Systemin Kontrol Dijital Data

A nan da zaka iya magana a cikin wannan makaranta game da abubuwa masu alamun kalmomi ko samun kalmomi ko kuma abubuwan digital data of control system. Idan ba a yi bayani a kan wannan batu ba ita ce, yana da kyau a fahimtar, me kisa mafi kyau na digital technology idan an samu analog systems?
Don haka zai yi lafiya a tattauna misali gaba daga cikin abubuwan digital system da suka fi analog system.

1. Yawan adadin shi ne a cikin digital system daga analog system.

2. Digital systems suna iya taimakawa wajen non linear system da ya fi kyau na digital data in control system.

3. Digital systems suna nuna amfani a kan logical operations don haka suna nuna amfani a kan decision making property wanda ya fi kyau a duniya na machines.

4. Sun fi mai amfani da analog systems.

5. Digital systems suna iya samun a cikin inganci da kuma suna da karfin lalace.

6. Suna nuna amfani a kan instructions suna iya program them as per our needs hence we can they are more versatile than analog systems.

7. Amfani gaba da digital technology suna iya taimakawa wajen karatu masu inganci da kuma suna nuna amfani a kan accuracy.

Idan kana da signal da ya dace, yadda za a yi hakan a cikin discrete signals? Amsa a nan ita ce ta daidai a kan sampling process.

Sampling Process

Sampling process ana nufin conversion of analog signal into the digital signal with the help of a switch (also known as sampler). A sampler is a continuous ON and OFF switch which directly converts analog signals into digital signals. We may have a series connection of sampler depending upon the conversion of signals we use them. For an ideal sampler, the width of the output pulse is very small (tending to zero). Now when talk about discrete system it is very important to know about the z transformations. We will discuss here about the z transformations and its utilities in discrete system. Role of z transformation in discrete systems is same as Fourier transform in continuous systems. Now let us discuss z transformation in detail.
We define z transform as

Where, F(k) is a discrete data
Z is a complex number
F (z) is Fourier transform of f (k).

Important Properties of z transformation are written below
Linearity
Let us consider summation of two discrete functions f (k) and g (k) such that

such that p and q are constants, now on taking the Laplace transform we have by property of linearity:

Change of Scale: let us consider a function f(k), on taking the z transform we have

then we have by change of scale property

Shifting Property: As per this property

Now let us discuss some important z transforms and I will suggest readers to learn these transforms:

Laplace transformation of this function is 1/s2 and the corresponding f(k) = kT. Now the z transformation of this function is

Function f (t) = t2: Laplace transformation of this function is 2/s3 and the corresponding f(k) = kT. Now the z transformation of this function is

Laplace transformation of this function is 1/(s + a) and the corresponding f(k) = e(-akT). Now the z transformation of this function is

Laplace transformation of this function is 1/(s + a)2 and the corresponding f(k) = Te-akT. Now the z transformation of this function is

Laplace transformation of this function is a/(s2 + a2) and the corresponding f(k) = sin(akT). Now the z transformation of this function is

Laplace transformation of this function is s/(s2 + a2) and the corresponding f(k) = cos(akT). Now the z transformation of this function is

Now sometime there is a need to sample data again, which means converting discrete data into continuous form. We can convert digital data of control system into continuous form by hold circuits which are discussed below:

Hold Circuits: These are the circuits which converts discrete data into continuous data or original data. Now there are two types of Hold circuits and they are explained in detail:

Zero Order Hold Circuit
The block diagram representation of the zero order hold circuit is given below:
Figure related to zero order hold.
In the block diagram we have given an input f(t) to the circuit, when we allow input signal to pass through this circuit it reconverts the input signal into continuous one. The output of the zero order hold circuit is shown below.
Now we are interested in finding out the transfer function of the zero order hold circuit. On writing the output equation we have

on taking the Laplace transform of the above equation we have

From the above equation we can calculate transfer function as

On substituting s=jω we can draw the bode plot for the zero order hold circuit. The electrical representation of the zero order hold circuit is shown below, which consists of a sampler connected in series with a resistor and this combination is connected with a parallel combination of resistor and capacitor.

GAIN PLOT – frequency response curve of ZOH

PHASE PLOT – frequency response curve of ZOH

First Order Hold Circuit
The block diagram representation of the first order hold circuit is given below: