Preliminary Automatics Course
Chapter 8. Integrating Unit
Chapter 8.1 Introduction
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
Fig. 8-2
Push “start”.
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
Fig. 8-4
Signal 0 draws y=0 line
Push “start” and make x(t) as previous.
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
Fig. 8-6
Wciśnij “start”
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”
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
Fig. 8-9
Click “Start”
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
Fig. 8-11
Click “Start”
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
Fig. 8-13
Wciśnij “Start”
Fig. 8-14
y(t) is a parabola!
Math says that
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
Fig. 8-16
Click “Start”
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
Fig. 8-18
Ideal Dirac pulse doesn’t exist. Our Dirac is a 0.01 sec. pulse with the 100 amplitude.
Click “Start”
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