory!
Check all opened windows as Fig. 6-2
It should be opened only:
1. Scilab 5.5.2 Console
2. Untitled (Xcos window covered by 3. here)
3. 01_proporcjonalny_bargraf…(Xcos window)
Close all others if are and do full screen.

Fig. 6-7
Proportional unit – full screen view
It’s the simplest dynamic unit–>Proportional Unit G(s)=1 as a quotient 1/1. Clock sends pulses every 0.01 sec.. They are used by Xcos for calculations. Don’t interest this subject too much. We arrange that You don’t see clock red lines? Ok? The block diagram rest is banal:
TK Scale-potentiometer for hand controlled signals. It will occure as a window Tkscale
Digital meters -You will see up-to-date signal values
Bargraf-Analog meter with the verical line as a window BARXY. I constructed it as a single block. Xcos editor enables it. It’s a very usefull function.
Object Go(s)=1/1 – no comment

Let’s set up the principal simulation parameters
1-Clock
2-Experiment time
3-Integration method used for differential equations solving. Don’t You know differential calculus? Take it easy. I will try to explain it later.

Clock setting

Fig. 6-8
Clock setting- no comment

Experiment time and integration method
All the dynamic phenomenons are described by differential equations. Differential equations are solved by integration. Integration is an area under the function calculation. There are different methods of integration. I choose Runge Kutta method. Why? Because it sounds funny as bunga-bunga. But be serious. It’s a good integration calculus method. By the way. Runge was an interesting guy. He lived in 19/20 century. Mathematicians thought he is a physicist and physicists he is a mathematician.

Fig. 6-9
Experiment time is in science notation given. But You can use normal “human” language when write
Check box will disappear when “ok” clicked. You see the diagram block again. The experiment with changed parameters (time and Runge-Kutta) is ready to start.
Click “Start” button!

Fig. 6-10
These 3 windows are openened on the main Scilab window background
-TK Source–>virtual potentiometer with hand operated x(t) signal – range-1…+1. It’s possible to set other range.
-BARXY–Digital meter with the vertical line as y(t) value.
-01_proporcjonalny_bargraf – Proportional unit with the the block diagram. You don’t see this window, because it’s covered by BARXY window here. You see the red clock only.
Simulation is working now. Why is the BARXY window empty?. The reason is very smply. The slider is in 0 position when started. Swing the slider by left mouse. The bargraf is swinging too!

I propose to move the windows by the left mouse to see covered -01_proporcjonalny_bargraf window. You have to see 2 digital meters.

Fig. 6-11
You are giving the x(t) input signal by the slider. The windows are living! The Xcos calculates all the time the slider position and gives the signals x(t) and y(t) to the digital meters and bargraf window.
The Proportional Units examples
– ideal amplifier
– lever
– voltage divider

We have chit-chat but the windows are living all the time!
Evidence that:
– Experiment finish button is red
– The text “simulation is going on”
Let’s finish the play and click the experiment finish button. The button colour changes from red to grey
Make sure that there are 3 windows opened only when clicking
– main Scilab window
– untitled Xcos window
Xcos window with the Proportional Unit

Chapter. 6.3 Proportional Unit Go(s)=2 with virtual potentiometer and bargraf
The previous -01_proporcjonalny_bargraf is opened now. It’s occasion to show how to change Go(s) object parameters. But friendly advice first. Don’t repair transmission when You drive and don’t change object parameters in Xcos when the simulation is going on.
We finished the experiment–>simulation is not going on and we can change the block diagram parameters now.

Fig. 6-12

Fig. 6-13
The new G(s)=k=2 will be set.
Note:
Remember the object parameters changing method!
Click “Start experiment” button again

Fig. 6-14
Swing lefmouse the slider. The bargraf amplitude is twice bigger now. Read the x(t) and y(t) from digital meters values and calculate k parameter. It should be k=2

Chapter. 6.4 Proportional Unit Go(s)=2 with virtual potentiometer and oscilloscope
Call Pulpit/PID/01_podstawowe_człony_dynamiczne/01_człon_proporcjonalny/02_proporcjonalny_oscyloskop.zcos.
Do it just as as in the Fig. 6-5

Fig. 6-15
Oscilloscope displays 2 signals – input x(t) and output y(t). Hand operated signal from the slider will be used. The experiment time is 1 min. only.
So be prepared to move quickly as possible the slider and oscilloscope windows.
Click “Start”

Fig. 6-16
The oscilloscope shows that I moved 5 sec the windows and I started to swing the slider then. This activity borrowed me after 30 sec.
The proportional unit y(t) response is immediate. The output y(t) is a copy of the input x(t) because k=1.

Chapter. 6.5 Conclusions
The proportional unit y(t) response is immediate. Every dynamic unit is almost a proportional unit for the first look!*
An example. You set the +120°C oven temperature . The thermometer will show this temperature after 10 min.
There is x(t)=y(t). It means that transfer function is G(s)=1–>proportional unit. But when you ignore this 10 min delay only!
When you observe this temperature on the oscilloscope with time base 24 hours (not 10 min! ) the response will be for you immediate. You will see an ideal step response. You don’t see intermediate state.
*Note
It does’nt involve so-called astatic units – integral unit for example. The static and astatic units will be discussed later.