Zbekiston Respublikasi Oliy ta’lim, fan va innovatsiyalar vazirligi

O‘zbekiston Respublikasi Oliy ta’lim, FAN VA INNOVATSIYALAR vazirligi
Islom Karimov nomidagi toshkent davlat texnika universiteti
“Elektronika va avtomatika» fakulteti
“Ishlab chiqarish jarayonlarini avtomatlashtirish» kafedrasi

“KASBIY PSIXOLOGIYA” fanidan

“Kasbiy xususiyatlarni tadqiq etish usullari” mavzuda
MUSTAQIL ISH
Bajardi: III kurs sirtqi
S12-20 TJIChAB (o‘zb) guruhi talabasi
J.U. G’aniyev
Qabul qildi: M. Galdiyeva

TOSHKENT-2023

Modeling of Digital Control Systems.

INDEX

1. 
   ADC model ………………………….…………………………………….4
   
2. 
   DAC model ……………………………...………………………………...5
   
3. 
   CHAPTER 3 Modeling of Digital Control Systems ……………………6
   
4. 
   Effect of the sampler on the transfer function of a cascade ……….…..8
   
5. 
   Modeling of Digital Control Systems ……………………..……………..9
   

OBJECTIVES

After completing this chapter, the reader will be able to do the following:
1. Obtain the transfer function of an analog system with analog-to-digital and digitalto-
analog converters, including systems with a time delay.
2. Find the closed-loop transfer function for a digital control system.
3. Find the steady-state tracking error for a closed-loop control system.
4. Find the steady-state error caused by a disturbance input for a closed-loop control
system.
As in the case of analog control, mathematical models are needed for the analysis
and design of digital control systems. A common configuration for digital control
systems is shown in Figure 3.1. The configuration includes a digital-to-analog
converter (DAC), an analog subsystem, and an analog-to-digital converter (ADC).
The DAC converts numbers calculated by a microprocessor or computer into
analog electrical signals that can be amplified and used to control an analog plant.
The analog subsystem includes the plant as well as the amplifiers and actuators
necessary to drive it. The output of the plant is periodically measured and converted
to a number that can be fed back to the computer using an ADC. In this
chapter, we develop models for the various components of this digital control
configuration. Many other configurations that include the same components can
be similarly analyzed. We begin by developing models for the ADC and DAC,
then for the combination of DAC, analog subsystem, and ADC.

3.1 ADC model
Assume that
• ADC outputs are exactly equal in magnitude to their inputs (i.e., quantization
errors are negligible).
• The ADC yields a digital output instantaneously.
• Sampling is perfectly uniform (i.e., occurs at a fixed rate).
Then the ADC can be modeled as an ideal sampler with sampling period T as
shown in Figure 3.2.