Negative Feedback is a process by which a fraction of the opposite output signal is used as an input.
Effect of negative feedback:
Negative feedback stabilizes the control system by counteracting the changes due to any reason.
Negative feedback reduces the overall gain of the system, with the degree of reduction being related to the open-loop gain.
Negative feedback reduces distortion noise, sensitivity to external change, as well as improves the system bandwidth and input and output impedance.
Analysis:
Since the negative feedback improves the stability of the system, the time required to settle the response is reduced i.e. setting time is reduced and the transient response decay very fast.
Transient Response of control system:
Settling time:
It is time required for the response to use and reach to the tolerance band.
For 2% tolerance band:
\({t_s} = 4\tau = \frac{4}{{\xi \;{\omega _n}}}\)
For 5% tolerance band:
\({t_s} = 4\tau = \frac{3}{{\xi \;{\omega _n}}}\)
Thus due to negative feedback transient response decay very fast.
Reduces the parameter variation by a factor 1 + GH.
Reduces the effect of noise and disturbance on the system performance.
Bandwidth increases by the factor of 1 + GH.
The system becomes more accurate.
Improves the sensitivity of the system, a good system should less sensitive to parameter variations but sensitive to the input command.
Important Points
Feedback affects the gain G of a non-feedback system by a factor of 1 ± GH.
Generally, feedback may increase or decrease the gain. In practical control cases, G and H are functions of frequency.
So, the magnitude of 1 ± GH may be greater than '1' for some range of frequency and it is less than '1' in another range of frequency.
Therefore, feedback could increase the gain of the system in one frequency range but decrease it in another.
Effect of feedback on stability:
The closed-loop system depends on loop gain. If the loop gain GH = - 1 for a negative feedback system, the output of a system becomes infinity for the finite input and the system is said to be unstable.
The feedback can improve stability or can be harmful to stability if it is not properly applied.
The body regulates its temperature continuously. It may increase or decrease its temperature when it finds that it is too cold or too hot.
The temperature is being regulated by a control system, and the control is called homeostasis. Somewhere in the brain, perhaps the Hypothalamus, the optimum or initial temperature of the body (set point) is stored (about 37°C).
That information is continuously available to some structure, which we call the comparator. The comparator sends signals to:
Heat gain mechanisms in the pre-optic area or anterior hypothalamus leading to:
Shivering
Increased thyroid hormone output
Increased activity in the sympathetic nervous system
Piloerection
Cutaneous vasoconstriction
Heat loss mechanisms in the posterior hypothalamus leading to:
Decreased thyroid hormone output
Sweating
Cutaneous vasodilation
The output of these mechanisms will end as either a net increase or a net decrease in body temperature. The body temperature is sensed by thermal receptors (thermo-receptors) in the brain and peripherally in the body, and the value is sent to the comparator where it is compared with the set point.
Negative feedback in a control system reduces the overall gain and increases stability.
It reduces the sensitivity of output to input variation, distortion, and noise reduction.
It improves bandwidth and input and output impedances (reducing impedance and increasing bandwidth which are desired in most cases)
Important Points
Positive feedback:
In open-loop system, we do not have any feedback path but in closed-loop system, we have a feedback path.
The transfer function of closed-loop transfer function, with positive feedback, is given by \(\frac{{G\left( s \right)H\left( s \right)}}{{1 - G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function increases with positive feedback.
Negative feedback:
The transfer function of closed loop transfer function, with negative feedback, is given \(\frac{{G\left( s \right)H\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function decreases with negative feedback.
A Feedback System is one in which the output signal is sampled and then fed back to the input to form an error signal that drives the system, and depending on the type of feedback used, the feedback signal which is mixed with the systems input signal, can be either a voltage or a current.
Feedback will always change the performance of a system and feedback arrangements can be either positive (regenerative) or negative (degenerative) type feedback systems.
If the feedback loop around the system produces a loop-gain that is negative, the feedback is said to be negative or degenerative with the main effect of the negative feedback is in reducing the system’s gain.
If however, the gain around the loop is positive, the system is said to have positive feedback or regenerative feedback. The effect of positive feedback is to increase the gain which can cause a system to become unstable and oscillate especially if GH = -1.
Effect of Feedback On Sensitivity:
Let us consider a closed-loop system as shown in fig below:
Let Transfer function = M = C / R = G / (1 + GH)
The sensitivity of the gain of the overall system M to the variation in G is given by
\(S_G^M = 1/(1 + GH)\) ……… (1)
The sensitivity of the gain of the overall system M to the variation in H is given by
\(S_H^M = ( - GH)/(1 + GH)\) ………. (2)
From the above equations, we can say that the output is more sensitive to variations in the feedback path parameter than the forward path parameter.
Negative feedback in a closed-loop reduces gain improves the bandwidth and disturbance rejection. Also, it reduces the sensitivity to parameter variation.
Negative feedback in a control system reduces the overall gain.
It reduces the sensitivity of output to input variation, distortion, and noise reduction. (Option (2) is False).
It improves bandwidth and input and output impedances (reducing impedance and increasing bandwidth which are desired in most cases)
Important Points
Negative feedback:
The transfer function of the closed-loop transfer function, with negative feedback, is given by:
\(\frac{{G\left( s \right)H\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function decreases with negative feedback.
Positive feedback:
In an open-loop system, we do not have any feedback path but in a closed-loop system, we have a feedback path.
The transfer function of the closed-loop transfer function, with positive feedback, is given by:
\(\frac{{G\left( s \right)H\left( s \right)}}{{1 - G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function increases with positive feedback.
Negative feedback in a closed-loop reduces gain improves the bandwidth and disturbance rejection. Also, it reduces the sensitivity to parameter variation.
Negative feedback in a control system reduces the overall gain.
It reduces the sensitivity of output to input variation, distortion, and noise reduction.
It improves bandwidth and input and output impedances (reducing impedance and increasing bandwidth which are desired in most cases)
Important Points
Positive feedback:
In open-loop system, we do not have any feedback path but in closed-loop system, we have a feedback path.
The transfer function of closed-loop transfer function, with positive feedback, is given by \(\frac{{G\left( s \right)H\left( s \right)}}{{1 - G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function increases with positive feedback.
Negative feedback:
The transfer function of closed loop transfer function, with negative feedback, is given \(\frac{{G\left( s \right)H\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function decreases with negative feedback.
Cybernetic or steering control is by far the most common type of control system.
The key feature of cybernetic control is its automatic operation.
As Figure shows, a system is operating with inputs being subjected to a process that transforms them into outputs.
In order to control the system, we must monitor the system output.
This function is performed by sensors that measure one or more aspects of the output.
A cybernetic control system that acts to reduce deviations from the standard is called a negative feedback loop. If the system output moves away from the standard in one direction, the control mechanism acts to move it in the opposite direction
Negative feedback in a closed-loop reduces gain improves the bandwidth and disturbance rejection. Also, it reduces the sensitivity to parameter variation.
Negative feedback reduces the error between the reference input, R(s) and system output.
Negative feedback in a control system reduces the overall gain.
It reduces the sensitivity of output to input variation, distortion, and noise reduction.
It improves bandwidth and input and output impedances (reducing impedance and increasing bandwidth which are desired in most cases)
Positive feedback will increase in gain and also can cause a stable system to become unstable.
Negative feedback:
The transfer function of the closed-loop transfer function, with negative feedback, is given by:
\(\frac{{G\left( s \right)H\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function decreases with negative feedback.
Positive feedback:
In an open-loop system, we do not have any feedback path but in a closed-loop system, we have a feedback path.
The transfer function of the closed-loop transfer function, with positive feedback, is given by:
\(\frac{{G\left( s \right)H\left( s \right)}}{{1 - G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function increases with positive feedback.
The introduction of negative feedback in a system decreases distortion.
Concept:
Negative feedback in a closed-loop reduces gain improves the bandwidth and disturbance rejection. Also, it reduces the sensitivity to parameter variation.
Negative feedback in a control system reduces the overall gain.
It reduces the sensitivity of output to input variation, distortion, and noise reduction.
It improves bandwidth and input and output impedances (reducing impedance and increasing bandwidth which are desired in most cases)
Important Points
Positive feedback:
In an open-loop system, we do not have any feedback path but in a closed-loop system, we have a feedback path.
The transfer function of the closed-loop transfer function, with positive feedback, is given by \(\frac{{G\left( s \right)H\left( s \right)}}{{1 - G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function increases with positive feedback.
Negative feedback:
The transfer function of the closed-loop transfer function, with negative feedback, is given \(\frac{{G\left( s \right)H\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)
The overall gain of the transfer function decreases with negative feedback.