Effect of feedback on stability, Electrical Engineering

Assignment Help:

Q. Effect of feedback on stability?

Let us consider the direct transfer function of the unstable first-order system of Figure (a). The transfer function is given by

396_Effect of feedback on stability.png

where p = d/dt is the differential operator. If a unit-step function is applied as the input quantity E, the output becomes

1886_Effect of feedback on stability1.png

for which the corresponding time solution is given by

c(t) = K(1 - et/τ)

which is clearly unstable, since the response increases without limit as time passes. By placing a negative feedback path H around the direct transfer function, as shown in Figure (b), the closed-loop transfer function is then

1979_Effect of feedback on stability2.png

where cf(t) denotes response with feedback. The system is now clearly stable with aK > τ . Thus, the insertion of feedback causes the unstable direct transmission system of Figure (a) to become stable. Such a technique is often used to stabilize space rockets and vehicles, which are inherently unstable because of their large length-to-diameter ratios. Note that the direct transfer function of Equation has a pole located in the right half p-plane at p = 1/τ , whereas the pole of the closed-loop transfer function of Equation with aK > τ is located in the left half p-plane.


Related Discussions:- Effect of feedback on stability

Define a voltmeter, Define a voltmeter A voltmeter is an instrument us...

Define a voltmeter A voltmeter is an instrument used to measure p.d. and must be linked in parallel with the part of the circuit whose p.d. is required.

Chemical vapour deposition, Explain chemical vapour deposition method for t...

Explain chemical vapour deposition method for the preparation of nanomaterial and its properties

Describe the meaning of standing wave ratio, a. Describe the meaning of sta...

a. Describe the meaning of standing wave ratio. What is the formula for it, if the load is purely resistive? Why is a high value of SWR often undesirable? b. Determine how the c

Self-inductance and the induced e.m.f, Self-inductance and the induced e.m....

Self-inductance and the induced e.m.f Inductance is the name given to the property of a circuit whereby there is an e.m.f induced into the circuit by alter of flux linkages pro

Calculate the mechanical speed of rotar, Calculate the mechanical speed of ...

Calculate the mechanical speed of rotar: An asynchronous machine of 460V, 25hp, 4 poles with rotor wound in Y has the following data (of the side stator): Resistance of the

Calculate the instantaneous and rms values, Q. The flux-density distributio...

Q. The flux-density distribution in the air gap of a 60-Hz, two-pole, salient-pole machine is sinusoidal, having an amplitude of 0.6 T. Calculate the instantaneous and rms value

Digital communication , Classify the following signals as energy signals or...

Classify the following signals as energy signals or power signals. Find the normalized energy or normalized power of each. a. ? ? , 0, 0 0, at Ae t a x t elsewhere

Trivalent impurity to a semiconductor, Addition of trivalent impurity to a ...

Addition of trivalent impurity to a semiconductor creates many (A) Holes. (B) Free electrons. (C) Valance electrons. (D) Bound electrons. Ans: Addition o

Working of an astable multivibrator, Q. With the help of a npn transistor c...

Q. With the help of a npn transistor circuit and wave forms explain the working of an astable multivibrator In astable multivibrator both transistors are coupled to each other

List few applications of microprocessor-based system, List few applications...

List few applications of microprocessor-based system. It is used: i. For measurements, display and control of current, voltage, temperature, pressure, etc. ii. For traff

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd