Sensitivity analysis and effect of feedback on noise, distortion analysis
Sensitivity analysis
One of the main motives to use feedback is to reduce the sensitivity of the closed-loop transfer function of the system, to changes in the transfer function of the plant.
Effect of feedback on disturbance or noise.
Another use of feedback is to reduce the effect of disturbance or noise generated inside the feedback loop. It works in the following way, firstly we need to consider a single-looped feedback system, the system has both the G and H parameters treated as constants, and it also includes a disturbance signal inside the loop.
As the system assumed is linear, the principle of superposition can be used to calculate the effects of externally applied input signal x and the disturbance signal separately and then add the results.
Distortion analysis
If a physical system is driven outside its linear range of operation, it will give rise to nonlinearity, to overcome that feedback can be applied around that system. This can be done by using one of the following two methods:
- The output of the system can be expressed as a nonlinear function of the input, and the input is a pure sine wave.
- The input of the system is a nonlinear function of the output.
Therefore, the benefits of the feedback can be summarized as follows:
- It gives control of sensitivity.
- It gives control of distortion in a nonlinear system.
- It gives control of the effect of an internal disturbance.
On the other hand, there are also disadvantages to using feedback. They are as follows:
- There is increased complexity. The application of feedback requires the addition of new components. Therefore, there is a cost of increased system complexity.
- There is reduced gain. When the feedback is absent, the transfer function of the plant is G(s), but when the feedback is applied to the system, the transfer function of the system is G(s)/ F(s), where F(s) is the return difference. As the benefits of feedback are acknowledged only when F(s) is greater than unity, it is known that the application of feedback results in a reduced gain.
- There is a possibility of instability. Open-loop systems are such systems in which the plant operates on its own. Usually, the open-loop system is stable, but when feedback is introduced to the system, there is a possibility that it may become unstable. To avoid that precautionary measures can be taken in the design of the feedback control system.
Reference
Sensitivity analysis and effect of feedback on noise, distortion analysis