Introduction to Linear Feedback systems
Introduction
Feedback is introduced into the system to improve the linear behavior of the system, reducing the sensitivity of the gain of the system to variations in the values of certain parameters, and to reduce the effect of external disturbances on the operation of the system. Though, these benefits are achieved only by a more complicated system behavior. There is also a chance that the feedback system may become unstable if special precautions are not taken during the design.
Linear feedback systems have two important operations that are:
- Operational amplifiers
- Feedback control systems.
What is feedback?
Feedback can be defined as the return of a fraction of the output signal of a system to its input, thereby forming a loop of dependencies among signals around the system. We can illustrate feedback with the help of an example. Let us take the example of an accumulator. An accumulator is used to add all previous values of a discrete-time input signal to its current value to produce the output signal.
The accumulator can be realized by a feedback forward system of infinite order. In which case, there will be no feedback.
Similarly, the accumulator can also be implemented as the first-order recursive discrete-time filter. In which case, the presence of feedback is acknowledged.
These two cases use an entirely different method to implement the accumulator, but they are still equivalent in terms of input-output behavior. Basically, they both have the same impulse response, of infinite duration. Yet, one gives no feedback, while the other is an example of a feedback system.
Why do we study linear feedback systems?
Two major reasons to study linear feedback systems are:
- Their wide use and benefits in engineering.
- The knowledge of stability problems ensures that the feedback system is stable under all operating conditions.
Basic feedback concepts
The system consists of three major components connected together forming a single feedback loop. The components are as follows:
- Plant: The plant acts on an error signal e(t) to produce the output signal y(t).
- Sensor: Sensor measures the output signal y(t) to produce the feedback signal y(t).
- Comparator: A comparator calculates the difference between the externally applied input signal and the feedback signal to produce the error signal.
There is a closed signal transmission loop around which signals may flow in the systems.
Negative and positive feedback
Let us assume the loop transfer function as g(x), and it is dependent on the complex frequency s. For s= jw, it can be noted that g(x) has a phase that varies with the frequency w. When the phase g(x) is 180 degrees, the system corresponds to positive feedback, and when the phase g(x) is zero, it corresponds to negative feedback. Therefore, for a single loop feedback system, there will be different frequency bands for which the feedback is both positive and negative, just alternatively.
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