Sistemanîn Rewşdariyê Piramerdên Dijital

Pêşkêşkirina Daneyên Dijital

Daneyên dijital di sisteman kontrolan de dêwehatin ji daneyên diskret an bîrzanînên ku nişaneyên pêwistan yên di formatê dijital de nîşan dênin.

Prosesa Bîrzanîna

Bîrzanîna vekirina ye ku nişaneyên analîg bi karberdanê ya birbendekarê, ku ON û OFF dike.

Prosesa bîrzanîna nişaneyên analîg biguherîne bi nişaneyên dijital bi karberdanê ya birbendekarê, ku birbendekar in e ku ON û OFF dike. Ji bo birbendekara ideyal, girêka pulsu têkildar yek (gotarên sifir). Di sisteman diskretan de, guhertoyên Z rolê mezin dike, wek Fourier transform di sisteman pêwistanan de. Heta ez bikin serbestiyên guhertoyên Z û karanûnya herî xebitandin.

Mîna z transform hatine çêkirin

Lê, F(k) heye daneya diskret

Z heye taymûra cêm

F (z) heye guhertoya Fourier f (k).

Malperên werazher û maher û malperên guhertoyên z li jêr nehatiye nivîsandin

Cizî

Heta ez bicîhin serbestiya du funksiyonên diskret f (k) û g (k) lêke

lêke p û q da destpêk e, ewa heta ez Laplace transform bikin nehatiye bi malpera cizî:

Guhartina Mafey: heta ez bicîhin funksiyona f(k), ewa heta ez z transform bikin nehatiye

ewa heta ez bi malpera guhartina mafey nehatiye

Malpera Shifting: Li ser bervê malpera wê

Ewa heta ez bikin serbestiyên guhertoyên z wan û ez ê zêde bikam ku wan bixwînin guhertoyên:

Laplace transformation of this function is 1/s 2 and the corresponding f(k) = kT. Now the z transformation of this function is

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/(s 2 + a2) and the corresponding f(k) = sin(akT). Now the z transformation of this function is

Laplace transformation of this function is s/(s 2 + 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:

First Order Hold Circuit

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 first order hold circuit is shown below: Now we are interested in finding out the transfer function of the first 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 (1-e -sT)/s. on substituting s=jω we can draw the bode plot for the zero order hold circuit.

The bode plot for the first order hold circuit is shown below which consists of a magnitude plot and a phase angle plot.The magnitude plot starts with magnitude value 2π/ωs.