## Preliminary Automatics Course

Chapter 14. Delay unit and Substitute transfer function
Chapter. 14.1 Delay unit
Chapter. 14.1.1 Introduction

Fig. 14-1
Delay unit transfer function in comparison to the  typical transfer function.
Delay unit delays input signal x(t). The signal shape doesn’t change. It’s difficult to give an clear example. Sand conveyor belt ? The input x(t) is a sand level at the beginning and the output y(t) is a sand level at the end? It’s rather necessary to construct substitute transfer function–>see later.

Chapter. 14.1.2 Delay unit To=5 sec with the virtual potentiometer and bargraf
Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_człon_opóźniający/01_opóźniajacy_bargraf.zcos

Fig. 14-2
Click “Start”

Fig. 14-3
Swing the slide ruler. The unit delays the slide ruler movements for To=5 sec. It’s transfer function is:

Fig. 14-4

Chapter. 14.1.3 Delay unit To=5 sec with the virtual potentiometer and oscilloscope
Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_człon_opóźniający/02_proporcjonalny_oscyloskop.zcos

Fig. 14-5
Click “Start”

Fig. 14-6
Output is 5 sec dealyed.

Chapter 14.2 Substitute transfer function
Chapter 14.2.1 Introduction

Fig. 14-7
Substitute transfer function
consists of the inertial and dealy unit. Many dynamic units, especially in the chemical industry are multiinertial type units. We can approximate these objects by Substitute transfer function with parameters:
T – constant time
To – delay
We use these parameters to set optimal PID controller parameters.

Chapter 14.2.2 Substitute transfer function designating
Let’s find the substitute transfer function for the triple inertial unit
Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_człon_opóźniający/03_troj_inercyjny_skok_oscyloskop.zcos

Fig. 14-8
T
riple inertial unit
Click “Start”

Fig. 14-9
Construct the ABC triangle and designate the  substitute transfer function  parameters k=1, T=6.2 sec i To=1.8 sec

Chapter 14.2.3 Triple inertial transfer function and its substitute transfer function comparison
Call Desktop/PID/01_podstawowe_człony_dynamiczne/08_człon_opóźniający/04_znormalizowana_oscyloskop.zcos

Fig. 14-10
This same x(t) signal is given to the triple inertial unit and to its  substitute transfer function .
Click “Start”

Fig. 14-11
I didn’t expect that 2 responses will be exactly the same. There are differences. The substitute transfer function is an approximation of the real object only.