intro and methodology lab cpdc frequency analysis

8/6/2019 Intro and Methodology Lab Cpdc Frequency Analysis

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INTRODUCTION & BACKGROUND STUDY

Frequency response is a method of testing systems by introducing sinusoidal changes in

their inputs and studying the output. Frequency response is usually measured within the range of

human hearing, from a low of 20Hz to a high of 20000 Hz. Frequency of above and below thisrange are also equally important. Frequency response specifications indicate how well the device

remains uniform. For example, a frequency response specification of 20Hz-20000Hz with +/-

3dB indicates that the maximum variation in level or volume from the lowest to the highest tone

will not exceed three decibels. A range of three dB is common in frequency response

specifications.

In this experiment, the system that is going to be under test is simplified in the following

experimental set up.

When the system input is a sine wave, for a linear system the output will also be a sine

wave of the same frequency. However, the output amplitude will be less and the output will lag

the input. See the figure below which show the input and output sine curve.



In this experiment as well, in order to get the value of time constant and the order of the

system, a Bode diagram for each system is needed. Bode diagram of amplitude ratio (AR) versus

omega () in log-log scale and phase angle (F) versus in linear log scale are plotted in order to

get the mentioned value above.

AR is calculated from the formula below.

In the present electrical system, B=A for =0 (DC output Dc input) and hence AR () =

(B/A). The phase lag is the angle radians by which the output waveform lags behind the input

waveform. The phase can be calculated from the time, t as expressed in the equation below in

which T is the period.

As increases, the value of AR progressively decreases and that of F decreases. This

data is later on represented in the form of Bode diagram.

The order of the system A and B is the first order system, but this statement will be

proved in the discussion part of this documentation as we getting the result done. Whereas for

the system C, it has higher order of system.

PROBLEM STATEMENT

y The time constant and the order of system A, B and C are unknown.

y Transfer function of these three systems is unknown.



OBJECTIVES

y To determine the Bode diagram of two first order of the systems separately.

y To determine the Bode diagram of a second order system and compare it with the result

obtained by combining the first order diagram.

y To study the frequency response of a system with delay time.

y To study the frequency response of a higher order system.

METHODOLOGY

For this frequency response experiment, the required equipments are:

y The PID board.

Figure 3B.3: PID board.

There are several types of control components on this PID board. Every component has

different functions and it is combined together to make different type of system. In this

experiment we will consider 1st order of system A, 1st order of system B and 2nd order of A and B

system in series.



y Function generator.

Figure 1: Function generator.

This function generator is electronic test equipment that used to generate electrical

waveforms. The waveforms can be either repetitive or single-shot and also used as a signal

source to test amplifiers or to initiate an error signal into a control loop.

y X-t recorder.

This equipment used to illustrate the waveforms on screen and give readings on certain

point of estimation.



PROCEDURES

The function generator and x-t recorder is turned on

The time is set constant to 1second and constant gain is

used for system A

The frequency value onfunction generator is set to

0.1Hz

The x-t screen is observedand the wave form is start to

be generated

Reading forV1max,V1min,V2max,V2min

and time of each is recordedfrom the wave forms

The steps 3 to 5 is repeatedwith another set of

frequencies.(0.2,0.4,0.5)

For system B, the timeconstant is tuned to 0.5s and

also 1 for the gain

The steps 3 to 7 is repeated

intro and methodology lab cpdc frequency analysis

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