Chapter 8.1 Introduction

8-1a
Fig. 8-1
Integrating unit transfer function G(s)
Ti -integrating time
is a single Integrating unit parameter–>p.8.4.
Note
Don’t you know integration and differentiation? Don’t bother yourself. Your job is only connotation step response y(t) with the Ti parameter.

Chapter 8.2  Virtual potentiometer–>x(t)  bargraf–>y(t)
Call desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/01_całkujący_suwak_bargraf.zcos
8-2a

Fig. 8-2
Push “start”.
8-3a
Fig.8-3
Move Tk Source and BARXY windows and you see both digital meters. Intial virtual potentiometer value=0 and y(t)=0.
Set x(t)=0.025. The y(t) is rising with the constant speed. Double the x(t) up to x(t)=0.05. The y(t) is rising with the doubled speed.
Set x(t)=0. You have to use digital meter here.  The  y(t) comes to a stop. Note that x(t)=0 and y(t) is nonzero. It’s typical for integrating  unit.
Set x(t)=-0.025 
Set x(t)=-0.05
Repeat experiments with the Ti=0.5 sec and Ti=2 sec and make conclusions.
How to change parameter Ti ? See Fig. 7-4 and Fig. 7-5 in the previous chapter.

Chapter 8.3  Virtual potentiometer–>x(t)  oscilloscope–>y(t)
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/02_całkujący_suwak_oscyloskop.zcos
8-4a
Fig. 8-4
Signal 0 draws y=0 line
Push “start” and make x(t) as previous.
8-5a
Fig. 8-5
Make x(t) as previous and make conclusions.

Chapter 8.4  step generator–>x(t)  oscilloscope–>y(t)
The step generator enables  more accurate analysis than a virtual potentiometer.
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/03_całkujący_1_skok_oscyloskop.zcos
8-6a
Fig. 8-6
Wciśnij “start”
8-7a
Fig. 8-7
Integrating unit response when x(t)=0.1.
There is state x(t)=y(t) after time t=Ti=1 sec.
Change the parameter Ti for Ti=2 sec. and repeat the experiment.
We don’t  call a new block diagram but:
– close the oscilloscope window
– change Ti=1 sec. –>Ti=2 sec.
– click “start”
8-8a
Fig. 8-8
The output y(t) is double slower now!
The new integrating time Ti=2 sec. is according to Ti definition on the  Fig. 8-7.

Chapter 8.5  “2 steps” generator–>x(t)  oscilloscope–>y(t)
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/04_całkujący_2_skoki_oscyloskop.zcos
8-9a
Fig. 8-9

Click “Start”8-10a

Fig. 8-10
y(t) speed double rises when x(t) double rises.

Chapter 8.5  “4 steps” generator–>x(t)  oscilloscope–>y(t)
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/05_całkujący_4_skoki_oscyloskop.zcos
8-11a
Fig. 8-11
Click “Start”
8-12a
Fig. 8-12
The conclusions is obvious. y(t) speed rises when x(t) speed rises.
The “4 steps” x(t) signal is similar to linear function  x(t)=t and y(t) signal is similar to parabola.
Will be the y(t) parabola when x(t) is  linear function  x(t)=t ?

Chapter 8.7  Ramp generator–>x(t)  oscilloscope–>y(t)
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/06_całkujący_pila_oscyloskop.zcos

8-13a
Fig. 8-13
Wciśnij “Start”
8-14a
Fig. 8-14
y(t) is  a parabola!
Math says that
8-15a
Fig. 8-15
The conclusion is that the theory is acc. to practice.

Chapter 8.8  “positive and negative  step” generator–>x(t)  oscilloscope–>y(t)
It’s more excellent Fig. 8-5 experiment version
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/ 07_całkujący_skok_dodatni_ujemny_oscyloskop
8-16a
Fig. 8-16
Click “Start”
8-17a
Fig. 8-17
It similar to volume TV pilot controller. But our “pilot” is better. We can speed control and change its sign!
The electrical actuator is the other examle. x(t)–>input motor voltage and y(t)–>actuator level position

Chapter 8.9  Dirac pulse generator–>x(t)  oscilloscope–>y(t)
Call Desktop/PID/01_podstawowe_człony_dynamiczne/03_człon_całkujący/08_całkujący_dirac_oscyloskop.zcos

8-18a
Fig. 8-18
Ideal Dirac pulse doesn’t exist. Our Dirac is  a 0.01 sec. pulse with the 100 amplitude.
Click “Start”
8-19a
Fig.8-19
Dirac “loaded” in a flash the y(t) up to y(t)=1 value. This y(t)=1 though x(t)=0 after t=3sec. It’s like ideal condenser loading process!

Chapter 8.10 Inegrating units examples
Condenser.
Input x(t) – loading current
Output y(t) – condenser voltage

Filling the tank without hole.
We assume that the tank is a cuboid.
Input x(t) – water flow Q(t) to the tank
Output y(t) – water tank level h(t)

Electrical actuator.
We assume ideal motor and transmission.
Input x(t) – motor voltage
Output y(t) – actuator position angle

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