Feedback systems are used to stabilize amplifiers and control systems. Negative feedback reduces the gain of an amplifier, making it less sensitive to variations and more stable. While feedback stabilizes systems, it can also cause oscillations if the loop gain exceeds 1. Researchers like Bode and Nyquist analyzed stability and developed criteria to determine when feedback amplifiers will become unstable. Oscillators are designed to produce stable oscillations by ensuring the feedback is positive. Frequency domain analysis using Fourier techniques can be used to analyze linear and time-invariant systems. Design specifications for control systems include parameters for time response, steady state error, and gain/phase margins.
2. Feedback
If the output or some part of the output is given back to the
input of the system then it is known as feedback of the
system.
Input + Output
-
Here,
A – Amplification Factor
β – Loop gain
A
Control System
β
Feedback
3. Stabilizing the system
After the introducing the negative feedback to the amplifier, the
new gain of the amplifier is
𝐴
1 + 𝐴β
≃
1
β
Thus, the new gain of amplifier is less than original gain of
amplifier without feedback.
Thus, it is less sensitive to the variations happening in the itself.
Therefore, the concept of closed loop system was introduce to
reduce error occurred due to the disturbance in the system.
Hence, stabilizing the gain of the system will make the system
stable under any chances in system parameters.
It will eventually desensitize the amplifier.
4. Instability of amplifier oscillations
Feedback was the solution of the problem of effect of
parameter changes but it led to the possibility of the
oscillations.
Amplifier produces oscillations even when there is no input.
Henric Bode did a detailed analysis on stability and
instability of the systems.
Also, Harry Nyquist did the analysis and gave a criterion,
which is known as Nyquist criterion, which tells when the
feedback amplifier will become unstable.
5. Oscillators
Oscillator is a device which generates oscillating electric
signal.
It can convert DC signal into AC signal.
When oscillations occurs, one can say that the feedback
which was intended to be negative has now became positive.
Thus, one found a way to design oscillators.
Novel way of producing oscillations is to have only one of the
reactive elements i.e. inductor or capacitor.
Hence, RC phase shift oscillator was designed in order to not
to use LC circuit (tank circuit).
6. Sinosuidal Signal
For example, any music or speech signal that is almost a
sinosuidal signal or say almost sine wave of particular
frequency called pitch.
Some signal consists of different frequencies altogether.
And this different frequencies are basically harmonics of
fundamental frequency.
So, these speech signal or music signals are not always in
pure tone and hence it is complicate to analyse them.
Such signals can be analysed by fourier analysis.
7. Frequency domain analysis
In general, any sound signal were analysed by fourier series
method.
But all signals are not periodic in nature and hence fourier
series can’t analyse them so fourier integral was introduced.
And, any electric signal which is in sinosuidal form has a
particular frequency term in it.
Thus, the method of analysis that made use of fourier series,
fourier integral fundamentals and harmonic decomposition of
components became known frequency domain analysis.
The analysis of any signal w.r.t frequency is called frequency
domain analysis.
8. Linear Time Invariant System
All the signals occurring in the surroundings are not
sinosuidal in nature.
Still these non-sinosuidal signals can be analysed by
frequency domain analysis if the system is linear and time
invariant.
Any linear time invariant system can be characterized by
impulse of the system.
As all signals don’t have any sort of periodicity earlier
people also used differential equations as a tool for
analizing.
9. Speed control of electric motors
During mid 20th century, electrical power finally replaced steam
power and the use of motor was as prime movers.
Electric motor is a machine that converts electrical energy into the
mechanical energy.
Voltage and frequency are major parameters of the power supply
system.
Power supply whether for domestic or industrial use must produce
contant voltage and or say the constant purely sinosuidal
alternating voltage of particular RMS value.
Major problem is to maintain the continuity of power supply .
Hence, main purpose was to control the speed of the electric
motors.
10. Time Domain Analysis
In time domain analysis, the dynamic response to input of the
system is the function of time.
The dynamic behaviour of the system is analysed under the
application of standard test signals.
Example of standard test signals are impulse signal, step signal,
ramp signal and parabolic signals.
11. Design Specifications
There is much importance of specifications for designing any control
system and as it affects the performance of the system.
In general, while designing a control system if we meet more than one
design with same specifications then we will obviously choose design
which is less expensive.
Now they are of course dependent on the particular control application
that is the particular system that is being controlled and so the
specifications go with the system but they can also go with the method of
analysis that is used to study and design the control system.
There might be some parameter which are required to remain constant
but they will not remain constant.
Thus, we have to allow some variation that might specify the percentage
variation it is sometimes called percentage regulation.
Basically, percentage regulation is how much inaccuracy it can you
tolerate.
12. Time Response Analysis
Any control system gives an output response for any given input.
Time response of the system is defined as the output response of
system when subjected to an input which is expressed in function
of time.
Time response analysis is
divided into two parts
i. Transient response
ii. Steady state response
13. Time Response Specifications
To design any control system, some specifications required are
associated with the time response of the system.
Specifications required are:
1. Delay time (𝑡 𝑑)
2. Rise time (𝑡 𝑟)
3. Peak time (𝑡 𝑝)
4. Maximum peak
overshoot (𝑚 𝑝)
5. Settling time (𝑡 𝑠)
6. Steady state
error (𝑒 𝑠𝑠)
14. Amplifier Specifications
In audio communication system, amplifier works with audio
signals and these signals are sinosuidal.
Hence, they are analysed in frequency domain.
Gain and phase shift are the example of amplifier
specifications.
For an ideal amplifier, the gain should be constant and
should not change with frequency over a frequency range.
Bode introduced some parameters called gain margin and
phase margin.
15. References
Control System Engineering book by U.A. Patel
https://youtu.be/pAnxnLMTtIc?list=PL42816CBDEAC1E82E
(NPTEL lecture)
