TABLE OF CONTENT

Theory/Abstract

Procedure

Result

Discussion

Conclusion

References

FACULTY OF ELECTRICAL ENGINEERING

UNIVERSITI TEKNOLOGI MARA

ELECTRONIC ENGINEERING LABORATORY 1 (ELE350)

EXPERIMENT 5

FREQUENCY RESPONSE OF SYSTEM (BODE DIAGRAM & NYQUIST PLOT)

OBJECTIVES

1. Obtain the frequency response of a process experimentally.2. Plot the Bode diagram (magnitude and phase plot) from experimental data.3. Plot the Nyquist plot from experimental data.

LIST OF EQUIPMENT/COMPONENTS

Name QuantityProcess Control Trainer PT 37-100 1

Function Generator 1Oscilloscope 1

THEORY

Frequency Response

Frequency response is the quantitative measure of the output spectrum often the amplitude response of a system or device in response to a stimulus; in electrical terms this stimulus would be an input signal. In the audible range it is usually referred to in connection with electronic amplifiers, microphones and loudspeakers. Radio spectrum frequency response can refer to measurements of coaxial cable ,twisted-pair cable, video switching equipment, wireless communications devices, and antenna systems. Infrasonic frequency response measurements include earthquakes and electroencephalography.

While frequency response of a system is a frequency dependent function which expresses how a sinusoidal signal of a given frequency on the system input is transferred through the system. Time-varying signals — at least periodical signals — which excite systems, as the reference signal or a disturbance in a control system or measurement signals which are inputs signals to signal filters, can be regarded as consisting of a sum of frequency components. Each frequency component is a sinusoidal signal having a certain amplitude and a certain frequency. The frequency response expresses how each of these frequency components is transferred through the system. Some components may be amplified, others may be attenuated, and there will be some phase lag through the system.

Frequency Response.

Bode Diagram

The bode diagram is a special function graph and consists a graph of the amount amplitude again and one for the argument phase shift of a complex transfer function. Bode plots find their application in the representation of linear time-invariant systems in the field of electronics and electrical engineering , control engineering and mechatronics , as well as in the impedance spectroscopy .

Bode diagram (Magnitude & Phase Plot.

Nyquist Plot

A Nyquist plot is used in automatic control and signal processing for assessing the stability of a system with feedback. It is represented by a graph in polar coordinates in which the gain andphase of a frequency response are plotted. The plot of these phasor quantities shows the phase as the angle and the magnitude as the distance from the origin. This plot combines the two types of Bode plot magnitude and phase on a single graph, with frequency as a parameter along the curve.

Nyquist Plot.

Determine Stability

From the plotted Bode diagram and Nyquist plot, stability of a system can be determined. Two quantitative measurement is used to determined how stable is a system. These quantities are gain margin, ΦM. System with greater GM and ΦM will have better stability condition. For a system to be stable both values must be positive.

Evaluating gain margin, GM and phase margin,ΦM via bode diagram

Evaluating gain margin,GM and phase margin,ΦM via nyquist plot

PROCEDURE

1- The equipments was set accordingly,

Process Trainer

-The connection was made and the switch was setting according to figure.

-The set value was adjusted to 35°

-The blower throttle control was adjust to 4

-The detector probe was placed in the 11 position

Oscilloscope

-Channel 1 was set to 1V/div and was connected to socket ‘X’ on PT37-100

-Channel 2 was set to 1V/div and was connected to socket ‘Y’ on PT37-100

-Time base was set to 2. 0sec/div, internal trigger

-Channel 2 was set to invert ON mode

Function Generator

-Sine wave output was set to 4Vp-p amplitude and 0. 1 Hz frequency

-The socket ‘X’ was connected to PT37-100

2-The PT37-100 was switched on ancillary equipments.

3-At an input frequency of 0.1 Hz measure

-Vin and Vout (peak-peak values)

-∆t (time different at maximum peak of the same cycle at both waveform)

4-The test was repeated over a range of frequency up to 1Hz.

RESULT

Frequency, (Hz) Vin, (V) Vout, (V) Δt (sec) G(jw) G(jw) (db) <G(jw)0.10.20.30.40.50.60.70.80.91.0

QUESTION/DISCUSSION

From the figure above, the input equation represent the sinusoid. The process equation represent by the magnitude and phase. Hence the output is a product of input and the process which is also sinusoid. This is because when the input is multiplied with magnitude and phase only, the original waveform will not be changed. The changed of waveform will occur if integration or differentiation process occur.

When only a multiplication process of input and the process occur, the changes between input and output are only in term of magnitude and phase. These changes are represent by the figure above.

Base on the bode diagram plot in the next sheet, the system seem to be stable because both GM value and M value are positive.

GM = 0db – ΔG(jw) 1dbM (degree) = Δ<G(jw) +180 191

OutputInput

CONCLUSION

From this experiment, we can obtain the frequency response of a process experimentally. Then, from the result we conclude that, when the frequency increased, a time different at maximum peak will decreased and the output voltage also decreased while the input voltage will steady at 4V. We set the channel 1 to 4V and channel 2 to invert ON mode because the process control trainer circuit already have inverting amplifier that initially invert the output. Other than that, we have able to plot the bode diagram from experimental data. Bode diagram are commonly used to display the steady state frequency response of a stable system. Then, the value has been to 35 to control and maintain the temperature at 35˚. Frequency response techniques can be used more effectively than transient response to model physical system in the laboratory. Other than that, the method is made on open loop systems which are not subject instability problems. Besides that, in completing tests it can be difficult to generate low-frequency signals and obtain the necessary measurements. Normal frequencies of 0, 1 to 10 Hz are used. However for process control frequencies of one cycle over several hours may be required while for fluid servos frequencies of > 100 Hz may be experienced .

Based on the experiment, stability of a system can be determined by its input and output relationship. Two methods are evaluated from this relationship that is Bode diagram and Nyquist Plot which will be determine its stability. Stability can be said when:

For a system to be stable both Gain and phase margin must be positive

REFERENCE

Nuryanti Salleh, ESE353(Introduction To Control System). UITM Pulau Pinang.

Laboratory manual. Electrical Engineering Computer. ECE123. UITM Pulau Pinang.

Norman Nise, Control Systems Engineering, JW Wiley, Asia

http://en.wikipedia.org/wiki/Frequency_response

http://www.mediacollege.com/audio/microphones/frequency-response.html