In the system shown in figure below, the sensitivity of the closed loop transfer function w.r.t. parameter a is
The closed loop transfer function is given by
∴
Now,
∴
For the system shown in figure below, is equal to (where, T = closed loop transfer function)
The CLTF is
In control system, the feedback
For the closed loop transfer function shown below, E(s)/R(s) is given by
We have: E(s) = R(s) + C(s) H(s) ...(i)
Also, C(s) = E(s) G(s) ...(ii)
From (i) and (ii), we have:
E(s) = R(s) + E(s) G(s) H(s)
or, E(s) (1G(s)H(s)] = R(s)
or,
Due to positive feedback
Consider the following statements:
1. Closed loop system is less sensitive to variations in feedback path parameters than variations in forward path parameters.
2. Feedback can improve the stability or may be harmful to stability if it is not properly designed and applied.
3. Feedback controls the time response of the system by adjusting the location of poles.
Q. Which of the these statements are correct?
For the closed loop control system shown above, let, H = C/R transfer function.
Thus, closed loop system is more sensitive to variation in feedback path parameters than variation in forward path parameters. Hence statement1 is false. Thus, statements 2 and 3 are only correct.
An unity feedback control system has a transfer function of The open loop transfer function of this system is
∴
Assertion (A): Feedback in control system improves the time response of the system.
Reason (R): Time constant of an open loop system is less than the time constant of a closed loop system.
Time constant of open loop system is more than that of closed loop system. Lesser is the time constant of the system, faster is its' time response.
For the unity feedback system shown below, if the input to the system is a unitstep signal, then the integral square error (t) dt for infinite value of gain k will be
Thus, when K = ∞, I_{e} = 0.
Introduction of feedback to a system
Introduction of feed back to a system will increase the stability if negative feedback is introduced while it will reduce the stability if positive feedback is introduced.
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